Devikamalam, et al., International Journal of Advanced Engineering Technology Research Paper RESOURCE SCHEDULING OF CONSTRUCTION PROJECTS USING GENETIC ALGORITHM Devikamalam. J 1, Jane Helena. H 2 Address for Correspondence 1 PG student, 2 Assistant Professor, Division of Structural Engineering, Anna University, Chennai, India ABSTRACT Resource allocation and leveling are among the top challenges in project management, due to the complexity of projects. The main objective of this project is to optimize the schedule of construction project activities in order to minimize the total cost with resource constraints using Genetic Algorithm (GA optimization technique). This work describes a genetic algorithm approach to Resource Constraint Project Scheduling Problems (RCPSP) in construction industry. The GA procedure searches for an optimum set of tasks and priorities that produce shorter project duration and better-leveled resource profiles using GeneHunter software. Major advantage of the procedure is its simple applicability within commercial project management software systems to improve the performance. KEYWORDS: Genetic Algorithm, Resource Scheduling, Resource constraint Scheduling, Construction management 1.0 INTRODUCTION Resource management is one of the most important aspects of construction project management in today s economy because the construction industry is resource-intensive and the costs of construction resources have steadily risen over the last several decades. Every project schedule has its own precedence constraints, which means that each activity can be processed when all its predecessors are finished. In general, the purpose of project scheduler is to minimize the completion time or make span, subject to precedence constraints. This paper brings out the drawback in existing scheduling software and the method of using GA for resource constraint scheduling by means of a case study. Traditional scheduling methods use scheduling rules (heuristics) specific to the project model or constraint formulation, this method uses a direct representation of schedules and a search algorithm that operates with no knowledge of the problem space. The representation entation enforces precedence constraints, and the objective function measures both resource constraint violations and overall performance. The advantages of using GA based optimization technique for resource based scheduling has been proved by several researchers (Weng-Tat Chan, et al., 1996, Cengiz 2002, Ahmed 2008). Compared with traditional heuristic and mathematical models, the GA scheduler has several advantages as it can consider the objectives of time/cost trade-off, resource-constrained allocation, and resource levelling simultaneously; it is difficult for traditional models to have such a function. It has more flexibility to solve scheduling problems of different types, because no heuristic rules are necessary. 1.2 Genetic Algorithm Genetic Algorithms (GA) are inspired by Darwin's theory about evolution. The GA is a global search procedure that searches from one population of solutions to another, focusing on the area of the best solution. It models with a set of solutions (represented by chromosomes) called initial population, computation is performed through the creation of an initial population of individuals and modifying the characteristics of a population of solutions (individuals) over a large number of generations followed by the evolution, a satisfactory solution is found. This process is designed to produce successive populations that mean the solutions from one population are taken and used to form a new E-ISSN 0976-3945 population. This is motivated by a hope, that the new population will be better than the old one and so on through generations. 1.2.1 Fitness Function The fitness function is the function to be optimized. For standard optimization algorithms, this is known as the objective function. 1.2.2 Individuals An individual is any point to which the fitness function can be applied. The value of the fitness of an individual is its score; an individual is a single solution. A chromosome is a set of parameters which define a proposed solution to the problem that the genetic algorithm is trying to solve. The chromosome is often represented as a simple string. 1.2.3 Populations and Generations A population is an array of individuals. At each iteration, the genetic algorithm performs a series of computations on the current population called parents to produce a new population called children. Each successive population is called a new generation. Typically, the algorithm is more likely to select parents that have better fitness values. 1.2.4 Encoding A chromosome is subdivided into genes. A gene is the GA representation resentation of a single factor for a control factor. The process of representing the solution in the form of a string that conveys the necessary information is called Encoding. Each gene controls a particular characteristic of the individual; similarly, each bit in the string represents a characteristic of the solution. Encoding Methods are Binary Encoding, Permutation Encoding (Real number encoding), and Value Encoding. For eg, the GA chromosome is represented as follows 2.0 BASIC OUTLINE OF GENETIC ALGORITHMS Figure 1 shows the various steps involved in Genetic Algorithm process. Fig. 1 Flowchart showing the Genetic Algorithm Process
Devikamalam, et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 2.1 Importance of GA Genetic algorithm technique provides best solutions in comparison with the other classic approach. Because traditional techniques like Microsoft project and Primavera scheduling software do not consider resource constraints, actual cost and duration may vary from the estimated one. An effective GA representation and meaningful fitness evaluation are the keys to the success in GA applications. The method of solving resource constraint problem using the software GeneHunter which uses GA optimization technique is presented in this paper. GeneHunter is a powerful software solution for optimization problems which utilizes a state-of-the-art genetic algorithm methodology. GeneHunter includes an Excel Add-In which allows the user to run an optimization problem from Microsoft Excel, as well as a Dynamic Link Library of genetic algorithm functions that may be called from programming languages such as Microsoft Visual Basic or C. 3.0 PROBLEM FORMULATION In order to solve a project scheduling problem involving resource constraint, activities involved in a real-time construction project has been considered. The resource constraint in the form of number of skilled and unskilled labourers available per day is taken. 3.1.2 GeneHunter's Excel Interface Creating a problem solving model in GeneHunter requires that the relevant data is entered into a Microsoft Excel spreadsheet and specify problem solving parameters. GeneHunter actually solves the problem by allowing the less fit individuals in the population to die, and selectively breeding the fit individuals. The process is called selection, as in selection of the fittest. Two individuals are taken and mated (crossover), the offspring of the mated pair will receive some of the characteristics of the mother and some of the father.in nature, offspring often have some slight abnormalities, called mutations. Usually, these mutations are disabling and inhibit the ability of the offspring to survive, but once in a while, they improve the fitness of the individual. GeneHunter occasionally causes mutations to occur. As GeneHunter mates fit individuals and mutates some, the population undergoes a generation change. The population will then consist of offspring plus a few of the older individuals which GeneHunter allows to survive to the next generation. These are the most fit in the population, and we will want to keep them breeding. These most fit individuals are called elite individuals. After dozens or even hundreds of "generations," a population eventually emerges wherein the individuals will solve the problem very well. In fact, the fit individual will be an optimum or close to optimum solution. 3.1.3 GeneHunter Dialog Screen The GeneHunter Dialog screen shown in Figure 2 to identify the cells in the spreadsheet involved in solving the problem. The list of constraints that should be met by the solution can also be listed. 3.1.4 Fitness Function Cell The Fitness Function box tells GeneHunter the location of the cell which contains the formula that measures GeneHunter's success in finding a solution to the problem. The formula may be created using any of the Excel functions that are available from the Insert menu, such as average, sum, percentage, etc., Use of Excel macros or Visual Basic functions to create a formula that allows solving very complex problems. A neural net may even be used to model the process if an appropriate mathematical formula is not available. 3.1.5 Chromosomes Chromosomes are the variables whose values are adjusted in order to solve the problem. Their value is related in some way to the fitness function. GeneHunter uses two types of chromosomes to solve the problems. Continuous Chromosomes are used when the adjustable cell can take on a value that may be within a continuous range, such as the value 1.5 with the range 0 to 2. Continuous chromosomes may also be integers if the search space is to be restricted. Enumerated Chromosomes are used when the problem involves finding an optimal combination of tasks, resources, duties, etc. 3.1.6 Constraints The constraint portion of the GeneHunter dialog box allows doing the following: Limit the range of values that GeneHunter will search for a solution, thus limiting the time taken to find an optimal solution. This is called hard constraint. Add restrictions or sub-goals to the original fitness function. This is called a soft constraint. Solutions are attempted to be found that meet the soft constraints, as well as optimize the fitness function. 4.0 CASE STUDY A real time project named Aqualily at Mahindra world city with resources is chosen. Details of the project are shown in Appendix A. 4.1 Objective function: The objective function is to find the best schedule that gives minimum total project duration (T), Minimize (T) where, T depends on start date (Si) of activity and its duration (Di), i.e, T=Maximum(Si+Di) subjected to resource constraint 4.1.1 Resource limit: The following table shows the range of resource limits. Requirements of resources per day and duration in shown in Appendix B. This is input in GeneHunter, Table 1 Resource Limit Fig.2 GeneHunter dialog Screen
Devikamalam, et al., International Journal of Advanced Engineering Technology E-ISSN 0976-3945 Table: 3 Comparison Actual usage of Resources and Cost 5.0 RESULTS 5.1 Microsoft Project Solution: Implementation of this problem in MSP with unlimited resources gives total project duration as 430days. Resource Profile for a resource is shown in the Figure 3, Fig: 3 Resource Profile After carrying out levelling operation, the total duration of the project is 504 days. 5.2 Genehunter solution Problem is executed by using many generations. The converging result obtained was T = 760 days by applying resource constraints. Best fitness is obtained in 200 generations. Fig. 4 GeneHunter solution 5.3 Comparison between two solutions Intended goal of achieving the best schedule with resource constraints gives optimized duration of the project is T = 760 days. Solution obtained from MSP is practically not possible for tracking process and for execution. Hence optimized duration is 760 days. Table: 2 Comparison of Results Input can be real values or variables in GenrHunter whereas it is only variables in MSP. Both GeneHunter and MSP undertake time and Predecessor constraint, but resource constraint can be incorporated in GeneHunter alone. 6.0 CONCLUSION An implementation of the GA developed model for resource-constrained constrained project scheduling has resulted in optimized output with reduced cost. A real time project solved using this optimization software shows that best converging result can be obtained. REFERENCES 1. Ahmed B. Senouci and Neil N. Eldin, (2008), " Use of Genetic Algorithms in Resource Scheduling of Construction Projects", Journal of Construction Engineering and Management, Vol. 130, No. 6, pp. 869-877. 2. Cengiz Toklu Y.C (2002), "Application of GA to Construction Scheduling with or without Resource Constraints", Canadian Journal of Civil Engineering, Vol.29, No. 3, pp 421-429. 3. Jin-Lee Kim and Ralph D. Ellis Jr. (2008), Permutation-Based Elitist Genetic Algorithm for Optimization of Large-Sized Resource-Constrained Project Scheduling, Journal of Construction Engineering and Management,, Vol. 134, No.11, pp. 904-913. 4. Sou-Sen Leu, An-Ting Chen, and Chung-Huei Yang (1999), Fuzzy Optimal Model for Resource- Constrained Construction Scheduling, Journal of Computing in Civil Engineering,, Vol. 13, No. 3, pp. 207-216. 5. Tarek Hegazy and Moustafa Kassab (2003), Resource Optimization Using Combined Simulation and Genetic Algorithms, Journal of Construction Engineering and Management, Vol. 129, No. 6, pp. 698-705. 6. Tarek Hegazy, (1999), "Optimization of Resource Allocation and Leveling Using Genetic Algorithms", Journal of Construction Engineering and Management, Vol. 125, No. 3, pp. 167-175. 7. Weng-Tat Chan, David K. H. Chua, and Govindan Kannan (1996), "Construction Resource Scheduling with Genetic Algorithms", Journal of Construction Engineering and Management,, Vol. 122, No. 2, pp. 125-132. Table 3 shows the Resource Limit and Actual usage
Devikamalam, et al., International Journal of Advanced Engineering Technology APPENDIX A. PROJECT DETAILS: S.No 1 2 3 4 Description Name of the project Location of the project Client 5 6 7 8 9 10 11 12 Consultant Architect PMC Quantity surveyor Contract value in Crores Type of Contract Type of structure Type of Building Building Configuration 13 Scope of work 14 15 16 17 18 Duration of the project Contractual start Contractual finish (Milestones if any) Working hours Mobilisation advance 19 CAR policy 20 Defect liability period 21 Penalty / Liquidated Damages 22 Material supply by client 23 24 Water & power Retention & Release of retention Taxes 25 Particular "AQUALILY "Mahindra World City Natham Post, Chengalpet, Tamilnadu. Mahindra Residential Developer Limited. M/s. Ecalibre Engineering Consultant Pvt Ltd. M/s. Edifice Consultants Pvt Ltd. M/s. CB Richard Ellis. M/s. KPK Quantity Surveyor. Rs, 44.01 Item rate contract Structural and Identified Finishes works Residential Building Block D1-Block D8 Structural and Identified Finishes works Basement + Ground Floor + 7 Floors Number of Blocks - 8 Number of units - 178 18 Months Immediately after award of LOI Nil 24hours 10% of contract value at the time of acceptance of work order against B.G Car Policy will be obtained by Contractor The defects liability period will be 12 Months from the date of issue of virtual completion Contractor shall be liable for liquidated damages of 1% per week of delay and Max 5% on the final Contract Value Cement,Reinforcement steel & Structural steel Supplied but chargeable 5% will be deducted from the running bill. The contract value is inclusive of all taxes. A. LAYOUT OF THE PROJECT : Fig : 5 Layout of Aqualily Project Int J Adv Engg Tech/IV/III/July-Sept.,2013/113 113-119 E E-ISSN 0976-3945
B. RESOURCE REQUIREMENT PER DAY Activities Duration R1 R2 R3 R4 R5 R6 R7 R8 R9 R10 R11 R12 R13 R14 R15 R16 R17 R18 R19 Days /d /d /d /d /d /d /d /d /d /d LS LS LS LS /d /d /d /d /d Letter of Indent 1 1 1 Handing Over 15 1 1 Initial Mobilization 1 1 1 Receipt of Setting out Drg 5 1 1 Setting out and Surveying 1 5 1 Basement Works 150 Dewatering Works 1 1 12 1 1 2 4 1 1 2 5 4 Zone A&B (Basement) Sub Structure works Excavation 40 1 2 4 1 1 1 2 5 4 Sandfilling 41 1 1 2 4 1500 1 1 2 5 4 P.C.C 42 1 2 30 1200 10000 1 1 2 5 4 Waterproofing 40 1 4 12 2 2 950 20000 1 2 5 4 Raft Slab 40 1 10 60 8 8 2 2500 200000 18000 1 1 2 5 4 Retaining wall & Column works 40 1 10 60 8 8 2 3200 480000 24000 1 1 2 5 4 Backfilling 45 1 40 1 1 2 5 4 Basement slab 1 10 30 8 8 2 3500 200000 25000 1 1 2 5 4 Zone C&D (Basement) Sub Structure works Excavation 40 1 2 4 1 0 1 1 2 5 4 Sandfilling 41 1 1 2 4 1500 1 1 2 5 4 P.C.C 42 1 2 30 1200 10000 1 1 2 5 4 Waterproofing works 40 1 4 12 2 2 950 20000 1 1 2 5 4 Raft Slab 40 1 10 60 8 8 2 2500 200000 18000 1 1 2 5 4 Retaining wall & Column works 40 1 10 60 8 8 2 3200 480000 24000 1 1 2 5 4 Backfilling 45 1 40 1 1 2 5 4 Basement slab 1 10 30 8 8 2 3500 280000 25000 1 1 2 5 4 Basement Finishing Works Zone A& B Brick Work 100 1 16 20 3800 6750 20000 1 1 2 5 4 Plastering 80 1 18 20 2 4200 23000 1 1 2 5 4 Painting 1 20 20 8 1 1 2 5 4 Zone C&D Brick Work 100 1 16 20 3800 6750 20000 1 1 2 5 4 Plastering 80 1 18 20 2 4200 23000 1 1 2 5 4 Painting 1 20 20 8 1 1 2 5 4
Super Structure D4 Block Structure G.F Slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 F.F slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 Slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 Third Floor Slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 Fourth Floor slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 Fifth Floor Slab 16 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 Terrace Slab 12 1 8 32 8 8 2 2 4500 360000 25000 1 1 2 5 4 LMR 1 15 40 10 8 2 2 4800 384000 26000 1 1 2 5 4 Finishing Works Ground Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 First Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Slab 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Third Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Fourth Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Fifth Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Sixth Floor 45 1 12 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Header Room 55 1 15 30 3 2 3 2 5 3800 360 30000 1 1 2 5 4 Structural Works 76 1 15 35 8 5 3200 1 1 2 5 4 plastering 60 1 20 35 3500 35000 1 1 2 5 4 painting 1 22 35 8 1 1 2 5 4 D2,D1,D3,D6&D7,D5 Structure G.F Slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 F.F slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Third Floor Slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Fourth Floor slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Fifth Floor Slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Terrace Slab 25 1 48 192 48 6 18 12 27000 2160000 150000 1 6 12 30 24 LMR 1 90 240 48 6 18 12 27000 2160000 150000 1 6 12 30 24 Finishing Works Ground Floor 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 First Floor 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Third Floor 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Fourth Floor 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Fifth Floor 60 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Sixth Floor 20 1 72 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Header Room 75 1 90 180 18 12 12 30 22800 2160 180000 1 6 12 30 24 Structural Steel Works 90 1 90 210 48 6 19200 87500 1 6 12 30 24 85 1 120 210 12 12 21000 210000 1 6 12 30 24
plastering painting 218 1 132 210 48 1 6 12 30 24 D8 Block Structure G.F Slab 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 F.F slab 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 Slab 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 Third Floor 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 Fourth Floor slab 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 Fifth Floor Slab 18 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 Terrace Slab 15 1 4 25 8 1 3 2 4500 360000 25000 1 1 2 4 4 LMR 1 4 25 8 1 3 2 4800 360000 26000 1 1 2 4 4 Finishing Works Ground Floor 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 First Floor 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Seecond Floor Slab 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Third Floor 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Fourth Floor 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Fifth Floor 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Sixth Floor 25 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Header Room 45 1 15 30 3 2 2 5 3800 360 30000 1 1 2 4 4 Structural Steel Works 65 1 10 40 8 1 3200 87500 1 1 2 4 4 plastering 60 1 15 45 3500 35000 1 1 2 4 4 painting 60 1 20 30 8 1 1 2 4 4 Total 85 1969 5427 16 819 196 339 290 400 4 627100 36540 25079000 4082000 85 174 350 856 700