NORTHEASTERN UNIVERSITY. Graduate School of Engineering. Mechanical and Industrial Engineering

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1 NORTHEASTERN UNIVERSITY Graduate School of Engineering Dissertation Title: Author: Department: Algorithms for Sequence-Dependent Disassembly Line Balancing Problem Can Berk Kalayci Mechanical and Industrial Engineering Approved for the Dissertation Requirement for the Doctor of Philosophy Degree Dissertation Adviser, Dr. Surendra M. Gupta Date Dissertation Committee Member, Dr. Sagar S. Kamarthi Date Dissertation Committee Member, Dr. Seamus M. McGovern Date Interim Department Chair, Dr. Jacqueline Isaacs Date Graduate School Notification of Acceptance: Director of the Graduate School, Dr. Sara Wadia-Fascetti Date

2 ALGORITHMS FOR SEQUENCE-DEPENDENT DISASSEMBLY LINE BALANCING PROBLEM A Dissertation Presented by Can Berk Kalayci to The Department of Mechanical and Industrial Engineering in partial fulfilment of the requirements for the degree of Doctor of Philosophy in the field of Industrial Engineering Northeastern University Boston, Massachusetts July 2012

3 Copyright 2012 by Can Berk Kalayci and Surendra M. Gupta All rights reserved.

4 Dedicated to my family.

5 Abstract Recent technological advancements have given birth to the growth in electronics and the availability of inexpensive products with high quality. Due to human nature, consumers constantly look for newer products although what they have may be still functional. Functional or not, used products are routinely discarded. This trend has led to extreme depletion of virgin resources to satisfy the ever increasing demands of the customers. In addition, the waste created by products reaching the end of their useful lives pose challenges for the environment. Environmental and economic concerns together with the stricter government regulations and public awareness on the disposal of end-of-life (EOL) products have led to the concept of Product Recovery. Product recovery seeks to obtain materials and parts from old or outdated products through recycling and remanufacturing in order to eliminate environmental negative impact in a cost effective manner. The first crucial and the most time consuming step of product recovery is disassembly. Disassembly is defined as the systematic extraction of valuable parts and materials from discarded products to be used in remanufacturing or recycling after appropriate cleaning and testing operations. Disassembly operations can be performed at a single workstation, in a disassembly cell or on a disassembly line. Just as assembly line is considered to be the most efficient way to assemble a product, the disassembly line is the most efficient way to disassemble a product. Disassembly operations have unique characteristics and cannot be considered as the v

6 reverse of assembly operations. The quality and quantity of components used in the stations of an assembly line can be controlled by imposing strict conditions. However, there are no such conditions on EOL products moving on a disassembly line. In a disassembly environment, the flow process is divergent; a single product is broken down into many subassemblies and parts while the flow process is convergent in an assembly environment. There is also a high degree of uncertainty in the structure, quality, reliability and the condition of the returned products in disassembly. Additionally, some parts of the product may be hazardous and may require special handling that will affect the utilization of disassembly workstations. Since disassembly tends to be expensive, disassembly line balancing becomes significant in minimizing resources invested in disassembly and maximizing the level of automation. The multi-objective Disassembly Line Balancing Problem (DLBP) seeks to obtain a feasible disassembly solution sequence while minimizing the number of workstations, minimizing the total idle time, ensuring similar idle times at each workstation as well as addressing other disassembly specific concerns such as demand criteria and handling hazardous components. DLBP is sequence-dependent in nature and therefore it is required to consider sequence-dependent setup times in addition to standard part removal times for a more realistic scenario. In this dissertation, DLBP, which has been proven to be NP-complete, is extended to Sequence-Dependent Disassembly Line Balancing Problem (SDDLBP) and mathematically formalized. By setting all sequence-dependent time increments to zero, SDDLBP reduces to DLBP. Therefore, SDDLBP is a generalization of DLBP. Since SDDLBP falls into the NP- Complete class of combinatorial optimization problems, when the problem size increases, the solution space is exponentially increased and an optimal solution in polynomial time cannot be found as it can be time consuming for optimum seeking methods to obtain an optimal solution vi

7 within this vast search space. Therefore, it is necessary to use alternative methods in order to reach (near) optimal solutions faster. For this reason, fast and effective algorithms such as Ant Colony Optimization (ACO), River Formation Dynamics (RFD), Tabu Search (TS), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Hybrid Genetic Algorithms (HGA) and Artificial Bee Colony (ABC) optimization approaches are modified, developed and implemented to solve SDDLBP. Various scenarios are considered to illustrate the application of each methodology. Quantitative, and qualitative analyses and comparisons are provided. Conclusions drawn include the consistent generation of (near) optimal solutions, the ability to preserve precedence, the speed and the efficiency of the techniques and their practicality for implementation. The various techniques presented in this research form a body of knowledge directed at addressing problems involving disassembly lines. vii

8 Acknowledgments The day I had dreamt of is finally here. Maybe I did not save the world, but I am living the indescribable excitement of gathering the fruits of my sincere efforts and adding a tiny drop to the ocean of science. I can feel my hands shaking in excitement as I try to write these sentences. The tweets of the birds, the sound of the T (Boston subway train) and the wind are synchronized in harmony as they break the news of a beautiful day. Here, as I take a deep breath, I would like to acknowledge the encouragement I received from people who made this dissertation possible. Pursuing a Ph.D. is a difficult and sometimes a lonely path. In pursuing this path, first and foremost, I would like to thank Dr. Surendra M. Gupta whose constant encouragement was vital in making this dissertation a reality. He spent endless hours proofreading my research papers and giving me excellent suggestions which always resulted in improved versions of documents. Evaluating new topics with him was always interesting for me to investigate and provided me with alternative ways to improve my dissertation. He taught me how to be a researcher and encouraged me to determine appropriate solution methodologies to organize research findings. How come a person can be busy and available at the same time? In fact, he is. I was full of motivation whenever I left his office. I wanted to see him often as it brought new energy in me and left me with a glimpse of smile on my face after our meetings. When I mention about him to my friends, they always tell me how lucky I am. Years taught me how he is a source of knowledge and wisdom. Let me put it this way: stay near him and learn something viii

9 new! Dr. Gupta is not only my adviser, but also, sometimes acts as a father or a big brother under different circumstances. Best feature of his unique character is being a great listener. He was always there to listen and to give me sincere advice about anything I hoped for. I may not be the easiest student, but he never gave up on me and always preserved his confidence in my ability to complete this Ph.D. Without his encouragements and continuous guidance, I could not have finished this dissertation. We went to Washington D.C., Providence and Boston conferences together which gave me the opportunity to know him as a travel companion as well as his academic skills. Among these conferences I cherish the most are the Northeast Decision Science Institute Conferences which took place in Washington D.C. and Providence, in 2009 and He traveled with us and showed us how good an adviser he is by not abandoning us in the presentations away from home. His sense of humor will leave those trips as fun times in my memory. The many skills I have learnt from Dr. Gupta will constantly guide me how to be a great adviser throughout my life. I will certainly try to be as good as him. This is a promise I would like to make to my prospective students. I can never thank Dr. Gupta enough. I gave my youth to this Ph.D., but it wasn t for nothing. I would not hesitate a minute to start another dissertation adventure with Dr. Gupta! I would like thank Dr. Sagar Kamarthi for giving me the opportunity to study at Northeastern University. Also, his valuable comments were very helpful to improve this dissertation. Next, I would like to send my special thanks to Dr. Seamus McGovern. I respect Dr. McGovern s work on disassembly line balancing. His work was the basis of my research. In fact, this dissertation is an extension of his research. His work inspired me to develop new ix

10 methodologies to solve various problems in disassembly research. Also, he was very kind to me for giving valuable comments and ideas on my research. I really appreciate what he has done for me. I cannot continue from here without thanking Dr. Askiner Gungor who played the major role in sending me to U.S.A. for pursuing my Ph.D. degree. In my Ph.D. path, he not only provided academic guidance, but also ran for my help when I needed most. I will not forget his help and I am looking forward to working with him at Pamukkale University where I will start working as an assistant professor. I will create extra time to share with him. Onder Ondemir was a great friend and a very valuable lab mate during my Ph.D. We went to Computers and Industrial Engineering conference held in Los Angeles, California in 2011 and had a great time together. It was a great opportunity to have somebody who was able to understand and share ideas about my research. I thank him with all of my heart. I am looking forward to attending his wedding and wish him a wonderful life. Mehmet Ali Ilgin was a great friend and a smart lab mate. He encouraged me to attend at Northeastern University. His hard working characteristic always inspired me. I congratulate him for always being one step ahead of his competitors. I will always remember him as the most dedicated student I have ever met. I thank him for his valuable friendship and I am looking forward to meeting him in various conferences since he is a fellow colleague from now on. I would like to thank my roommates Cihan Yilmaz, Huseyin Ozkan, Kivanc Kerse, Ata Karamanli, Seyhmus Guler and Adnan Korkmaz for not leaving me alone during the years I spent in Boston. Their friendship will not be forgotten. One day we will come across in some x

11 place again since the world is a small place. That day we will remember those joyful moments and share our stories. I thank them all for every minute that we lived together. I would like to thank my fiancée, my true love, Ece Adak who gave me moral support every single day. I am counting the days to marry her. Our journey will start soon and we will share our lives together. I want a boy and a girl. Dear God; please let them be healthy and smart. Ayberk Soner Kalayci is my little brother and the smart member of our family. I thank him for being such a good brother. I am proud of him. The computer games we played together were very helpful to get rid of stress during my Ph.D. I thank to my father, Mustafa Kalayci who is the true leader of our family. He makes me laugh all the time with his sense of humor. He becomes more and more enjoyable as the years pass. Finally, I would like to thank my mother, Oznur Kalayci who always cries with my sadness and laughs with my happiness. Her heart always beats for me. As usual, she was sleepless when I was most stressful. She is a real source of happiness for me. University. This dissertation was fully supported by Turkish Education Council and Pamukkale xi

12 Contents Abstract... v Acknowledgments... viii Contents... xii List of Figures... xviii List of Tables... xx 1. Introduction Overview Motivation Research Scope and Contribution Outline Literature Review Assembly Line Balancing Disassembly Problem Statement and Research Objectives Statement of the Problem xii

13 3.2. Notation SDDLBP Model Considerations Research Objectives Description of SDDLBP and the Mathematical Model Introduction Problem Overview Mathematical Formulation Experimental Instances Introduction Part Instance Part Mobile Phone Instance The Combinatorial Optimization Searches Introduction Combinatorial Optimization Methodologies Hardware, Software and Analysis Considerations Core Functions Introduction Solution Representation Feasible Solution Construction Strategy Moving Strategy xiii

14 Swap Insert Feasibility Check and Repair Objective Functions Balance Measure Hazard Measure Demand Measure Multi-Criteria Decision Making Considerations Exhaustive Search Introduction Model Description Conclusions Ant Colony Optimization Introduction Model Description Conclusions River Formation Dynamics Introduction Model Description Conclusions xiv

15 11. Tabu Search Introduction Model Description Conclusions Particle Swarm Optimization Introduction Model Description Modified Continuous Representation Initialization PSO iteration Neighbourhood-based mutation Conclusions Simulated Annealing Introduction Model Description Conclusions Hybrid Genetic Algorithm Introduction Model Description Initial Population, Fitness Evaluation and Selection xv

16 Crossover and Mutation Operators Local Search and New Generation Conclusions Artificial Bee Colony Introduction Model Description Population Initialization Employed Bee Phase Onlooker Bee Phase Scout Bee Phase Conclusions Quantitative and Qualitative Comparative Analyses Introduction Experimental Results Parameters of Algorithms First scenario and experimental results of the algorithms Second scenario and experimental results of the algorithms Comparison summary of the proposed algorithms Conclusions Conclusions and Future Research xvi

17 17.1. Research Contributions Future Research Bibliography Appendix A: Acronyms xvii

18 List of Figures Figure 2-1: Classification of general assembly line balancing problems Figure 4-1: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 8-part PC example Figure 5-1: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 10-part disassembly instance Figure 5-2: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 25-part disassembly instance Figure 7-1: Assignment of tasks to workstations Figure 7-2: SWAP operator Figure 7-3: INSERT operator Figure 11-1: Flow diagram of the proposed tabu search approach Figure 13-1: The flow diagram of the proposed SA approach Figure 14-1: Flow diagram of the proposed HGA approach Figure 14-2: Crossover operation in the proposed HGA Figure 15-1: The flow diagram of the proposed ABC algorithm Figure 16-1: Time performance comparison of the proposed methods for the first scenario (10- part product disassembly) xviii

19 Figure 16-2: Best solution found by the proposed methods for 25-part mobile phone disassembly Figure 16-3: f 1 performance comparison of ABC, HGA, SA, PSO, TS, RFD and ACO for 25 parts mobile phone disassembly instance Figure 16-4: f 2 performance comparison of ABC, HGA, SA, PSO, TS, RFD and ACO for 25 parts mobile phone disassembly instance Figure 16-5: f 3 performance comparison of ABC, HGA, SA, PSO, TS, RFD and ACO for 25 parts mobile phone disassembly instance Figure 16-6: f 4 performance comparison of ABC, HGA, SA, PSO, TS, RFD and ACO for 25 parts mobile phone disassembly instance xix

20 List of Tables Table 2-1: Classification of simple assembly line balancing problems... 9 Table 4-1: Knowledge base for 8-part PC example Table 4-2: Knowledge base of sequence-dependent part removal time increments for 8-part PC instance Table 5-1: Database of the 10-part instance Table 5-2: Knowledge base of sequence-dependent part removal time increments for 10-part product disassembly Table 5-3: Database of 25-part mobile phone instance Table 5-4: Knowledge base of sequence-dependent part removal time increments for 25-part mobile phone disassembly Table 7-1: Pseudo code for feasible solution construction strategy Table 7-2: Pseudo code for creating assignable task list (AS) Table 7-3: Pseudo code for creating available task list (AV) Table 7-4: Pseudo code for SWAP operation Table 7-5: Pseudo code for INSERT operation Table 7-6: Pseudo code for feasibility check function Table 7-7: Pseudo code for repair function Table 7-8: Pseudo code for balance measure function xx

21 Table 7-9: Pseudo code for hazard measure function Table 7-10: Pseudo code for demand measure function Table 7-11: Pseudo code for selecting better solution Table 8-1: Pseudo code for the exhaustive search procedure Table 9-1: Pseudo code for Ant Colony Optimization algorithm Table 9-2: Pseudo code of priority function Table 10-1: Pseudo code for River Formation Dynamics algorithm Table 10-2: Pseudo code for droppriority Function Table 11-1: Pseudo code for tabu search algorithm Table 11-2: Pseudo code for tabu check function Table 11-3: pseudo code for tabu update function Table 12-1: Pseudo code for Particle Swarm Optimization algorithm Table 12-2: Task to position representation for SDDLBP Table 12-3: A set of random numbers for transforming to continuous representation Table 12-4: Continuous representation of Table Table 14-1: Pseudo code for the Hybrid Genetic Algorithm Table 14-2: Pseudo code for crossover function Table 15-1: Pseudo code of the modified ABC for SDDLBP Table 16-1: The experiment of ACO parameters with levels using a full factorial design Table 16-2: The experiment of PSO parameters with levels using a full factorial design Table 16-3: The experiment of HGA parameters with levels using a full factorial design Table 16-4: An optimal solution for 10-part product disassembly xxi

22 Table 16-5: Parameter results of ant colony optimization algorithm for the first scenario (10-part product disassembly) Table 16-6: Multi-run test results of ACO algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-7: Parameter results of river formation dynamics approach for the first scenario (10- part product disassembly) Table 16-8: Multi-run test results of RFD approach with best parameter set for the first scenario (10-part product disassembly) Table 16-9: Parameter results of tabu search algorithm for the first scenario (10-part product disassembly) Table 16-10: Multi-run test results of TS algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-11: Parameter results of particle swarm optimization algorithm for the first scenario (10-part product disassembly) Table 16-12: Multi-run test results of PSO algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-13: Parameter results of simulated annealing algorithm for the first scenario (10-part product disassembly) Table 16-14: Multi-run test results of SA algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-15: Parameter results of hybrid genetic algorithm for the first scenario (10-part product disassembly) xxii

23 Table 16-16: Multi-run test results of HGA with best parameter set for the first scenario (10-part product disassembly) Table 16-17: Parameter results of artificial bee colony algorithm for the first scenario (10-part product disassembly) Table 16-18: Multi-run test results of ABC algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-19: Parameter results of ant colony optimization algorithm for the second scenario (25- part mobile phone disassembly) Table 16-20: Multi-run test results of ACO algorithm with best parameter set for the second scenario (25-part mobile phone disassembly) Table 16-21: Parameter results of river formation dynamics approach for the second scenario (25-part mobile phone disassembly) Table 16-22: Multi-run test results of RFD approach with best parameter set for the second scenario (25-part mobile phone disassembly) Table 16-23: Parameter results of tabu search algorithm for the second scenario (25-part mobile phone disassembly) Table 16-24: Multi-run test results of TS algorithm with best parameter set for the second scenario (25-part product disassembly) Table 16-25: Parameter results of particle swarm optimization algorithm for the second scenario (25-part mobile phone disassembly) Table 16-26: Multi-run test results of PSO algorithm with best parameter set for the second scenario (25-part mobile phone disassembly) xxiii

24 Table 16-27: Parameter results of simulated annealing algorithm for the second scenario (25-part mobile phone disassembly) Table 16-28: Multi-run test results of SA algorithm with best parameter set for the first scenario (10-part product disassembly) Table 16-29: Parameter results of hybrid genetic algorithm for the second scenario (25-part mobile phone disassembly) Table 16-30: Multi-run test results of HGA with best parameter set for the second scenario (25- part mobile phone disassembly) Table 16-31: Parameter results of artificial bee colony algorithm for the first scenario (10-part product disassembly) Table 16-32: Multi-run test results of ABC with best parameter set for the second scenario (25- part mobile phone disassembly) Table 16-33: Detailed average and standard deviation values of proposed methods for two scenarios Table 16-34: Detailed standard error and confidence interval values of objectives for each method xxiv

25 Chapter 1. Introduction This chapter provides an introduction to the dissertation. In Section 1.1 an overview of disassembly is presented. Section 1.2 discusses the motivation behind the specific research areas. A brief statement of research scope and objectives is presented in Section 1.3. Finally, the outline of the dissertation is given in Section Overview Day by day, new products are being brought into the market at an increasing rate with rapid technology advancements and innovations. As a result, the products are becoming outdated more quickly and thus, are discarded faster than ever before. Product recovery is a trend that many manufacturers practice to minimize the fast depletion of virgin resources and to realize economic benefits from recovering end-of-life (EOL) products. Product recovery seeks to obtain materials and parts from old or outdated products through recycling and remanufacturing via disassembly activities in order to minimize the amount of waste sent to landfills. Recycling is a process performed to retrieve the material content of used and non-functioning products while 1

26 2 remanufacturing is an industrial process in which worn-out products are restored to a desired level of quality preserving the product s identity. The first crucial and the most time consuming step of product recovery is disassembly. Disassembly has received a great deal of attention in the literature due to its role in product recovery. Product disassembly is almost always needed in remanufacturing, recycling, and disposal. Disassembly facilitates a systematic extraction of valuable parts and materials from discarded products through a series of operations to use in remanufacturing or recycling after appropriate cleaning and testing operations. Disassembly operations can be performed at a single workstation, in a disassembly cell or on a disassembly line. Although a single workstation and disassembly cell are more flexible, the highest productivity rate is provided by a disassembly line and hence is the best choice for automated disassembly processes, a feature that will be essential in the future disassembly systems. Disassembly operations are labour intensive, can be costly, have unique characteristics and cannot be considered as the reverse of assembly operations. A disassembly system faces many challenges such as significant inventory problems because of the disparity between the demands for certain parts and their yield from disassembly. The quality and quantity of components used in the stations of an assembly line can be controlled by imposing strict conditions. However, there are no such conditions of EOL products through a disassembly line. In a disassembly environment, the flow process is divergent; a single product is broken down into many subassemblies and parts while the flow process is convergent in an assembly environment. There is also a high degree of uncertainty in the structure and the quality of the returned products. The condition and the reliability of the received component are usually unknown. Additionally, some parts of the product may be hazardous and may require special handling that will affect the utilization of disassembly workstations. Another difference between

27 3 assembly and disassembly is that disassembly involves additional precedence relations among tasks due to processing alternatives or physical restrictions. An essential performance objective of a disassembly process is the benefits it brings, that is the revenue brought by the retrieved parts and material, diminished by the cost of their retrieval operations. Since disassembly tends to be expensive, disassembly line balancing becomes important in minimizing resources (time and money) invested in disassembly and maximizing the level of automation. A disassembly line facilitates a sequence of disassembly tasks, which begins with a product to be disassembled and terminates in a state where all of the parts of interest are separated. A well balanced line will decrease the cost of disassembly operations. In this dissertation the sequence-dependent disassembly line balancing problem (SDDLBP) is solved using metaheuristics. Exhaustive search works well enough in obtaining optimal solutions for small sized instances; however its exponential time complexity limits its application on the large sized instances. A search technique needs to be employed to attain a (near) optimal condition with respect to objective functions. The techniques selected for application in this research seek to provide a feasible disassembly line balance, in which no precedence constraints are violated since some tasks cannot be performed until their predecessors have been completed. Minimizing the number of workstations, minimizing the total part removal time, removing hazardous components as early as possible and removing high demand components before low demanded components in the disassembly process are the objectives to be achieved in addition to providing a feasible disassembly sequence. Data sets are developed

28 4 and these instances are used with all of the solution techniques to illustrate implementation of the methodologies, measure performance and enable comparisons Motivation Today s manufacturers are under tremendous pressure to design and produce new products at an increasing rate in order to stay competitive in their respective markets. The introduction of new products to the market put psychological pressure on the customers to acquire the most up-todate products. As new products are bought, a huge number of products are discharged into the waste stream. Since the environmental laws, regulation and taxation methods are tightening up, hundreds of different EOL products are turning up into product recovery facilities. The computer chips are being recovered from computers to use in appliances and toys; cell phones are being refurbished, etc. Most types of product recovery involve some level of disassembly. Disassembly has unique characteristics. While disassembly has similarities to assembly, it is not the reverse of the assembly process. Efficient approaches and methodologies are needed to effectively perform disassembly line operations. The difficulty in obtaining efficient disassembly line sequence solutions stems from the fact that any solution sequence would consist of a permutation of numbers that would be proportional to as many elements as there are parts in the product. The importance of disassembly line s role in EOL processing, its NP-complete characteristics make the disassembly line balancing problem both academically interesting and scientifically challenging and hence provides much of the primary motivation behind this dissertation.

29 Research Scope and Contribution Sequence-dependent disassembly line balancing problem (SDDLBP) is an extension of the simple disassembly line balancing problem (DLBP). In order to deal with high level complexity and uncertainty associated with the disassembly process, the scope is limited to the following factors: A single product type is to be disassembled on a disassembly line. The supply of the endof-life product is infinite. The exact quantity of each part available in the product is known and constant. A disassembly task cannot be divided between two workstations. Each part has an assumed associated resale value which includes its market value and recycled material value. The line is paced. Part removal times are deterministic, constant, and discrete. Each product undergoes complete disassembly even if the demand is zero. All products contain all parts with no additions, deletions, modifications or physical defects. Each part is assigned to one and only one workstation. The sum of part removal times of all the parts assigned to a workstation must not exceed cycle time. The precedence relationships among the parts must not be violated. The primary contribution of this research is to explore various techniques for the solution of multi objective SDDLBP. While there are studies on the development of sequence-dependent assembly line balancing problem (SDALBP) and DLBP, there is no study evaluating the SDDLBP. Basically this study is a combination of SDALBP, DLBP and the new evaluation criteria defined for SDDLBP. Since DLBP was proved to be NP-complete (as well as NP-hard), the optimization version of SDDLBP is NP-hard and its decision version is NP-complete, too. This combinatorial optimization problem is mathematically defined, quantitative and qualitative evaluation criteria are developed and problem instances are introduced. Next, metaheuristics as

30 6 combinatorial optimization techniques are employed to solve the instances. Finally, the methodologies are compared to each other Outline This dissertation is concerned with the disassembly of products on a paced disassembly line for component or material recovery purposes. It investigates the multi-criteria solution sequences generated using various techniques. Chapter 2 presents a literature review of assembly line balancing, disassembly. Chapter 3 presents the problem statement and research objectives of this dissertation. Chapter 4 provides a detailed description of sequence dependent disassembly line balancing problem including all objectives and mathematical formulation. Chapter 5 introduces the problem instances. These include the 10-part instance and the 25-part mobile phone instance. Both instances are modified case studies from the literature. In Chapter 6, each of the combinatorial optimization searches is introduced. Also, the computer processor hardware, software and the analysis considerations are documented. Chapter 7 introduces the core functions used in the combinatorial optimization methodologies are presented. Solution representation, feasible solution construction strategy, moving strategy, feasibility check and repair, objectives and the multi-criteria decision making format are also revealed.

31 7 Chapter 8 through 15 present an exhaustive search procedure and the combinatorial optimization methodologies of ant colony optimization, river formation dynamics, tabu search, particle swarm optimization, simulated annealing, hybrid genetic algorithm and artificial bee colony optimization algorithms, respectively. Chapter 16 compares all of the methodologies using the same qualitative and quantitative processes as used in Chapters 8 through 15. These include depictions of time complexity and fitness functions performances. Finally, Chapter 17 summarizes the conclusions and discusses areas for future research. Appendix A provides the acronyms that are referred to throughout the dissertation.

32 8 Chapter 2. Literature Review This chapter presents a literature review related to the issues discussed in this dissertation. Section 2.1 reviews the work that has been done on the issues associated with assembly line balancing. In Section 2.2 a background on the variety of approaches that have been proposed to solve the disassembly related problems is provided Assembly Line Balancing An assembly line consists of work stations arranged along a conveyor belt or a similar mechanical material handling equipment. The line is designed to assemble component parts and to perform any related operations necessary to produce a finished product. The tasks are consecutively carried out through the line and are moved from one station to another. At each station, certain operations are repeatedly performed depending on the cycle time (maximum time available for each work station). Upon exiting the final station, the product is complete. In general, the assembly line balancing problem (ALBP) consists of assigning tasks to an ordered sequence of stations such that the precedence relations among the tasks are satisfied and some

33 9 performance measures are optimized. Due to technological and organizational conditions precedence constraints between the tasks have to be observed. A feasible solution is the assignment of tasks to stations ensuring that no precedence relationship is violated. When a fixed cycle time is given (paced line), a line balance is feasible only if the station time of any station exceeds the given cycle time. Assembly line balancing problems can be classified as simple assembly line balancing problem (SALBP) and general assembly line balancing problem (GALBP) according to the main characteristics considered in their several constraints and different objectives. SALBP arises in the mass production of a single product on a paced assembly line. Due to technological restrictions, precedence constraints partially specifying the sequence of tasks have to be considered. SALBP is relevant for straight single product assembly lines where only precedence constraints between tasks (parts) are considered. Scholl and Becker (2006) classified SALBP as SALBP-1 (type 1), SALBP-2 (type 2), SALBP-E (type E) and SALB-F (type F). These problem versions arise from varying the objective as shown in Table 2-1. Table 2-1: Classification of simple assembly line balancing problems Cycle time Given Minimize # of work stations Given SALBP-F SALBP-2 Minimize SALBP-1 SALBP-E SALBP-1 consists of assigning tasks to workstations such that the number of stations is minimized for a given, fixed cycle time. SALBP-2 aims to minimize cycle time (maximize production rate) for a given number of workstations. SALBP-E is the most general problem version maximizing the line efficiency thereby simultaneously minimizing cycle time and

34 10 number of workstations considering the interrelationship. SALBP-F is a feasibility problem which is to establish whether or not a feasible line balance exists for a given combination of work stations and cycle time. The first mathematical formulization of ALBP is given by Salveson (1955). Since then, much research has been done, numerous methods have been proposed to solve SALBP, successfully resolving important issues and narrowing the focus of future research. These methods consist of exact algorithms, heuristic and metaheuristic approaches. Scholl and Becker (2006) provided literature review on both exact and heuristic approaches for the solution of SALBP. Tasan and Tunali (2007) provided a literature review on the current applications of GA on ALBP. Baybars (1986a) develop a heuristic method to solve for the SALBP. Saltzman and Baybars (1987) present a two phase enumeration algorithm for the SALBP that traverses two branch-and-bound trees, one assigning tasks that appear earlier in the precedence network at lower levels of the tree, the other assigning later tasks at lower levels. The two processes alternately expand nodes of their respective trees, and share information about each other's progress in the form of global bounds. Hackman et al. (1989) develop a branch-and-bound algorithm that combines with a heuristic for reducing the size of the branch-and-bound tree for the solution of SALBP-1. Hoffmann (1992) develop a hybrid system called EUREKA that introduces a bounding rule using a branch and bound algorithm combined with the Hoffmann heuristic for solving SALBP.

35 11 Leu et al. (1994) use genetic algorithms (GA) with heuristic-generated initial population to solve the SALBP with multiple criteria. Klein and Scholl (1996) describe a branch and bound procedure for the SALBP-2 by using an enumeration technique combined with the local lower bound method. Scholl and VoB (1997) describe heuristics for SALBP-1 and SALBP-2. Chiang (1998) describe the step by step application of tabu search to SALBP-1. McMullen and Frazier (1998) present a simulated annealing (SA) based technique to address the ALBP consists of multiple products, which were sequenced in a mixed model fashion for multiple objective problems. Task times were assumed to be stochastic, and parallel workstations were permitted. Two primary performance objectives of total cost (labour and equipment) per part, and the degree to which the desired cycle time was achieved. Ponnambalam et al. (1999) present comparative evaluation of six popular assembly line balancing heuristics: ranked positional weight, Kilbridge and Wester, Moodie and Young, Hoffman precedence matrix, immediate update first fit, rank and assign heuristic. The evaluation criteria used were number of excess stations given, line efficiency, smoothness index and CPU time. Among the six considered heuristics the Hoffmann enumeration procedure performed best; but, the execution time for the Hoffmann procedure was longer because this procedure enumerates all the feasible alternative sets of tasks for the stations. Sabuncuoglu et al. (2000) propose a GA with a chromosome structure that is partitioned dynamically through the evolution process. Elitism is also implemented in the model by using some concepts of SA.

36 12 Carnahan et al. (2001) incorporate physical demand criteria to ALBP that consider both the time and physical demands of the assembly tasks and solve the problem using a ranking heuristic and GA. Simaria and Vilarinho (2001) develop a simulated annealing approach to solve the SALBP with parallel workstations. It simultaneously minimizes the number of workstation and evenly distributes the workload among them. This work allows the user to control the way workstations are parallelized and to define a minimum task time to trigger the replication of the workstations. Gonçalves and de Almeida (2002) present a hybrid genetic algorithm (HGA) for SALBP- 1 and use a local search method to improve the resulting solution. The chromosome representation of the problem is based on random keys and the assignment of the operations to the workstations is based on a heuristic priority rule in which the priorities of the operations are defined by the chromosomes. Kilincci and Bayhan (2006) develop an algorithm for SALBP-1 based on the reachability analysis of Petri nets. The algorithm searches enabled transitions (or assignable tasks) in the Petri net model of precedence relations between tasks, and then the task minimizing the idle time is assigned to the station under consideration. SALBP. Peeters and Degraeve (2006) provides a linear programming based lower bound for the Tasan and Tunali (2006) propose a HGA approach combining genetic algorithms (GA) and tabu search (TS) to solve SALBP.

37 13 Baykasoglu (2006) presents a multi-objective SA algorithm for the solution of SALBP and UALBP with the aim of maximizing smoothness index and minimizing the number of workstations. The algorithm makes use of task assignment rules in constructing feasible solutions. Lapierre et al. (2006) present a tabu search algorithm for SALBP-1. Chong et al. (2008) provide a comparison between a randomly generated initial population and a heuristics-treated initial population of GA for the solution of SALBP and showed that the heuristics-treated population which is a mix of randomly and heuristics generated individuals in the initial population generates better solutions. Nearchou (2008) propose a population heuristic based on the general differential evolution method to solve the multi-objective single-model deterministic ALBP with the aim of minimizing the cycle time, minimizing the balance delay time of the workstations and minimizing the smoothness index of the workload by formulating the cost function of each individual ALB solution as a weighted-sum of multiple objectives functions with self-adapted weights, maintaining a separate population with diverse Pareto-optimal solutions, injecting the actual evolving population with some Pareto-optimal solutions and using a new modified scheme for the creation of the mutant vectors. Kilincci and Bayhan (2007) develop a heuristic approach based on the P-invariants of Petri nets to solve SALBP. Liu et al. (2006) present exact branch and bound algorithms for solving the SALBP-1.

38 14 Toksarı et al. (2008) introduce learning effect into ALBP and show that in many realistic settings, the produced workers (machines) develop continuously by repeated same or similar activities. Thus, the production time of product shortens if it is processed later. 2. Pastor and Ferrer (2009) present a mathematical program to solve SALBP-1 and SALBP- Baykasoglu and Dereli (2009) propose an ACO based metaheuristic algorithm for solving simple (straight line) and U-shaped ALBP. Özcan and Toklu (2008a) present a hybrid improvement heuristic approach to simple straight and U-type assembly line balancing problems which is based on the idea of adaptive learning approach and simulated annealing. The proposed approach uses a weight parameter to randomize task priorities of a solution to obtain improved solutions and the weight parameters are then modified using a learning strategy. The minimization of the number of stations and the equalization of workloads among stations are considered as the performance criteria. Yu and Yin (2009, 2010) present an adaptive genetic algorithm for the ALBP. The probability of crossover and mutation is dynamically adjusted according to the individual s fitness value such that the individuals with higher fitness values are assigned to lower probabilities of genetic operator, and vice versa. Zacharia and Nearchou (2010) present a multi-objective genetic algorithm to solve a fuzzy extension of the SALBP-2 with fuzzy job processing times since uncertainty, variability, and imprecision are often occurred in real-world production systems. The jobs processing times are formulated by triangular fuzzy membership functions. The total fuzzy cost function is

39 15 formulated as the weighted-sum of two bi-criteria fuzzy objectives: (a) Minimizing the fuzzy cycle time and the fuzzy smoothness index of the workload of the line. (b) Minimizing the fuzzy cycle time of the line and the fuzzy balance delay time of the workstations. Petri net is a mathematical and graphical tool to model and analyse for discrete event systems. Kilincci (2009) present a Petri net-based heuristic to solve SALBP-2. The presented heuristic determines available tasks and assign task to current workstation by using reachability analysis and token movement. Solution of SALBP-2 is implemented by iteratively solving the problem for several trial cycle time. If the cycle time is infeasible for given number of workstations, the heuristic increases the cycle time by a value until finding a feasible solution. To improve the solution, a binary search procedure is implemented between the first feasible solution and the last infeasible solution. Three versions of the heuristic are developed by integrating with forward, backward, and bidirectional procedures. Zacharia and Nearchou (2010) present and solve a fuzzy extension of the SALBP-2 using a multi-objective genetic algorithm with fuzzy job processing times since uncertainty, variability, and imprecision are often occurred in real-world production systems. The jobs processing times are formulated by triangular fuzzy membership functions. The total fuzzy cost function is formulated as the weighted-sum of two bi-criteria fuzzy objectives: (a) Minimizing the fuzzy cycle time and the fuzzy smoothness index of the workload of the line. (b) Minimizing the fuzzy cycle time of the line and the fuzzy balance delay time of the workstations. Kilincci (2011) present a heuristic algorithm based on Petri net approach to solve the SALBP-1. The presented algorithm makes an order of firing sequence of transitions from Petri

40 16 net model of precedence diagram. Task is assigned to a workstation using this order and backward procedure. Nearchou (2011) presents a method based on particle swarm optimization (PSO) for the SALBP. Two criteria are simultaneously considered for optimization: to maximize the production rate of the line (equivalently to minimize the cycle time), and to maximize the workload smoothing (i.e. to distribute the workload evenly as possible to the workstations of the assembly line). Emphasis is given on seeking a set of diverse Pareto optimal solutions for the bicriteria SALBP. The classical Simple Assembly Line Balancing Problem (SALBP) has been widely enriched over the past few years with many realistic approaches and much effort has been made to reduce the distance between the academic theory and the industrial reality. The SDALBP is an extension of the standard SALBP which has significant relevance in real-world assembly line balancing (ALB). Scholl et al. (2006) define SDALBP and gives the example on assembly of a car where several components have to be installed at the same mounting place or at neighbouring ones. Installing a seat before the appendant seat belt may prolong the latter task, because the seat is an obstacle which requires additional movements and/or prevents from using the most efficient installation procedure. The other way around, mounting the seat may be restricted by the already installed seatbelt resulting in an enlarged task time. In order to model this very typical situation adequately, Scholl et al. (2006) introduce the concept of sequence dependent task time increments. Whenever a task is performed after another task has been finished, its standard time is increased by a time value. This sequence dependent increment measures the prolongation of task forced by the interference with the status of already having processed task. Andrés et al.

41 17 (2008) formulate a binary linear program and propose priority-rule-based and GRASP procedures by additionally considering sequence dependent setup times of classical SALBP-1. In the literature, all problem types which generalize or remove some assumptions of SALBP are called GALBP. Andrés et al. (2008) introduce the general assembly line balancing problem with setups (GALBPS). GALBPS not only requires that the assembly line has to be balanced, but also that the sequence of tasks assigned to every workstation must be defined (due to the existence of sequence-dependent setup times). This reflects a more realistic scenario for many assembly lines, especially those from the electronics industry or similar sectors featuring low cycle times. Martino and Pastor (2010) propose heuristic procedures based on priority rules for solving GALBPS. Scholl et al. (2011) extend the mathematical formulation of GALBPS and propose several heuristic components to solve. Seyed-Alagheband et al. (2011) develop a mathematical model and a simulated annealing (SA) algorithm to solve the general assembly line balancing problem type 2 (GALBPS-2). GALBP class of problems is very large and contains all problem extensions that might be relevant in practice including line models, task times, objective oriented models, layout type, parallelism, assignment restrictions and design problem. Based on the concepts given in Becker and Scholl (2006), the classification of general assembly line balancing problem is illustrated in Figure 2-1. For another classification of assembly line balancing problems, we refer to Boysen et al. (2007).

42 18 Figure 2-1: Classification of general assembly line balancing problems If only one product is assembled, all workpieces are identical and a single-model line is present. Depending on the type of the units mixed together, a mixed-model line produces the units of different models in an arbitrarily intermixed sequence, whereas a multi-model line produces a sequence of batches (each containing units of only one model or a group of similar models) with intermediate setup operations. A further important characteristic defining different versions of ALBP is the variability of task times. Whenever the expected variance of task times is sufficiently small, as in case of, e.g., simple tasks or highly reliable automated stations, the task times are considered to be deterministic. Considerable variations, which are mainly due to the instability of humans with

43 19 respect to work rate, skill and motivation as well as the failure sensitivity of complex processes, require considering stochastic task times. McMullen and Tarasewich (2003) use ant colony optimization (ACO) technique to address the assembly line balancing problem with the factors of parallel workstations, stochastic task durations, and mixed-models. The assembly line layouts obtained from these solutions are used for simulated production runs to obtain output performance measures such as cycle time. Özcan et al. (2010c) develop a genetic algorithm (GA) to solve the mixed-model u- shaped line balancing and sequencing problem with stochastic task times. Cakir et al. (2011) propose a simulated annealing (SA) approach that includes tabu list, repair algorithms and a diversification strategy to solve single-model stochastic ALBP with parallel stations with the aim of minimizing the smoothness index and the design cost. In cost oriented models, the objective is to minimize short-term operating costs such as wages, material, set-up, inventory and incompletion costs over all stations. The cost-oriented models may be extended by additionally considering profits. Zhang and Gen (2009) propose a generalized Pareto-based scale-independent fitness function GA for solving MALBP to minimize the cycle time based on demand ratio, minimize the variation of workload and minimize the total cost under the constraint of precedence relationships at the same time. Traditionally, an assembly line is organized as a serial line, where single stations are arranged along a straight conveyor belt. In U-shaped layout problem the assembly line is arranged in a U-shape, so that during the same cycle two workpieces at different positions on the line can be handled:

44 20 Gökçen et al. (2005) presents a shortest route formulation for U-type assembly line balancing problem (UALBP). Hwang and Katayama (2009) propose a multi decision evolutionary approach to deal with workload balancing problems in mixed-model U-shaped lines. The performance criteria considered are the number of workstations (the line efficiency) and the variation of workload, simultaneously. Sabuncuoglu et al. (2009) propose ACO approach to solve the single-model UALBP. For the assembly of heavy workpieces it may be necessary to operate a two-sided line which consists of two connected serial lines in parallel. Instead of single stations, pairs of opposite stations work in parallel, i.e., they work simultaneously at opposite sides of the same workpieces: Hu et al. (2008) propose a station-oriented enumerative algorithm integrated with the Hoffmann heuristic for solving two-sided assembly lines balancing problem (TALBP). The start time is designed to assign tasks, starting from the left station to the right station of the position considering the precedence, direction and cycle time constraints. Kim et al. (2009) present a mathematical model and a GA for TALBP. Özcan and Toklu (2008b) present a tabu search (TS) algorithm for two-sided assembly line balancing in which line efficiency and the smoothness index are considered as the performance criteria.

45 21 Özcan and Toklu (2009) present a mathematical model and a simulated annealing (SA) algorithm for the mixed-model two-sided assembly line balancing problem. The proposed mathematical model minimizes the line length as the primary objective and minimizes the number of stations as a secondary objective for a given cycle time. In the proposed simulated annealing algorithm, two performance criteria are considered simultaneously: maximizing the weighted line efficiency and minimizing the weighted smoothness index. Simaria and Vilarinho (2009) present an ACO based approach to solve the two-sided mixed-model ALBP with the main goal of minimizing the number of workstations. In the proposed procedure two ants work simultaneously, one at each side of the line, to build a balancing solution which verifies the precedence, zoning, capacity, side and synchronism constraints of the assembly process. Özcan (2010) propose a chance-constrained, piecewise-linear, mixed integer program (MIP) to model and a simulated annealing (SA) algorithm to solve TALBP with stochastic task times. Özcan et al. (2010b) develop a tabu search (TS) algorithm for two-sided parallel assembly line balancing problem (TPALBP). Özbakır and Tapkan (2011) develop artificial bee colony (ABC) algorithm to solve TALBP with zoning constraints. Further improvements in flexibility and failure sensitivity of an assembly line system may be achieved by introducing some type of parallelism. As is the case with parallel lines, the

46 22 equipment has to be installed several times which often allows better balances and increased productivity: (PALBP). Lusa (2008) provided a literature review on parallel assembly line balancing problem parallel lines. Gökçen et al. (2006) propose a mathematical model on the single model ALBP with Kara et al. (2010) propose goal programming (GP) approaches to balance parallel assembly lines with precise and fuzzy goals. Three conflicting goals; number of workstations, cycle time, and number of tasks assigned to a workstation are optimized in crisp and fuzzy environments. Özcan et al. (2010a) develop a SA approach for parallel mixed-model assembly line balancing (PMALBP) which is an extension of the parallel assembly line balancing problem (PALBP). In PALBP, the aim is to balance more than one assembly line together. Balancing of the lines simultaneously with a common resource is very important in terms of resource minimization. The proposed approach maximizes the line efficiency and distributes the workloads smoothly across stations. Ozbakir et al. (2011) develop a multiple-colony ant algorithm for PALBP. Even with a single line the advantages of parallelization can be utilized by installing parallel stations where the workpieces are distributed among several operators who perform the same tasks:

47 23 Askin and Zhou (1997) propose a nonlinear integer program as a model that allows mixed-model production and the use of identical parallel workstations at each stage of the serial production system for the ALBP with an objective function that trades off between idle workstation time and duplication of task-dependent equipment/ tooling cost. Vilarinho and Simaria (2002) present a mathematical programming model for the mixedmodel assembly line balancing problem with parallel workstations and zoning constraints. The two objectives to be achieved are; (1) to minimize the number of workstations and (2) to balance the workloads between and within workstations. A two-stage simulated annealing approach was developed to deal with the objectives. Simaria and Vilarinho (2004) present a mathematical programming model and an iterative genetic algorithm-based procedure for the mixed-model assembly line balancing problem (MALBP) with parallel workstations considering zoning constraints and workload balancing, in which the goal is to maximize the production rate of the line for a pre-determined number of operators. Vilarinho and Simaria (2006) presents an ant colony optimization (ACO) algorithm for balancing mixed-model assembly lines considering zoning constraints and parallel workstations with the aim of minimizing the number of operators in the assembly line for a given cycle time and smoothing the workload among workstations. Becker and Scholl (2009) consider an extension of the basic ALBP to the case of flexible parallel workplaces as they typically occur in the automobile and other industries assembling large products and propose a branch-and-bound procedure to solve the problem using ILP.

48 24 Akpınar and Bayhan (2011) propose a HGA that includes Kilbridge & Wester Heuristic, Phase-I of Moodie & Young Method, and Ranked Positional Weight Technique to solve mixedmodel assembly line balancing problem of type I (MALBP-I) with parallel workstations and zoning constraints. The three objectives to be achieved are: (1) to minimize the number of workstations, (2) maximize the workload smoothness between workstations, and (3) maximize the workload smoothness within workstations. Another possibility of reducing the global cycle time below the largest task time is the concept of parallel tasks. Respective tasks are assigned to several stations of a serial line which cyclically perform them completely on different workpieces: Pinto et al. (1975) develop a branch and bound algorithm by allowing parallel tasks to increase production rate at the cost of additional facilities. Especially in case of complex products it is usually not possible to have all stations equipped equally resulting in station related assignment restrictions. Additionally, the assignment of tasks may be restricted by task related constraints such as incompatibilities between tasks, minimum or maximum distances (in terms of time or space) between stations performing a pair (or subset) of tasks. Bautista and Pereira (2007) presents and solves Time and Space constrained Assembly Line Balancing Problem (TSALBP) that arise in the automobile industry, among others, due to alterations in demand using ACO. Furthermore, position related constraints are relevant for workpieces which are heavy, large or fixed at the conveyor belt such that they cannot be turned in any position which is required for performing a task in a certain station. Another type of assignment restrictions is operator related, because operators have different

49 25 levels of skill such that only certain task combinations are possible when an operator is assigned to a particular station. The conventional approach to the assembly line balancing problem assumes that the manufacturing methods to be used have been predetermined. However, in practice the design engineer has several alternatives available in the choice of processing, typically involving a trade-off between labour or capital intensive operations. A design engineer may also consider non-identical station types or equipment alternatives and minimize the total equipment costs for a given cycle time. The worker selection problem is equivalent to an equipment selection problem, where workers with different qualifications in terms of production speed or quality are available and are paid according to their qualifications. Bukchin and Rubinovitz (2003) develop an integer linear programming (ILP) formulation for assembly line design problem (ALDP) focusing on station paralleling and equipment selection. Two problem formulations, minimizing the number of stations, and minimizing the total cost, are discussed considering labour and equipment intensive assembly system conditions. A branch and bound optimal algorithm is used to solve equipment selection and parallel station problem. We refer the reader to a book by Rekiek and Delchambre (2006) for the detailed information on the assembly line design. A mixed-model assembly line (MAL) is a type of production line which is capable of producing a variety of different product models simultaneously and continuously. The design and planning of such assembly lines involves several long- and short-term problems. Among these problems, determining the sequence of products to be produced has received considerable attention from the researchers. This problem is known as the Mixed-Model Assembly Line Sequencing Problem (MALSP). Akgündüz and Tunalı (2010) review the genetic algorithm based

50 26 MAL sequencing approaches presented in the literature and provides two hierarchical classification schemes to classify academic efforts according to both specifications of MALSP and specifications of GA-based approaches. Mixed-model assembly lines allow for the simultaneous assembly of a set of similar models of a product, which may be launched in the assembly line in any order and mix. As current markets are characterized by a growing trend for higher product variability, mixed-model assembly lines are preferred over the traditional single-model assembly lines: Noorul Haq et al. (2006) propose hybrid genetic algorithms (HGA) approach for MALBP incorporating modified ranked positional method for the initial solution of GA to reduce the search space within the global space, thereby reducing search time. Yu et al. (2006) presents a multi-objective genetic algorithm (MOGA) for scheduling of the MALBP. The Pareto ranking method and distance-dispersed approach are employed to evaluate the fitness of the individuals. Rahimi-Vahed et al. (2007a) propose a hybrid multi-objective algorithm based on particle swarm optimization (PSO) and tabu search (TS) to obtain the locally Pareto-optimal frontier where simultaneous minimization of total utility work, total production rate variation and total setup cost. Ozturk et al. (2010) propose Mixed Integer Programming (MIP) and Constraint Programming (CP) formulations for simultaneous balancing and scheduling of flexible MAL with sequence-dependent setup times.

51 27 Giard and Jeunet (2010) present an integer programming formulation for the sequencing problem in mixed-model assembly lines where the number of temporarily hired utility workers and the number of sequence-dependent setups are to be optimized simultaneously through a cost function. Yagmahan (2011) proposes a multi objective ant colony optimization (MOACO) to solve MALBP with the objective of minimizing the number of stations for a given cycle time. Flexibility and automation in assembly lines can be achieved by the use of robots. The robotic assembly line balancing problem (RALBP) is defined for robotic assembly line, where different robots may be assigned to the assembly tasks, and each robot needs different assembly times to perform a given task, because of its capabilities and specialization. The solution to the RALBP problem includes an attempt for optimal assignment of robots to line stations and a balanced distribution of work between different stations. It aims at maximizing the production rate of the line. Levitin et al. (2006) propose GA approach for robotic assembly line balancing problem (RALBP). The results of the GA are improved by a local optimization (hill climbing) work-piece exchange procedure. In spite of the great amount of extensions of basic ALBP there remains a gap between requirements of real configuration problems and the status of research. Boysen et al. (2008) structure the vast field of ALB according to characteristic practical settings and highlights relevant model extensions which are required to reflect real-world problems. Assembly sequence planning (ASP) and assembly line balancing (ALB) play critical roles in designing product assembly systems. Tseng et al. (2008) propose hybrid evolutionary

52 28 multiple-objective algorithms for solutions of integrating assembly sequence planning and assembly line balancing Disassembly Product recovery seeks to obtain materials and parts from old or outdated products through recycling and remanufacturing via disassembly activities in order to minimize the amount of waste sent to landfills. Gungor and Gupta (1999), Ilgin and Gupta (2010) provide extensive reviews of product recovery. The first crucial step of product recovery is disassembly. Disassembly is defined as the systematic extraction of valuable parts and materials from discarded products through a series of operations to use in remanufacturing or recycling after appropriate cleaning and testing operations. Disassembly is an important process in material and product recovery since it allows for the selective separation of desired parts and materials. We refer the reader to a book by Lambert and Gupta (2005) for the detailed information on the general area of disassembly. Disassembly sequencing deals with the problem of determining the best order of disassembly operations in the separation of a product into its parts. Disassembling complex products is formally approached via network representation and subsequent mathematical modelling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. Mathematical programming techniques are used for the solution of disassembly sequence generation. In contrast with heuristics and metaheuristics, which select a near-optimum solution,

53 29 mathematical programming guarantees the selection of the global optimum. Naturally, it is possible for small sized problems. Lambert (1999) develop and describe a linear programming approach for solving general optimal disassembly sequence generation problems. This problem is relatively simple if the disassembly costs can be assumed sequence independent. In practice, however, sequence dependent disassembly costs are frequently encountered. Lambert (2006) propose a methodology based on the iterative use of Binary Integer Linear Programming (BILP) in case of sequence dependent costs and disassembly precedence graph representation. Lambert (2007) applies the same methodology for the problems with AND/OR representation. Gungor and Gupta (2001a) present a branch and bound algorithm to generate disassembly sequence plans automatically for product recycling and remanufacturing. Kang et al. (2003) propose a branch and bound procedure included algorithm based on mini-max regret criterion to solve disassembly sequencing problem with internal profit values in the objective function. Heuristic approaches are developed to solve disassembly sequence generation problem: Gungor and Gupta (1997) present a methodology to evaluate different disassembly strategies so that the best one could be chosen. They also propose a disassembly sequence generation heuristic which gives a near optimum disassembly sequence for a product. Gungor and Gupta (1998) address the uncertainty related difficulties in disassembly sequence planning (DSP) and present a methodology to deal with uncertainty in DSP implementation for products with defective parts.

54 30 Kuo (2000) provides the disassembly sequence and cost analysis for the electromechanical products during the design stage. He divides disassembly planning into four stages: geometric assembly representation, cut-vertex search analysis, disassembly precedence matrix analysis, and disassembly sequences and plan generation. The disassembly cost is categorized into three types: target disassembly, full disassembly, and optimal disassembly. Erdos et al. (2001) focus on the modelling and evaluating product end-of-life options, which is the problem of representing products and determining disassembly sequences with the objective of maximizing revenue. They develop algorithms to generate the product recovery graph, to obtain optimal disassembly plans that maximize revenue using the generated product recovery graph and to cope with uncertainties of the end-of-life products. Mascle and Balasoiu (2003) propose a wave propagation based disassembly algorithm to select the disassembly sequence of a specific component of a product. Sarin et al. (2006) formulate disassembly optimization problem as precedence constrained asymmetric traveling salesman problem and develop an iterative procedure to minimize the costs associated with the disassembly process while maximizing the benefits resulting from the recovery of components and subassemblies that constitute the product. Lambert and Gupta (2008) develop a heuristic algorithm and apply BILP approach (Lambert, 2006) for disassembly sequencing problems subjected to sequence dependent disassembly costs using disassembly precedence graph of a cell phone that consists of 25 parts.

55 31 Adenso-Díaz et al. (2008) propose a greedy randomized adaptive search procedure (GRASP) and path-relinking-based heuristic methodology to solve such bi-criteria disassembly planning problem. Hsin-Hao et al. (2000) present the economic analysis method of the disassembly process and develop an artificial neural network approach for disassembly sequence generation problem. Due to combinatorial nature of disassembly sequencing problem, there is an increasing trend in the use of metaheuristics. Seo et al. (2001) develop a genetic algorithms (GA) based heuristic approach for an optimal disassembly sequence considering economic and environmental aspects. Li et al. (2005) develop an object-oriented intelligent disassembly sequence planner for maintenance based on the disassembly constraint graph (DCG) using GA to generate near optimal disassembly sequence from all the feasible combination of the disassembly operations. products. Kongar and Gupta (2005) present a genetic algorithm for disassembly sequencing of EOL Chung and Peng (2006) propose EA approach to generate a feasible and optimal plan for selective disassembly in remanufacturing, ensuring both batch disassembly of components and tool accessibility to fasteners. Shimizu et al. (2007) use GA to develop a system supporting strategic decision-making on disassembly for recycling at the design stage of the product life cycle. The issue of

56 32 uncertainty modelling and management arises in the context of the optimal disassembly planning problem, one of the problems to be addressed by remanufacturing processes. Reveliotis (2007) presents a reinforcement learning approach for providing (near) optimal solutions to the optimal disassembly problem considering uncertainties. Giudice and Fargione (2007) propose a GA based approach to disassembly process planning that supports the search for the disassembly sequence best suited for both aspects, service of the product and recovery at the end of its useful life. Duta et al. (2008) propose an evolutionary algorithms (EA) approach for the multicriteria optimization problem of the disassembly scheduling. problem. Hui et al. (2008) propose a GA based method to solve disassembly sequence planning Tripathi et al. (2009) present a fuzzy disassembly optimization model by considering the uncertainty inherent in the quality of the returned products and develop an algorithm based on ant colony optimization (ACO) for determining the optimal disassembly sequence as well as the optimal depth of disassembly to maximize the net revenue at the EOL disposal of the product in the real world situations. Disassembly of returned products can be performed at a single workstation, in a disassembly cell or on a disassembly line. Even though a single workstation or the disassembly cell provides the most flexible environment for sorting parts according to their quantity and quality, the disassembly line provides the highest productivity rate. The disassembly line setting is most suitable for disassembly of large products or small products with large quantities.

57 33 Furthermore, the disassembly line is the best choice for automated disassembly process (Gungor and Gupta, 2002). DLBP concerns with the assignment of disassembly tasks to a set of ordered disassembly stations while satisfying the disassembly constraints and optimizing the effectiveness of several measures. Mathematical programming techniques, heuristics and metaheuristics are used to solve DLBP. Gungor and Gupta (2002) discuss the disassembly related complications and their effects. They also demonstrate the applicability of some important factors in disassembly to balance a paced disassembly line by modifying the existing concepts of assembly line balancing. In a disassembly line, if a task(s) cannot be performed because of some defect, some or all of the remaining tasks may be disabled due to the precedence relationships among tasks which may result in various complications in the flow of workpieces on the disassembly line, e.g. early-leaving, self-skipping, skipping, disappearing and revisiting workpieces.gungor and Gupta (2001b) investigate the DLBP in the presence of task failures (DLBP-F), discuss these complications and highlight their effects on the disassembly line. A disassembly line balancing algorithm is presented to assign tasks to workstations such that the effect of the defective parts on the disassembly line is minimized. Ranky et al. (2003) focus on the challenges of dynamically scheduling and balancing lean, reconfigurable disassembly cells and lines. They create a set of methods, software tools and industry validated cases that enable disassembly enterprise managers to execute different computer controlled production control and management programs that will help them to run their real-world disassembly lines and factories.

58 34 Johar and Gupta (2006) identify the issue of unbalanced inventories generated at various workstations of a disassembly line and discuss how to overcome this issue. Some researchers use mathematical programming techniques to solve DLBP: Altekin et al. (2004) consider partial disassembly under limited supply of a single product as well as availability of its subassemblies and assume that part revenues and demand, task times and costs, inventory holding costs, and station opening costs are given. They propose two DLBP formulations to maximize the profit per disassembly cycle and over the whole planning horizon. Altekin et al. (2008) develop mixed integer programming (MIP) formulation for profit maximization in partial DLBP, which simultaneously determines (1) the parts whose demand is to be fulfilled to generate revenue, (2) the tasks that will release the selected parts under task and station costs, (3) the number of stations that will be opened, (4) the cycle time, and (5) the balance of the disassembly line, i.e. the feasible assignment of selected tasks to stations such that various types of precedence relations are satisfied. They propose a lower- and upper-bounding scheme based on linear programming relaxation of the formulation. Koc et al. (2009) develop integer programming (IP) and dynamic programming (DP) formulations for DLBP by using AND/OR graph to ensure the feasibility of the precedence relations among the tasks. Goksoy (2010) propose mathematical programming techniques to solve DLBP with fixed number of workstations and finite supply. Tang and Zhou (2006) develop a two phase Petri Net (PN) and Discrete Event Simulation (DES) based methodology to maximize system throughput and system revenue by dynamically

59 35 configuring the disassembly system into many disassembly lines while considering line balance, different process flows and meeting different order due dates. Gungor et al. (2001) address the DLBP and the challenges that come with it. They also present a heuristic to demonstrate how several important factors in disassembly can be incorporated into the solution process of a DLBP. Turowski et al. (2005) propose a fuzzy coloured PN model to characterize the impact of uncertain factors on disassembly and develop a heuristic algorithm to form a balanced disassembly line while considering the uncertainties involved such as in human factors and product condition. Gupta et al. (2004) introduce a cell phone case on a disassembly line and solve the disassembly sequencing problem for seeking a sequence which is feasible, minimizes the number of workstations (and hence idle times), provides for early removal of high demand/value parts, provides the removal of parts that lead to the access of greatest number of still-installed parts, and early removal of hazardous parts as well as for the grouping of parts for removal having identical part removal directions. The increased use of metaheuristics for solving complex optimization problems and the fact that disassembly line balancing problem is NP-complete have resulted in the application of GA and ACO. McGovern and Gupta (2005a) propose ACO based approach for multi objective disassembly sequencing problem and solve 8 parts, 10 parts benchmark data sets created for disassembly line balancing problem. The four objectives to be fulfilled are: (1) Minimize the

60 36 number of disassembly workstations and hence minimize the total idle time; (2) Balance the disassembly line (i.e., ensure the idle times at each workstation are similar); (3) Remove hazardous components early in the disassembly sequence; (4) Remove high demand components before low demand components; (5) Minimize the number of direction changes required for disassembly. A collaborative ACO based algorithm is proposed by Agrawal and Tiwari (2008) for stochastic mixed model U-shaped disassembly line balancing problem. In McGovern and Gupta (2005b) an ACO based algorithm and a Hunter-Killer heuristic are proposed for disassembly line balancing problem and solve 25 part mobile example. McGovern and Gupta (2007b) applied a number of combinatorial optimization techniques (exhaustive search, GA, ACO, greedy/hill climbing and greedy/2-optimal heuristics) to obtain near optimal solutions. They develop a known, optimal, varying size data set to illustrate the implementation of the methodologies, measure performance and enable comparisons. McGovern and Gupta (2007a) develop a new formula for quantifying the level of balancing. They also present a set of a priori instances to be used in the evaluation of disassembly line balancing solution techniques. A GA is presented for obtaining (near) optimal solutions. McGovern and Gupta (2004) develop a two optimal algorithm to balance the part removal sequence and attempt to further reduce the total number of workstations while addressing hazardous and high demand components.

61 37 Duta et al. (2008) use GA to deal with the multi-criteria optimization problem of the disassembly scheduling. Ding et al. (2010) propose a multi objective ant colony optimization (MOACO) algorithm for solving this multi-objective DLBP. They use station-oriented assignment procedure in the solution construction and apply pareto filtering operation at the end of each cycle. We refer the reader to a book by McGovern and Gupta (2011) for the detailed information on the DLBP.

62 38 Chapter 3. Problem Statement and Research Objectives This chapter discusses the specific issues related to sequence-dependent disassembly line balancing that the dissertation addresses in Section 3.1. Section 3.2 reviews the notation used throughout the dissertation. Section 3.3 addresses considerations and assumptions about SDDLBP model and Section 4 provides the research objectives Statement of the Problem Efficient material reutilization is a rational way to facilitate sustainable technology because it can save resources and energy while decreasing the environmental loads at the same time. Decrease in product life along with the strict regulations and environmental consciousness have led to increased concern for methodological product recovery through disassembly operations. At the EOL of a product, there are several options available for its processing including reuse, remanufacturing, recycling and disposing. Recycling and remanufacturing are particularly

63 39 important and involve product disassembly to retrieve the desired parts and/or subassemblies. Disassembly constitutes a major portion of the product recovery process. There are several situations in a product recovery environment where products may be disassembled for economic and regulatory reasons. Disassembly is part of the remanufacturing and it is meant to obtain components and materials from EOL products. An essential performance objective of a disassembly process is the benefits it brings, that is the revenue brought by the retrieved parts and material, diminished by the cost of their retrieval operations. Items that are demanded for reuse and those to be stored are disassembled using non-destructive disassembly. The rest of the items which are demanded for recycling or subject to disposal are disassembled by using destructive disassembly. The disassembly line is the most suitable setting for disassembly of large products as well as small products received in large quantities. The objective of the disassembly line is to utilize the available resources as efficiently as possible while meeting the demand for recovered parts. DLBP involves determining a line design in which used products are completely disassembled to obtain useable components in a cost-effective manner. Because of the growing demand for a cleaner environment, this problem has become an important issue in reverse manufacturing. A decision must be taken to balance an automatic disassembly line. A well balanced line will decrease the cost of disassembly operations and is essential for the efficient processing of a product at the end of its life. Since the complexity of determining the best disassembly line balance increases with increase in the number of parts of the product, it is extremely crucial that an efficient methodology for disassembly line balancing be developed. One of the ways of dealing with

64 40 increasing complexity is to employ heuristic or metaheuristic methodologies to solve the problem. Many researchers took advantage of these approaches to solve NP-complete problems due to their ability to reduce high calculation times. Even though these methods do not always ensure optimal solutions, they often provide acceptable or near optimal solutions. In essence, this dissertation addresses the characteristics of the SDDLBP while providing efficient methodologies for balancing the line and providing a feasible disassembly sequence. Since single objective models are not enough to handle these problems, multiple-criteria decision making models are considered for all cases Notation The following notation is used in the remainder of the dissertation: 0 ij Relative importance of the pheromone trail in path selection Relative importance of heuristic information in path selection Constant parameter used to decrease inertia weight factor at iteration g ( Iw g ) Heuristic information (visibility) of task j (i.e., the priority rule value for task j ), Up gradient coefficient for climbing drops Evaporation coefficient Flat gradient coefficient for climbing drops Initial pheromone level Pheromone trail intensity in the path selecting task j after selecting task i

65 41 a altitude i an AS a ASi AV b b1 c c1 c2 ch cr cumulatedsediment di dr decreasinggradient ij dr DOWN i dn eb er erosionij erosionproduced f1 f1ave f1sd Ant count (1,,an) Altitude of part i Number of ants Assignable task list The set of assignable tasks for ant a after the selection of task i Available task list Bee count (1,,eb) Bee count (1,,eb) Cycle time (Maximum time available at each workstation) Cognitive parameter (weight factor) for the particle Social parameter (weight factor) for the particle Chromosome count for each member of the population (POP) Crossover rate The amount of sediment carried by the drop dr Demand; quantity of part i requested Drop count (1,,dn) Gradient value between part i and j The set of parts that are neighbours of part i that can be visited by drop dr and connected through a down gradient Number of drops Number of employed bees Elitism rate Erosion created between part i and part j The sum of erosions introduced in all graph in the previous phase First objective function; minimize number of workstations (m) Average of first objective results found by the algorithms Standard deviation of first objective results found by the algorithms

66 42 f2 f2ave f2sd f3 f3ave f3sd f4 f4ave f4sd F0 Fbest Fc Fe Fg Fs Fo Fx ( pg, ) pbest Fx pg, ( ) fitnessij Second objective function; balance measure Average of second objective results found by the algorithms Standard deviation of second objective results found by the algorithms Third objective function; hazard measure Average of third objective results found by the algorithms Standard deviation of third objective results found by the algorithms Fourth objective function; demand measure Average of fourth objective results found by the algorithms Standard deviation of fourth objective results found by the algorithms Fitness values vector of initial solution Fitness values vector of best solution Fitness values vector of current solution Fitness values vector for employed bees Fitness values vector at iteration g Fitness values vector for scout bees Fitness values vector for onlooker bees Fitness values vector associated to the position of the particle p at generation g Fitness values vector associated to the best so far position of the particle p at generation g Fitness value of the edge connecting part i and part j dr FLAT i g The set of parts that are neighbours of part i that can be visited by drop dr and connected through a up gradient Current iteration (generation) number of the algorithm h Binary value; 1 if part i is hazardous, else 0 i

67 43 i ial i it itk ilimit IP j Iw g Iwe Iws j1 k j2 j3 LB m m M mr n N notclimbingfactor ob Part identification, task count (1,,n) Initial altitude of part i Idle time counter at all workstations Idle time at station k Iteration limit to call scout bees for exploration Set (i,j) of parts such that task i must precede task j Inertia weight factor which gadgets the effect of the old velocity on the new one The highest value of inertia weight factor The least value of inertia weight factor Part identification, task count (1,,n) Part identification, task count (1,,n) Part identification, task count (1,,n) Part identification, task count (1,,n) Workstation count (1,,m) Line balance solution Number of workstations required for a given solution sequence Minimum possible number of workstations Sufficiently large number Mutation rate Number of parts for removal The set of natural numbers The variable used to decide whether drop dr can climb upward gradients Number of onlooker bees p Particle number (1,..., ps ) paramblockeddrop paramerosion Parameter to deposit sediment whenever a drop is blocked to climb. Parameter of the erosion process

68 44 P ij PA PDdr PE POPg ps PS i Transition rule: Probability of a part j being selected after part i from available task set (AV) Selected parents matrix for crossover operation Probability of a drop dr can climb towards upward gradients Selection probabilities vector for employed bees Population of solutions at iteration g Population size th i part in a solution sequence Q q0 q 1 Constant parameter (Amount of pheromone added if a path is selected) Selection probability parameter for the use of heuristic information Selection probability parameter for the use of pheromone trail information r Uniformly distributed random number between 0 and 1. r1 r2 Random integer created via r Random integer created via r ric S0 Sc Sbest Sg sb sdij t SUC j T0 Rest iteration count (The counter variable used to check release time of scout bees ) Initial solution Current solution Best solution Solution at iteration g Number of scout bees Sequence dependent time increment influence of i on j The number of all successors of task j Time count for part removal time of each task i Initial temperature

69 45 Tg ti t i time timeave timesd TL tlimit totalgradient ts tsize dr UP i vmax vmin v i pg, x jk gbest xpg xpmax xpmin xppg, yij Temperature at iteration g Part removal time of part i Part removal time of part i considering sequence dependent time increment Time count for algorithms Average of time count results found by the algorithms Standard deviation of time count results found by the algorithms Tabu list matrix Time limit of the algorithm to be executed Sum of the values of down, up and flat gradients Tournament size Tabu size The set of parts that are neighbours of part i that can be visited by drop dr and connected through a up gradient User defined fixed bound for particle s maximum velocity User defined fixed bound for particle s minimum velocity Velocity of the particle p at iteration g at dimension i Represents that task j is assigned to station k Best position of the particles found by iteration g User defined bound for particle s position User defined bound for particle s position Position of the particle p at iteration g Represents precedence matrix: task i precedes task j

70 SDDLBP Model Considerations The SDDLBP investigated in this dissertation is concerned with the paced disassembly line for a single model of product that undergoes complete disassembly. Model assumptions include the following: A single product type is to be disassembled on a disassembly line, The supply of the end-of-life product is infinite, The exact quantity of each part available in the product is known and constant A disassembly task cannot be divided between two workstations, Each part has an assumed associated resale value which includes its market value and recycled material value The line is paced, Part removal times are deterministic, constant, and discrete, Each product undergoes complete disassembly even if the demand is zero, All products contain all parts with no additions, deletions, modifications or physical defects, Each part is assigned to one and only one workstation, The sum of part removal times of all the parts assigned to a workstation must not exceed cycle time, The precedence relationships among the parts must not be violated

71 Research Objectives The overall objective of this dissertation is to contribute to the development of environmentally conscious manufacturing and product recovery systems by carrying out disassembly on a disassembly line such that operational characteristics of a disassembly system are improved. In attaining this, the first goal is to describe and then mathematically model the multi objective SDDLBP. The next goal is the determination of data sets and evaluation criteria for use in the analysis of the problem as well as in analysis of solution generating techniques. Appropriate methodologies are then employed and compared in solving the SDDLBP. These goals are achieved by making use of several fields of study. These include: probability and statistics, operations research, software engineering, computer science, combinatorial optimization, multiple criteria decision making, algorithm design, data structures, heuristics/metaheuristics/hybrids, scheduling and sequencing, production analysis, simulation and manufacturing.

72 48 Chapter 4. Description of SDDLBP and the Mathematical Model 4.1. Introduction This chapter provides the mathematical foundations for the remainder of the study. The multiple objectives for the SDDLBP are described. This chapter is organized as follows. Section 4.2 provides the generalized description of the sequence dependent disassembly line balancing problem and explains the four objectives in solving the problem. Mathematical formulation of the problem is presented in Section Problem Overview The particular problem investigated in this dissertation seeks to fulfil four objectives:

73 49 1. Minimize the number of disassembly workstations and hence, minimize the total idle time, 2. Minimize the total time required to complete disassembly, 3. Remove hazardous components early in the disassembly sequence. 4. Remove high-demand components before low-demand components A major constraint is to provide a feasible disassembly sequence for the product being investigated. The result is an integer, deterministic, multi-criteria decision making problem with an exponential search space. Testing a given solution against the precedence constraints fulfils the major constraint of precedence preservation. The sequence dependent disassembly line balancing problem (SDDLBP) investigated in this paper is concerned with a paced disassembly line for a single model of product that undergoes complete disassembly. Model assumptions include the following: a single product type is to be disassembled on a disassembly line; the supply of the end-of-life product is infinite; the exact quantity of each part available in the product is known and constant; a disassembly task cannot be divided between two workstations; each part has an assumed associated resale value which includes its market value and recycled material value; the line is paced; part removal times are deterministic, constant, and discrete; each product undergoes complete disassembly even if the demand is zero; all products contain all parts with no additions, deletions, modifications or physical defects; each part is assigned to one and only one workstation; the sum of part removal times of all the parts assigned to a workstation must not exceed cycle time; the precedence relationships among the parts must not be violated.

74 50 The difference between disassembly line balancing problem (DLBP) and sequencedependent disassembly line balancing problem (SDDLBP) is task time interactions. As opposed to the DLBP, in SDDLBP whenever a task interacts with another task, their task times may be influenced. For example, consider the disassembly of a personal computer, where several components have to be disassembled at the same workstation or neighbouring ones. Disassembling a particular component before another component from the same motherboard may prolong (or curtail) the task time, as opposed to disassembling them in reverse order, because one component could hinder the other because it requires additional movements and/or prevents it from using the most efficient disassembly process. In order to model this very typical situation adequately, the concept of sequence dependent task time increments is introduced. If task j is performed before task i, its standard time t j is incremented by sd ij. This sequence dependent increment measures the prolongation of task j forced by the interference of already waiting task i. Obviously, tasks i and j can only interact in the described manner if they do not have any precedence relationships, i.e., there is no path in the precedence graph directly connecting i and j. Illustrative example: The precedence relationships (solid line arrows) and sequence dependent time increments (dashed line arrows) for an 8-part personal computer (PC) disassembly process are illustrated in Figure 2-1 and their knowledge base is given in Table 4-1. This example is modified from Gungor and Gupta (2002).

75 51 Figure 4-1: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 8-part PC example Table 4-1: Knowledge base for 8-part PC example Part Task Time Hazardous Demand PC top cover 1 14 No 360 Floppy drive 2 10 No 500 Hard drive 3 12 No 620 Back plane 4 18 No 480 PCI cards 5 23 No 540 RAM modules 6 16 No 750 Power supply 7 20 No 295 Motherboard 8 36 No 720 Knowledge base of sequence-dependent part removal time increments for 8-part PC instance is given in Table 4-2. As can be seen in Table 4-2, sequence dependencies for the PC example are given as follows: sd23 2, sd32 4, sd56 1, sd65 3.

76 52 Table 4-2: Knowledge base of sequence-dependent part removal time increments for 8-part PC Sequence-dependent tasks sd ij instance Task i Task j Part removal time influence sd sd sd sd For a feasible sequence 1,2,3,6,5,8,7,4 ; since part 2 is disassembled before part 3, sequence dependency sd32 4 takes place because when part 2 is disassembled, the obstructing part 3 is still not taken out, i.e., the part removal time for part 2 is increased which results in t 2 t2 sd32 14 ; similarly since part 6 is disassembled before part 5, sequence dependency sd56 1 takes place because when part 6 is disassembled, the obstructing part 5 is still not taken out, i.e., the part removal time for part 6 is increased which results in t 6 t 6 sd For another feasible sequence 1,3,2,5,6,8,7,4 with the same PC disassembly example; since part 3 is disassembled before part 2, sequence dependency sd23 2 takes place because when part 3 is disassembled, the obstructing part 2 is still not taken out, i.e., the part removal time for part 3 is increased which results in t 3 t 3 sd ; since part 5 is disassembled before part 6, sequence dependency sd65 3 takes place because when part 5 is disassembled, the obstructing part 6 is still not taken out, i.e., the part removal time for part 5 is increased which results in t 5 t 5 sd

77 Mathematical Formulation The decision version of DLBP was proven to be NP-complete (and hence, the optimization version is NP-hard) (McGovern and Gupta, 2007a). Since SDDLBP is a generalization of DLBP (setting all sequence dependent time increments to zero, SDDLBP reduces to DLBP), the decision version of SDALBP is NP-complete and its optimization versions are NP-hard, too. In this paper, the precedence relationships considered are of AND type and are represented using the immediately preceding matrix [ yij ] n n, where y ij 1 if task i is executed after task j 0 if task i is executed before task j (4.1) In order to state the partition of total tasks, we use the assignment matrix [ x jk ] n m, where x jk 1 if part j is assigned to station k 0 otherwise (4.2) The matrix sd ij n n holds the sequence-dependent time increments data: sd ij sdij if part i prolongs removal time of part j 0 otherwise (4.3) The mathematical formulation of SDDLBP is given as follows: min f1 m (4.4)

78 54 min 2 m i 1 2 f c t (4.5) i n 1 hazardous min f3 i hps, h i PS (4.6) i 0 otherwise i 1 min f i d, d N, PS (4.7) 4 n i 1 PS PS i i i Subject to: m x 1, j 1,..., n (4.8) k 1 jk n ti i 1 m c j ij ij jk j 1 i 1 n n n t sd y x c (4.9) (4.10) m x x, ( i, j) IP (4.11) ik k 1 jk The first objective given in Equation (4.4) is to minimize the number of workstations for a given cycle time (the maximum time available at each workstation) (Baybars, 1986b). It rewards the minimum number of workstations, but allows the unlimited variance in the idle times between workstations because no comparison is made between station times. It also does not force to minimize the total idle time of workstations. The second objective given in Equation (4.5) is to aggressively ensure that idle times at each workstation are similar, though at the expense of the generation of a non-linear objective function (McGovern and Gupta, 2007a). The method is computed based on the minimum

79 55 number of workstations required as well as the sum of the square of the idle times for all the workstations. This penalizes solutions where, even though the number of workstations may be minimized, one or more have an exorbitant amount of idle time when compared to the other workstations. It also provides for levelling the workload between different workstations on the disassembly line. Therefore, a resulting minimum performance value is the more desirable solution indicating both a minimum number of workstations and similar idle times across all workstations. As the third objective (see Equation (4.6)), a hazard measure developed to quantify each solution sequence s performance, with a lower calculated value being more desirable (McGovern and Gupta, 2007a). This measure is based on binary variables that indicate whether a part is considered to contain hazardous material (the binary variable is equal to 1 if the part is hazardous, else 0) and its position in the sequence. A given solution sequence hazard measure is defined as the sum of hazard binary flags multiplied by their position number in the solution sequence, thereby rewarding the removal of hazardous parts early in the part removal sequence. As the fourth objective (Equation (4.7)), a demand measure was developed to quantify each solution sequence s performance, with a lower calculated value being more desirable (McGovern and Gupta, 2007a). This measure is based on positive integer values that indicate the quantity required of a given part after it is removed (or 0 if it is not desired) and its position in the sequence. A solution sequence demand measure is then defined as the sum of the demand value multiplied by the position of the part in the sequence, thereby rewarding the removal of high demand parts early in the part removal sequence.

80 56 The constraints given in; equation (4.8) ensures that all tasks are assigned to at least and at most one workstation (the complete assignment of each task), equation (4.9) guarantees that the number of work stations with a workload does not exceed the permitted number, equation (4.10) ensures that the work content of a workstation cannot exceed the cycle time and equation (4.11) imposes the restriction that all the disassembly precedence relationships between tasks should be satisfied.

81 57 Chapter 5. Experimental Instances 5.1. Introduction Since SDDLBP is a recent problem, very few problem instances exist to study the performance of different heuristic solutions. Three that are developed here include: the 8 part personal computer problem instance, the 10-part problem instance and the 25-part cellular telephone problem instance. Each of these instances is presented with a list of parts and their associated part removal times, hazardous content, demand, as well as their precedence diagram and sequence-dependent time influence data. 8-part personal computer (PC) instance that is presented in Chapter 4 is used as an illustrative example to define sequence-dependent disassembly line balancing problem (SDDLBP) since it is a trivial problem to solve. The remaining two instances given in Section 5.2 and Section 5.3 are used to compare the performance of the proposed algorithms in terms of time complexity and obtained objective values in Chapter 16. This chapter focuses on providing a through description of each of the two data sets as well as any modifications and enhancements made to the original case study data and any derivations performed. Section 5.2 describes the modified 10-part instance, a 10-part data set

82 58 developed from research on an actual product. Section 5.3 presents the mobile phone instance, a 25-part modified data set based on a study performed on a popular electronics product Part Instance Kongar and Gupta (2005) provided the basis for the 10-part SDDLBP instance. McGovern and Gupta (2005a) then modified this instance from its original use in disassembly sequencing and augmented it with disassembly line specific attributes. Kalayci and Gupta (2012) added sequence-dependent part removal time influence of parts obstructing each other. Here the objective is to completely disassemble a product consisting of n = 10 components and several relationships. The problem and its data were modified for used on a paced disassembly line operating at a speed which allows c = 40 seconds for each workstation to perform its required its disassembly tasks. The data for the 10-part product disassembly is shown in Table 5-1, Figure 5-1 and Table 5-2. In Table 5-1, the basic data including part removal time, information of if the part is hazardous or not, and demand of each part is given. Figure 5-1 represents precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 10-part disassembly instance. In Table 5-2, knowledge base of sequence-dependent part removal time increments for 10-part product disassembly is given. As can be seen in Table 5-2, the sequence dependencies for the 10 part product are given as follows: sd14 1, sd23 2, sd32 3, sd41 4, sd45 4, sd54 2, sd56 2, sd65 4, sd69 3, sd96 1.

83 59 Table 5-1: Database of the 10-part instance Task Time Hazardous Demand 1 14 No No No No No No Yes No No No 0 Figure 5-1: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 10-part disassembly instance

84 60 Table 5-2: Knowledge base of sequence-dependent part removal time increments for 10-part Sequence-dependent tasks sd ij product disassembly Task i Task j Part removal time influence sd sd sd sd sd sd sd sd sd sd Part Mobile Phone Instance Gupta et al. (2004) provided the basis for the 25-part cellular telephone SDDLBP instance. McGovern and Gupta (2005b) modified this instance from its original use in disassembly sequencing and augmented it with disassembly line specific attributes. Kalayci and Gupta (2012) added sequence-dependent part removal time influence of parts interacting each other. This realworld instance consisting of n = 25 components has several precedence relationships as well as sequence-dependent obstructing parts. The data set includes a paced disassembly line operating at a speed which allows c = 18 seconds per workstation. In Table 5-3, the basic data including part removal time, information of if the part is hazardous or not, and demand of each part is given. Figure 5-2 represents precedence

85 61 relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 25-part mobile phone disassembly instance. In Table 5-4, knowledge base of sequence-dependent part removal time increments for 25- part mobile phone disassembly is given. As can be seen in Table 5-4, the sequence dependencies for the 25 part product are given as follows: sd45 2, sd54 1, sd67 1, sd69 2, sd76 2, sd78 1, sd87 2, sd96 1, sd , sd , sd , sd , sd , sd , sd , sd Figure 5-2: Precedence relationships (solid line arrows) and sequence-dependent time increments (dashed line arrows) for the 25-part disassembly instance

86 62 Table 5-3: Database of 25-part mobile phone instance Part Task Part Removal Time Hazardous Demand Antenna 1 3 Yes 4 Battery 2 2 Yes 7 Antenna guide 3 3 No 1 Bolt (type 1) A 4 10 No 1 Bolt (Type1) B 5 10 No 1 Bolt (Type2) No 1 Bolt (Type2) No 1 Bolt (Type2) No 1 Bolt (Type2) No 1 Clip 10 2 No 2 Rubber Seal 11 2 No 1 Speaker 12 2 Yes 4 White Cable 13 2 No 1 Red/Blue Cable 14 2 No 1 Orange Cable 15 2 No 1 Metal Top 16 2 No 1 Front Cover 17 2 No 2 Back Cover 18 3 No 2 Circuit Board Yes 8 Plastic Screen 20 5 No 1 Keyboard 21 1 No 4 LCD 22 5 No 6 Sub-keyboard Yes 7 Internal IC Board 24 2 No 1 Microphone 25 2 Yes 4

87 63 Table 5-4: Knowledge base of sequence-dependent part removal time increments for 25-part Sequence-dependent tasks ( ) sd ij mobile phone disassembly Task i Task j Part removal time influence sd sd sd sd sd sd sd sd sd13 14 sd14 13 sd14 15 sd15 14 sd20 21 sd21 20 sd22 25 sd

88 64 Chapter 6. The Combinatorial Optimization Searches 6.1. Introduction Due to the complexity of SDDLBP, there is not currently any known way to optimally solve even moderately sized instances of the problem; therefore alternative search approached must be considered. In fully conducting a combinatorial optimization treatment of this problem, several combinatorial optimization techniques are used to solve SDDLBP. While each of them was selected based on its unique approach to obtain a solution, these methodologies are then analysed both by studying their solutions to varied problem instances given in Chapter 5 and then by comparing the solutions generated by each one to another. This chapter focuses on providing an introduction to each of proposed combinatorial optimization techniques as well as discussing hardware, software and analysis considerations. Section 6.2 introduces combinatorial optimization techniques that are used the solve SDDLBP. Section 6.3 reviews the hardware used for all tests as well as discussing software engineering and reusability.

89 Combinatorial Optimization Methodologies Chapter 4 mathematically defined the SDDLBP and stated that it belongs to the class of NPcomplete problems, necessitating specialized solution techniques. This dissertation makes use of techniques from combinatorial optimization which is a brand of optimization in applied mathematics and computer science that is related to operations research (OR), algorithm theory, artificial intelligence (AI) and computational complexity theory. Recent heuristic and metaheuristic innovations have tended frequently to become aligned with AI and OR. Hence in order to investigate what is current in heuristic or metaheuristic ideas, it is appropriate to examine procedures that have acquired some of the imprint of the AI and OR domain. In the domain of combinatorial optimization, the set of feasible solutions is discrete or can be reduced to one with the goal of finding the best possible solution. Solution methods including heuristics and metaheuristics generally provide near (optimal) solutions. While exhaustive search works well enough in obtaining optimal solutions for small sized instances, its exponential time complexity limits its application on the large sized instances. Combinatorial optimization techniques allow for the generation of a solution which may be optimal or sub-optimal. In this dissertation, seven techniques are proposed making use of wellknown metaheuristics for study and comparison. These include ant colony optimization (ACO), river formation dynamics (RFD), tabu search (TS), particle swarm optimization (PSO), simulated annealing (SA), hybrid genetic algorithms (HGA) and artificial bee colony (ABC) metaheuristics. These processed are then applied to the two instances from Chapter 5 for analysis, evaluation and comparison.

90 66 Exhaustive search (Brute-force search) requires the checking of every possible solution in order to determine the optimal solution. The drawback is that the most spaces are extremely large and an exhaustive search of combinatorial optimization problem instance will only take a reasonable amount of time for small sized examples. However, exhaustive search techniques will fail to find a solution for any instance except small sized instances within any practical length of time. Therefore, intelligent search techniques are required to solve such problems. A heuristic is any problem-specific step by step set of procedures or rules. In this dissertation, the following task assignment rules are used as heuristics integrated to the proposed methods: Greatest Ranked Positional Weight (GRPW), Longest Processing Time (LPT), Shortest Processing Time (SPT), Greatest Number of Immediate Successors (GNIS), Greatest Number Of Successors (GNS), Random Priority (RP), Smallest Task Number (STN), Greatest Average Ranked Positional Weight (GARPW), Smallest Upper Bound (SUB), Smallest Upper Bound Divided by the Number of Successors (SUBNUS), Greatest Processing Time Divided by the Upper Bound (GPTUB), Smallest Lower Bound (SLB), Minimum Slack (MS), Minimum Number of Successors Divided by Task Slack (MNSTS), Greatest Number of Immediate Predecessors (GNIP). A local search is a type of heuristic often used in solving combinatorial optimization problems. Given a search space, local search starts from an initial solution and then iteratively moves from one possible solution to another in search of a solution that is both feasible and better performing than the best found so far. This continues until some stopping condition is met. In this dissertation, some local search techniques are used as embedded to the proposed methods. A hybrid makes use of two or more solution generating techniques in sequence or repeatedly

91 67 during each iteration. This dissertation makes use of hybrids that combines local search with genetic algorithms. A metaheuristic is a general purpose heuristic that provides a top-level strategy to guide other heuristics in finding feasible solutions within the search space. In practice, they are often seen having a stochastic component. Metaheuristics may include iterative, deterministic or stochastic search methods such as evolutionary algorithms and swarm intelligence techniques. ACO first published by Dorigo et al. (1996) is a swarm intelligence based global search method for difficult combinatorial optimization problems like Travelling Salesman Problem (TSP) and Quadratic Assignment Problem (QAP). Inspired by colonies of ants, the ACO metaheuristic makes use of computer agents known as ants. A moving ant lays some pheromone in varying quantities on the ground, thus marking the path by a trail of this substance. While an isolated ant moves essentially at random, an ant encountering a previously laid trail can detect it and decide with high probability to follow it, thus reinforcing the trail with its own pheromone. The more ants follow a trail, the more attractive that trail becomes for being followed. The process is thus characterized by a positive feedback loop, where the probability with which an ant chooses a path increases with the number of ants that previously chose the same path. In brief, they consist in copying the method used by ants to find good paths from the colony to food sources. RFD first published by Rabanal et al. (2007) is also a swarm based global search method for solving combinatorial optimization problems. In RFD method, instead of associating pheromone values to edges as in ACO method, altitude values are associated to nodes. Drops (represents ants in ACO method) reduce or increase the altitude of nodes as they move. The

92 68 probability of the drop to take a given edge instead of others is proportional to the gradient of the down slope in the edge, which in turn depends on the difference of altitudes between both nodes and the cost of the edge. Drops are unleashed at the origin node until they fall in the destination node. New drops are inserted in the origin node to transform new paths. After some steps, good paths from the origin to the destination are found. These paths are given in the form of sequences of decreasing edges from the origin to the destination. TS first introduced by Glover (1989, 1990b) is a metaheuristic strategy to overcome local optimality in solving combinatorial optimization problems. The underlying idea is to forbid some search directions at a present iteration in order to avoid cycling, but to be able to escape from a local optimal point. This strategy can make use of any local improvement technique. The major theme behind TS is to incorporate flexible memory functions into the search procedure. TS is distinct from the SA and GA methods in that SA and GA in terms of memory such that SA and GA are memoryless and probabilistic random search methods, while TS is deterministic and takes advantage of the history of the search process. There are many problems that are successfully solved using tabu search. PSO first introduced by Kennedy and Eberhart (1995) is derived from the social behaviour of migrant birds and fish which migrate in flocks and schools, respectively, while sharing the information among themselves to locate their foods. In the PSO method, each member is called a particle. Each particle has a position and moves around in the multidimensional space with a velocity. To find the optimal solution, each particle adjusts its flying by constantly updating its velocity according to its own flying experience and its companions flying experience. A particle flies in the problem search space towards the optimal position.

93 69 SA initially proposed by Kirkpatrick et al. (1983) is a stochastic neighbourhood search method that is based on the analogy between the process of annealing of solids and the solution methodology of combinatorial optimization problems. Analogous to its use with the physical annealing of solids, the combinatorial optimization problem solution undergoes a series of changes while looking for an improved solution according to some objective function. As simulated annealing starts, an initial solution is generated and used as the current solution. If the objective function value is superior to that of the current solution, the neighbouring solution becomes the new current solution. If the neighbouring solution provides an objective function value inferior to that of the current solution, the neighbouring solution may still become the current solution if a certain acceptance criterion is met. As the temperature drops, new neighbouring solutions to the current solution are found. SA technique has the capability of jumping out of the local optima for global optimization which is achieved by accepting with probability neighbouring solutions worse than the current solution. The acceptance probability is determined by a control parameter ( T g ) which decreases during the SA procedure according to a cooling rate. The process of finding neighbouring solutions and accepting these as current solutions if acceptance criteria are met is repeated according to the cooling pattern until some stopping criteria is met. GA first proposed by Holland (1975) is an adaptive search method for solving complex optimization problems. Goldberg (1989) presented a number of applications of GA to search, optimization and machine learning problems. In general, the power of GA comes from the fact that the technique is robust, and can deal with a wide range of problem areas. A GA emphasises genetic encoding of potential solutions into chromosomes and applies genetic operators such as crossover and mutation to these chromosomes. Each individual represents a potential solution to

94 70 the problem at hand, and is evaluated to give some measure of its fitness. Some individuals undergo stochastic transformation by means of genetic operations to form new individuals. After several generations, the algorithm converges to the best individual, which hopefully represents an optimal or suboptimal solution to the problem (Gen and Cheng 2000). Inspired by the intelligent foraging behaviours of honeybee swarms, Karaboga (2005) proposed ABC algorithm that implemented a new swarm intelligence based optimization technique. It classifies foraging artificial bees into three groups as follows: employed bees, onlookers, and scouts. An employed bee is responsible for flying to a food source and collecting from the food that is exploited by the swarm. An onlooker decides on whether a food source is acceptable or not according to dances performed by the employed bees. A scout randomly searches for exploration of new food sources. In the ABC algorithm, each solution to the problem under consideration is called a food source and represented by an n dimensional vector where the fitness of the solution corresponds to the nectar amount of the associated food resource. As with other intelligent swarm-based approaches, the ABC algorithm is an iterative process. There are few control parameters in the ABC algorithm, which is the main advantage of the algorithm. Due to its simplicity and ease of implementation, the ABC algorithm has gained more attention and has been used to solve many practical engineering problems Hardware, Software and Analysis Considerations For consistency in software architecture, data structures and time complexity, all of the search algorithm software was designed, engineered, written, refined, tested and applied as a part of this dissertation. All computer programs were coded in MATLAB and tested on Intel Core2 1.79

95 71 GHz processor with 3GB RAM. After the software engineering was complete, each subroutine and each entire program was investigated on a variety of test cases. During data collection, no programs other than the executable evaluation and those required by the operating system were either running or open. All of the combinatorial optimization computer software was run at least thirty times to obtain an average of the computation time. Since methodologies possessed a probabilistic component, it was necessary to run several times with the results averaged for use in efficacy analysis to avoid reporting unusually favourable or poor results.

96 72 Chapter 7. Core Functions 7.1. Introduction This chapter focuses on providing an introduction to each of the core functions used in the proposed algorithms. Since these functions are shared among most of the proposed algorithms, an introduction chapter is constructed to initially explain them all. Solution representation is given in Section 7.2. Feasible solution construction strategy is explained in Section 7.3. Moving strategy is demonstrated in Section 7.4. Section 7.5 gives details of feasibility check and repair functions. Section 7.6 gives pseudo codes for objective functions formulated in Chapter 4. Finally, Section 7.7 reviews the multi-criteria approach used by all of the combinatorial optimization techniques Solution Representation One of the most important decisions in designing a metaheuristic lies in deciding how to represent solutions and relate them in an efficient way to the searching space. Also, solution

97 73 representation should be easy to decode to reduce the cost of the algorithm. In the proposed algorithms, permutation based representation is used, so elements of a solution string are integers. Each element represents a task assignment to work station. The value of the first element of the array shows which task is assigned to workstations first, the second value shows which task is assigned second and so on. For example, if there are 8 tasks to be assigned to workstations then the length of the solution string is 8. Figure 7-1 illustrates assignment of tasks to workstations as an example of PC instance given in Chapter 4. Figure 7-1: Assignment of tasks to workstations 7.3. Feasible Solution Construction Strategy The strategy of building a feasible balancing solution is the key issue to solve the SDDLBP. We use station-oriented procedure for a solution constructing strategy in which solutions are generated by filling workstations successively one after the other. The procedure is initiated by the opening of a first station. Then, tasks are successively assigned to this station until more tasks cannot be assigned and a new station is opened. In each iteration, a task is randomly chosen from

98 74 the set of candidate tasks to assign to the current station. When no more tasks may be assigned to the open station, this is closed and the following station is opened. The procedure finalizes when there are no more tasks left to assign. In order to describe the process to build a feasible balancing solution, assignable task and available task are defined as follows: A task is an assignable task if and only if it has not already been assigned to a workstation and all of its predecessors have already been assigned to a workstation. A task is an available task if and only if it belongs to the set of available task and the idle time of current workstation is higher than or equal to the processing time of the task. The generation procedure of a feasible balancing solution is given as follows: Step 1: Start. Step 2: According to the precedence constraints construct the assignable task set. Step 3: According to the cycle time construct the available task set. Step 4: If the set of available task is null, go to step 6. Step 5: Select the task with predetermined priority from the available task set and place the task to the current workstation; go back to step 2. Step 6: If the set of assignable task is null, go to step 8. Step 7: Open a new workstation, go back to step 2. Step 8: Stop the procedure. The predetermined priority strategy mentioned in Step 5 is different for each proposed algorithm. The details of each particular procedure are given in the following chapters. The pseudo code for feasible solution construction strategy is given in Table 7-1. The pseudo codes for sub-functions of feasible construction strategy (Table 7-1) are given in Table 7-2 (creating assignable task list) and Table 7-3 (creating available task list), respectively.

99 75 Table 7-1: Pseudo code for feasible solution construction strategy Function feasiblesolution AS = null, AV = null, k = 1 For each j of 1 x jk 1 For each i of y ij For each j of y ij If j assignable ( y, x ) Add j to AS End if End for End for For each j of AS j If j available( sd, k) Add j to AV End if End for If AV = null Call priority( AS ) and select j 1 from AS k = k +1 else Call priority( AV ) and select j 1 from AV End if Place task j 1 to station k Add j to 1 S c End for Return Sc and x End function ij ij j1k

100 76 Function assignable assign = true If j x jk assign = false break End if If assign = true For each i of x ik If y = true ij assign = false break End if End for End if Return assign End function Function available place = true ' t t sd j j ij If t ' j it place = false End if Return place End function k Table 7-2: Pseudo code for creating assignable task list (AS) Table 7-3: Pseudo code for creating available task list (AV) 7.4. Moving Strategy A new solution obtained from a current solution by using a specific move (mutation) is called a neighbourhood solution. In the proposed algorithms, interchanging two tasks (SWAP) or inserting a task to a different work station (INSERT) is implemented as a moving strategy such that the new neighbouring solutions are ensured to be feasible. By guaranteeing feasibility in each operation, the necessity of the repair function is prevented. While SWAP operator forces

101 77 the algorithm to work in an infinite loop until it finds a feasible move, INSERT operator shuts itself down if it cannot find any feasible move in a single step. Obviously, worst case complexity of SWAP operator is much higher than INSERT operator Swap SWAP operator works as follows: Two randomly selected tasks from two randomly selected workstations are exchanged while satisfying the precedence constraints. A single SWAP operation is given in Figure 7-2 for PC example given in Chapter 4. SWAP operator forces the algorithm to make a move within a loop in each step. Figure 7-2: SWAP operator The pseudo code for a SWAP operation is given in Table 7-4.

102 78 Function swap move = false While move = false Create r (0,1) r1 2,length of S c r2 r1 1 If y = false rr 12 End while Return S c End function Insert move = true temp = S ( ) c r 2 S ( r ) S ( r ) c 2 c 1 ( ) c 1 S r = temp End if Table 7-4: Pseudo code for SWAP operation INSERT operator works as follows: A randomly selected task from a randomly selected workstation is inserted into another randomly selected workstation while satisfying the precedence constraints. A single INSERT operation is given in Figure 7-3 for PC example given in Section 4.2. Unlike SWAP operator, INSERT operator shuts itself down if it cannot find any feasible move in a single step. Figure 7-3: INSERT operator The pseudo code for INSERT operation is given in Table 7-5.