A STUDY OF A HEURISTIC CAPACITY PLANNING ALGORITHM FOR WEAPON PRODUCTION SYSTEM

Transcription

1 46 International Journal of Electronic Business Management, Vol. 9, No. 1, pp (2011) A STUDY OF A HEURISTIC CAPACITY PLANNING ALGORITHM FOR WEAPON PRODUCTION SYSTEM James C. Chen 1, Kou-Huang Chen 2*, Chien-Hsin Lin 3,5, Chia-Wen Chen 4 and Chia-Lin Yang 5 1 Department of Industrial Management National Taiwan University of Science and Technology Taipei (106), Taiwan 2 Department of Industrial Engineering and Management China University of Science and Technology Taipei (11581), Taiwan 3 Chemical Systems Research Division Chung-Shan Institute of Science & Technology, Armaments Bureau, M.N.D. Taoyuan (481), Taiwan 4 Department of Industrial and Information Management, National Cheng Kung University Tainan (701), Taiwan 5 Department of Industrial and Systems Engineering Chung Yuan Christian University Chung Li (320), Taiwan ABSTRACT This research developed a capacity planning heuristic for a weapon production system (WPS) with characteristics of low order volume, high order variety, complex processes, uncertain order and frequent changes of orders. The heuristic capacity planning algorithm allocates orders to resources, determines appropriate order release time to the factory, and estimates the expected loading of all machines. With these, plant managers can take actions to manage capacity shortage of bottleneck machines and make necessary change of order planning. The proposed algorithm was programmed in Microsoft Visual Basic, and real data from a weapon production factory were used to evaluate the effectiveness and efficiency of this algorithm. Comparing the performance of results, it reveals that the proposed capacity planning heuristics outperforms current manual capacity planning policy used in practice. Keywords: Weapon Production System, Heuristic Algorithm, Capacity Planning * 1. INTRODUCTION The processes of Weapon production system are precise and complex, with characteristics of long processing time, multiple resource constraints, frequent changes in orders, and long processing time. The R&D phase of weapon production process has features of high order variety, low order volume, and frequent design changes. If urgent demand were to be met in the R&D phase, the manufacturing plan would probably need to be readjusted. After the R&D phase is completed, another problem is encountered. The increasing demand in quantity might result in the imbalance of resource allocation or the shortage of * Corresponding author: [email protected] capacity. Therefore, it becomes extremely important to allocate limited budget on the required resources as well as to rearrange production plan quickly when the time and the quantity demanded for products alter. The objectives are to understand the situation of capacity allocation and loading instantly. Weapon production system (WPS) involves two process types- Job Shop and Flow Shop, as illustrated in Figure 1. The processes are precise and complex, with characteristics of long processing time, multiple resource constraints, frequent changes in orders, and long processing time. In the first part of the production system, machines with the same functions are displayed in the same area in the factory based on the concept of Job Shop. After resources are processed in specific processing places, they are stored as semi-finished products and assembled at the

2 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 47 latter part of the assembly line. In the latter part of the production system, based on the concept of Flow Shop, machines are displayed according to their operation sequences, which is similar to the way electronic assembly industry allocates machines. Due to the changes in product and manufacturing technology, the quantity of machines for WPS might be difficult to predict, resulting in capacity shortage or capacity surplus. Therefore, it is critical to determine the required number of machines providing sufficient capacity in various time periods to meet the due date of customers orders. If simulation can be carried out in advance, analysis for resource integration can be performed prior to release, the factory capacity loading can be determined and allocation of capacity per unit can be effectively planned. Therefore, resource integration and dynamic capacity allocation can take place in the shortest time frame, uneven distribution of capacity resulting from inappropriate order release time can be effectively reduced, and planning optimization can be obtained. Infinite capacity concept is used to decide the required number of machines to balance the loading of machines for various time periods. Then, finite capacity concept can be use to decide the finished time of each order considering the required capacity and available capacity of each machine in different time periods. Figure 1: Production module of weapon production system In order to solve the problems above, this research utilizes heuristic algorithm to develop a capacity planning module for WPS, and perform system dynamic analysis to decide on the optimal resource investment portfolio. Next, appropriate order release time is determined in order to balance the loadings for bottleneck resources and to reschedule for the changes in order. This research develops a system for capacity planning to enhance the responsiveness of system to demand changes and to balance the utility rate of machines. The objectives are increasing productivity and enhancing overall performance of the system. 2. LITERATURE REVIEW In the highly competitive environment, there is an urgent need to develop innovative technologies, enhance system performance and reduce production cost. The most effective method to improve production performance is to carry out effective capacity planning. Effective capacity planning not only can enhance machines utilization, but also can reduce work in process, inventories, costs, defect rate as well as improving inventory turnover rate. Researches about capacity planning are considered important in both academia and industry. As enterprises have different manufacturing types, they counter different challenges in capacity planning. This problem is extremely serious in recent market as there are problems of high order variety, low order volume, and uncertain orders. As system resource constraints and production performance are closely related, it is extremely important to construct a dynamic capacity planning module based on dynamic changes. Figure 2 is the capacity allocation diagram for type m machine in the planning phase. When the number of machines is 1, the diagram shows a shortage of capacity. When the number of machines increases to 2, there is still a shortage in capacity and the shortage is shown in Figure 3. Through overworking or increasing the number of machines by one, the capacity requirements can be fulfilled at all time. Therefore, how to effectively decide on the number of different type of machines is necessary to prevent double investment and uneven resource allocation. In researches, capacity is defined as the upper limit of a production unit that could be a factory, a department, a machine or an operator. On the other hand, some scholars define capacity as the rate of producing products in a production process. Usually, units produced per unit time or time required per unit is used as the standard of measurement. Generally, there are two ways in which capacity requirement planning can be carried out. One way is Infinite Loading and another way is Finite Loading, as illustrated in Figure 4. Figure 2: Capacity allocation diagram of type m machine in the planning phase (number of machines=1)

3 48 International Journal of Electronic Business Management, Vol. 9, No. 1 (2011) Figure 3: Comparison between available capacity and required capacity of different numbers of machines Figure 4: Comparison between infinite capacity planning and finite capacity planning Schönsleben [14] mentioned two class techniques for scheduling and capacity management: finite and infinite loading. Both infinite loading and finite loading are important concepts in capacity planning. Based on an assumption of infinite loading, it is not necessary to alter the order due date because the equipment capacity is unlimited. When finite loading is assumed, the capacity utilization cannot exceed the upper threshold on equipment capacity, but the order due date can be changed according to the limit on the capacity of the equipment. Infinite capacity planning is suitable for the production control department. Under infinite capacity planning, the machine utilization rate can be higher than capacity, orders may have no fixed sequences but must have fixed due date. As a result, load can be estimated, serving as a reference for machine backup, machine preventive maintenance, outsourcing or overworking for both manufacturing and production control departments. Finite capacity panning is suitable for the sales department. Under finite capacity planning, the utilization rate of machine must be lower than its capacity, and orders may have no fixed sequences and due dates. Chen et al. [4] has developed an infinite capacity planning system for wafer fabrication plants. The system consists of four modules: WIP- pulling module, Lot Release Module, Workload Accumulation Module, Workload Balance Module. Jiang et al. [12] proposed Backward/Forward heuristic (FBH) approach which involves four modules which include a Capacity Resource module (CRM), Scheduling module (SM), Demand module (DM), and Production Activity Control Module (PACM). The FBH considers not just shop floor capacity constraints, but it also considers inventory and bill of material constraints, inventory stocking and replenishment levels, and order generation policies. Chen [7] developed an integrated system for capacity planning in weapon production factory based on capabilities and capacity constraints. The system presented a production planning and scheduling framework. The Backward/Forward Heuristic (BFH) method is used to integrate manufacturing, planning, and control. It is capable of producing accurately and rapidly up-to-date information necessary for decision-making under a collaborative planning logic, where all relevant activities are triggered by customers demands and coordinated. On the other hand, that is integrating backward finite loadings and minimum routing yield best performance in both mean absolute deviation (MAD) and standard deviation of machine utilization for delayed orders. Wortman et al. [16] sorted and demonstrated concepts utilized in capacity planning softwares, including rough cut capacity planning, capacity requirement planning, workload leveling, Input/output planning as well as scheduling. They compared the sensitivity of each type of capacity planning method and pointed out the interaction between planners and capacity planning. They found out that planners influence the effectiveness of planning to a great extent. Bermon and Hood [2] presented a linear programming (LP) model for the product/volume mix problem to maximize long-term profit, assuming technical compatibility and cost preference exist among resources for each product type. Hung and Leachman [11] modulized production plan based on the characteristics of semiconductor industries: mass production, vast production quantities and large number of customers, through Linear Programming (LP). On the other hand, Capacitated Loading Module was proposed for the benefit of capacity usage in the wafer production process. Based on different needs for different types of products, the capacity of machines for each workstation is allocated through LP. Bard et al. [1] developed a nonlinear programming (NP) to study the capacity planning problem in the semiconductor manufacturing industry and proposed the use of simultaneous equations for approximation to improve the solution quality. Under the weapon system environment, problems of low order volume, high order variety, complex processes, and frequent changes are encountered. Therefore, it is critical to understand how to use the minimum production cost and adopt suitable capacity setting decisions to cater for the needs of demand changes. Chen et al. [5] developed a dynamic state-dependent dispatching heuristic, which dynamically uses different dispatching rules according to the state of a production system for a wafer fabrication plant with a job shop layout. Chen et al. [3] presented a mathematical model to aid an operations manager in an make-to-order (MTO) environment to select a set of potential customer orders to maximize the operational profit such that all

4 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 49 the selected orders are fulfilled by their deadline. Swaminathan [15] proposed an analysis model for the semiconductor industry, to calculate the number of machines required when facing uncertain demands. This analysis points out that it is difficult to estimate future demand for machines due to technology and product changes, long purchasing lead time, specific characteristics for production cost and demand. As the number of machines demanded is large, it is best to utilize heuristic algorithm to obtain the best policy for the most appropriate number of machines. Chou et al. [8] evaluated and determined the best capacity strategies in semiconductor manufacturing to meet the uncertain demand and unknown pricing. It was challenging to carry out capacity planning and investment in the semiconductor industry as the demand for products frequently fluctuates. Most advanced machines and process technologies are thus required. Chen et al. [6] develops a scheduling algorithm for the job shop scheduling problem with parallel machines and reentrant process. Corti et al. [8] propose a model supporting decision makers that have to verify the feasibility of DDs proposed by customers. It adopts a capacity-driven approach to compare the capacity requested by both potential and already confirmed orders with the actual level of available capacity. Specifically, it includes a procedure for robustness test helping to deal with high uncertainty about actual order pool composition, by identifying potential overload situations. Li and Tirupati [13] studied the capacity expansion issues and presented an investment model to determine optimal mix of technology and capacity choices to meet a preset service level for two product families with stochastic demands. Jiang et al., [11] discusses an optimal schedule of weapon production which was created by integrating the schedule operation model into one-stage scheduling and combining it with a mathematical programming model. For verification and evaluation of computational results, the software program implemented a mathematical programming model, concluding with a comparison of the first-come-first-served (FCFS) technique. The proposed model yielded a favorable outcome and benefits, clearly assigning schedules for labor and production, thus obtaining the total least performance indicator for tardiness cost, earliness cost, and machine group changeover cost. As problems of frequent changes and urgent demands are present in the WPS, effective capacity planning is therefore important. This research proposes a capacity planning system, programmed in Visual Basic, to provide quick responses to the changes in production. In this research, a heuristic algorithm is proposed for capacity planning. The main reason for proposing this algorithm is for the consideration of both Dynamic and Stochastic uncertainty in the WPS. This research comprises of two sections: infinite capacity and finite capacity. The first part of the research describes how the best release time is obtained through infinite capacity planning to balance the loadings of machines. The second part of the research describes how finite capacity planning is able to obtain the completion time of each order when the number of machines is known. By integrating the two sections about infinite capacity and finite capacity, order revenue, machine purchasing cost and cost of delay can be considered to maximize the profit. In the current WPS, each order is divided into several jobs according to Bill of Material, BOM, as illustrated in Figure 5. Each job includes several operations that must be processed at different workstations. Therefore, each order would be sent to different workstations. When considering the relationship of BOM hierarchy, Early Start Time can be obtained. Loading would start to accumulate within a fixed time frame between the Earliest Start Time and the Latest Start Time. When workload accumulation is completed, equipment loading can be obtained. Figure 5: Relationship among order, jobs and operations As real time operating environment for weapon system is considered in this research, precedence relationships need to be considered as well. As illustrated in Figure 6, it is necessary to ensure if the processing steps are parallel assembly line when calculating the latest release time (LRT) of each processing step. As shown in Figure 6, processing step 6 cannot be started until both processing step1~3 and processing step 4~5 are completed. Analyzing the completion time of both step 1~3 and step 4~5, the later completion time would be the start time for processing step 6. Capacity Planning System (CPS) can be divided into different modules according to different functions. Infinite capacity planning system comprises of: (1) Release module and (2) Workload

5 50 International Journal of Electronic Business Management, Vol. 9, No. 1 (2011) Accumulation Module. Whereas finite capacity planning system consists of: (1) Order selection and Priority Setting Module, (2) Release module, (3) Workload Accumulation Module and (4) Workload Balance Module. Fig (7) and Fig (8) are the flow diagram of infinite capacity planning system and the flow diagram of finite capacity planning, respectively. Notations used in this research are summarized in Table 1. Figure 6: Precedence relationships Table 1: Notation list j: job s: processing step o: order p: products,p = 1,, P t: time,t = 1,, T Op: Total occurrence of p in processing steps ART: Adjusted release time The cycle time in which product p CTp (s1, s2): moves from processing step s1 to processing step s2 DueDate (o): Due date o of order o L E (s): Loading of type E machines in processing step s LRT: Latest release time LOT o : Lot number in order ORT (o): Remaining time PTp (s): Processing time of product p in processing step s PST (s): Planned order start time in processing step s RCTp (s): Remaining cycle time of product p in processing step s SCTp (s): Cycle time of product p in processing step s Slack (o): Slack of order o SPTp (s): Production time of product p in processing step s TLt: Total estimated workload, with t as the release time of the equipment can thus be accumulated in the appropriate time bucket. In this study, SCT is estimated from the real factory s historical data. RCTp(s) means the product s remaining cycle time of operation s by summing the SCT from operation step s to the final step in the manufacturing of product p. The cycle time between operation step s1 and operation s2, CTp(s1, s2), is the difference between RCTp(s1) and RCTp(s2), where the step s1 precedes step s2 for product p. In the flow diagram, the order with the earliest due date (EDD) will be first selected. The release time of each order is calculated by Release Module considering the due date of orders and the capacity and capability of each machine. The objective of selecting order release time is to balance the loading of machines in each period under the condition that orders are not overdue, i.e. to prevent surplus or deficit of load. Workload Accumulation Module calculates the planned start time of the remaining process based on processing steps and step cycle time, serving as a reference for future workload accumulation. Figure 7: Flow diagram for infinite capacity planning system The step cycle time of product p in operation step s, represented as SCTp(s), including processing time, waiting and transportation time. The step cycle time is importantly involved in capacity planning system as it can be used to determine the WIP s arrival time and departure time. The required capacity

6 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 51 Figure 8: Flow diagram for finite capacity planning system 3.1 Infinite Capacity Planning Algorithm The objectives of infinite capacity planning algorithm is to calculate the quantity of machine shortage and LRT. On the other hand, as the actual relationship of BOM hierarchy needs to be considered, it would be beneficial to know the earliest start time. Meanwhile, workload starts to accumulate from the latest start time to earliest start time. After this part is completed, information about the shortage of machine would be obtained based on the amount of accumulated load. In deciding the release time, backward and forward scheduling are usually applied. Therefore, the core of the algorithm developed in this research is based on the concept of backward and forward scheduling. Through backward scheduling, if planned start time for the operation in the first workstation in the process is no later than the time now, it is applicable, as shown in the upper section of Figure 9. On the other hand, if the planned start time has already exceed the time now, forward scheduling would be adopted to determine the completion time of the operation in the last workstation in the process instead. This is shown in the lower section of Figure 9. However, if due date still cannot be met, increasing the number of machines to increase the capacity or delaying the due date would be considered. Figure 10 illustrates the concept of release time. If there is a need to release order A, latest release time t is obtained through backward scheduling. If t is the release time for order A, some machines would be overloaded in the future. This can be estimated by workload pre- accumulation. Therefore, release time is set earlier and the loading of machines in the future would be estimated through workload pre-accumulation again As the diagram shows, release at t-1 would be more appropriate than to release at t. However, the release time can again be set earlier to check if it is an even better release time based on the same concept. Then, the same procedure goes on until the adjust release time, Adjust Release Time (ART) is determined. 3.2 Order Release Module The algorithm for order release module is developed based on the concepts of Backward Scheduling and line balancing. As early release would lead to excess work in process and increased waiting time in each workstation, the latest release time decided by backward scheduling and product cycle time can be chosen instead. However, some problems would occur if the release time is too late. Problems include imbalance production line, overloading of machine, loading imbalance, etc. Therefore, instead of the latest release time, an earlier date can be chosen as long as the chosen date is not before the earliest release time, then workload pre-accumulation is utilized to decide on the best release time. Figure 9: Concept diagram of backward and forward scheduling The concepts of release module algorithm are illustrated as follows: Firstly, release module algorithm determines the latest release time for order o, and obtains the earliest release time from BOM. Next, the start time of each processing step can be decided. Meanwhile, the steps are assessed to see if they are parallel assembly lines and loading would be estimated by workload estimation. When all the processing steps are completed, the release time with the minimum loading would be utilized as ART. Then, Workload Accumulation Module would be introduced.

7 52 International Journal of Electronic Business Management, Vol. 9, No. 1 (2011) Figure 10: Diagram showing different release time Algorithm for release module is illustrated as follows: Step1 Calculate LRT of order o using Equation (1) Set t = LRT. LRT DD o RCT p (1) Step2 s = 1. Step3 If s <= Op, proceeds to Step4. If not, proceeds to Step5. Step4 Calculate start time of processing steps. If s precedence is a step of parallel assembly line, PST ( s) Max{ PST( s') CTp ( s', s)} Else PST( s) PST( s ) CTp ( s', s) CT ( s', s) RCT ( s') RCT ( s) (2) p S k s p RCT p ( s) SCT p ( k) s no parallel assembly line (3) RCTp ( s) MaxSCTp ( k) s successor includes Steps of parallel assembly line (4) Read L E (s)(pst(s)) TL t = TL t + L E (s) (PST(s)) (5) s = s + 1, proceed to Step3 Step5 If t >1 t t 1, proceeds to Step2 Else Go to Step6 p Step6 ART = arg Min t TL t, choosing release time with the minimum loading to be the ARM, determining ART, and returning to infinite capacity planning system. 3.3 Workload Accumulation Module The cycle time of each processing steps or the Flow Time decides the time in which work in process reach machines. The time of arrival can be useful information for workload accumulation. Figure 11 illustrates the concept of workload accumulation of parallel machines in order o. In this section, estimation for remaining cycle time discovers that all operations are completed before due date, i.e. no delay. This outcome is achieved by shifting loadings to the parallel machines. In Workload Accumulation Module, the planned start time of the remaining processing steps can be calculated based on the cycle time of processing steps. This can be used as a reference for workload accumulation of the parallel machines. If the precedence of current accumulated processes is parallel assembly line, its PST can be decided by Equation (6). PSTo ( s) Max{ PSTo ( s' ) CTp ( s', s)}, s precedence is a step of parallel assembly line, s precedence for step s (6) The precedence of s is parallel assembly line, i.e. it is the precedence for step s from step s.

8 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 53 Figure 11: Diagram of workload accumulation In the concept of workload accumulation, accumulation starts from the latest start time to the earliest start time. If more loading needs to be accumulated, accumulation would be carried out without considering the upper limit. The concept of workload accumulation algorithm can be summarized into steps. Firstly, start time of processing steps is calculated. After processed machines are determined, workload accumulation for machines would be performed and equipment loading would be recalculated. When all the processing steps are completed, workload accumulation is said to be finished. Algorithm for workload accumulation module is illustrated as follows: Step1 Calculate PST(s) of chosen processing Step5. L E(s) (PST(s)) = L E(s) (PST(s))+PT p (s)*(lot o ) (7) Step2 Perform workload accumulation for each machine. When machines for processing are determined, workload accumulation for machines in order o would be performed and equipment loading would be recalculated. Step3 Analyze if all the processing steps are completed. If any step is not completed, proceed to Step1. In contrast, return to CPS. If s < Op s= s + 1, proceeds to Step1. Else Return to infinite capacity planning system 3.4 Finite Capacity Planning Algorithm The objective of finite capacity planning algorithm is to calculate the completion time of each order. In this section, the concept of finite capacity is to set the upper limit of load for each machine. The upper limit of load for each machine should not exceed the load capacity of that particular machine by 100%. When the upper limit of loads is reached, the excess workload would have to be accumulated for other time periods. While deciding on the priorities of orders, workload starts to accumulate for the succeeding orders. After the priority of orders has been determined, release and workload accumulation are carried out. In addition, workload balancing is included in the algorithm, to balance the machine utilization rate in each planned time period. 3.5 Order Selection and Priority Setting Module In finite capacity planning, order selection and priority setting module sets the priorities for order selection. The expected target of this module is the maximization of on-time delivery. Slack time of each order is calculated through order analysis module. Based on the slack time of each order, priorities for orders are set. In order to meet the due date of orders, the priorities for order selection needs to be set. This is done by subtracting the remaining process time from the time difference between Time Now and the planned due date. The smaller the Slack(o), the nearer the due date. This is to say, an order with a smaller slack should be given priority over an order with a larger slack. The algorithm for order selection and priority setting module is as follows: Step1 o = 1. Step2 Calculate remaining cycle time, RCT (o). Step3 Slack (o) of order o. Slack (o) = Due Date(o) Time Now ORT(o) (8) Step4 If o < O o o + 1, go to Step2. If not, go to Step5. Step5 Based on the size of slack, set the priorities for orders and return to finite capacity planning system.

9 54 International Journal of Electronic Business Management, Vol. 9, No. 1 (2011) 3.6 Workload Balance Module After orders are selected, Release Module and Workload Accumulation Module are performed. The way Release Module and Workload Accumulation Module perform is similar to the way infinite capacity planning is carried out. Therefore, this section would not describe how Release Module and Workload Accumulation Module are performed in detail. In the Workload Balance Module, capacity constraint must be considered. If the capacity requirement of a machine exceeds its capacity by 100%, the release time should be adjusted. As a result, orders might become overdue. In order to improve the condition of high average machine utilization, workload balancing is critical to balance the average machine utilization. In the perspective of loading, idle capacity should be filled to solve the problem of machine overload. Figure 12 illustrates a case about workload balancing. As the result of workload accumulation shows, the capacity requires at day 1 and day t-1 exceeds the machine utilization by 100%. The capacity requirements of these two time periods can be pre-stacked in each day and the machine workload of each day can be assessed. The result of assessment shows that the machine utilization is the smallest at both day 4 and day t. Therefore, the excess workload can be shifted to day 4 and day t. This case shows that workload accumulation can be used to achieve workload balance on each day. Figure 12: Diagram of workload balance 4. RESULTS AND DISCUSSION 4.1 An Illustrative Example In this research, heuristic algorithm and Visual Basic were used to solve the problem. Based on the concept of capacity loading, capacity of each machine is studied. Assuming that the workload of machines per day is 8 hours and number of orders waiting to be handled is 2. The two orders are order A and order B, respectively. Order A has 26 processes and order B has 76 processes. Capacity planning is carried out for 11 machines. There are 7 types of machine, consisting of two type1 machine, two type 3 machine, three type 6 machine and one type,2, 4,5 and 7 machine. BOM shown in Figure 13 illustrates that, through scheduling, job with the earliest due date would be given first priority and an appropriate release time would be chosen for workload accumulation. In choosing the most appropriate release time, two scenarios would be considered. One scenario emphasizes on forward scheduling, obtaining the latest release time and performing workload accumulation. If any machine is overloaded, the release time would have to be adjusted. Then second scenario is considered. Workload accumulation is to be carried out and a time between the time frame of earliest release time and latest release time is chosen as the ART. Figure 13: Bill of materials (BOM) of order 4.2 Results This research carried out capacity planning for two product orders. The result of Infinite capacity planning is shown in table 2 below. LRT is executed to simulate current practice at the weapon production factory. For LRT, there are eleven days in which the capacity requirement exceeds the capacity and the amount of overload is 146 hours. For ART, there are four days in which the capacity requirement exceeds the capacity and the amount of overload is 40 hours. It shows that utilizing ART yields a better outcome than utilizing LRT. This demonstrates that the consideration of machine loading for different time buckets can effectively balance the machine workload on different time buckets. Table 2: Statistics about workload Days in which Amount of capacity requirement overload (hours) exceeds capacity LRT ART 4 40 The outcome of finite capacity is shown in table 3. If machines remain unchanged, order A and order B would both overdue 4 days and 3 days

10 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 55 separately. According to the result of infinite capacity planning, 100% on-time delivery is reached if one additional one type two machines and additional two type six machines are purchased. These results of performance for decision alternatives show that infinite capacity planning can determine the number of machines to be purchased and finite capacity planning can effectively calculate the days of delay for each order. The results can help managers to decide the number of machines to purchase by considering the machine cost and delay penalty in military orders. Based on the two decision alternatives for finite capacity planning, on-time delivery might be raised by adding the right number of machines. On the other hand, keeping the number of machine unchanged might lead to high delay cost for orders. Therefore, this research attempts to achieve a balance from the two alternatives through the newly proposed capacity planning system, in order to maximize total revenue. Table 3: Performance for decision alternatives Types of Days of On-time Decision alternatives order delay delivery Machines remain Order A 4 0% unchanged Order B 3 0% Adding one type two Order A 0 100% machine and two type six machines Order B 0 100% 5. CONCLUSION This research developed a dynamic technique analysis module to solve the problems of low order volume, high order variety, complex processes, uncertain order and frequent changes in the WPS environment. Based on the requirement of each plan and capacity, dynamic technique analysis is performed to assess capacity allocation and capacity loading. In addition, evaluation of resource integration and workload balancing are performed to allocate resources effectively in order to avoid double investment and uneven allocation of workload. As a result, overall performance would be enhanced. This research consists of two sections: (1) infinite capacity and (2) finite capacity. In the first section about infinite capacity planning, the best release time is determined and the number of machines to be added is decided. In the second part about finite capacity planning, the completion time of each order is calculated. Capacity planning module is developed through Visual Basic in this research. This module enables WPS to be simulated when demand fluctuates. As a result, R&D phase can be shortened, R&D costs can be reduced, and R&D quality can be enhanced. In addition, related information is feedback to the production system for the benefit of the adjustment and integration of the system. This way, the overall performance of R&D and management mechanism can be enhanced. Weapon production mechanism can be effectively managed and control to significantly enhance the overall production performance. Through capacity planning module, unit capacity can be effectively managed and number of machines required can be quickly calculated. As a result, best release time can be calculated and rescheduling can be performed to integrate resources as well as to allocate dynamic resources instantly to achieve optimization for capacity planning. ACKNOWLEDGMENTS This paper was supported in part by the Chung-Shan Institute of Science and Technology of Taiwan, R.O.C., under contract XR96403P803PE. REFERENCES 1. Bard, J. F., Srinivasan, K. and Tirupati, D., 1999, An optimization approach to capacity expansion in semiconductor manufacturing facilities, International Journal of Production Research, Vol. 37, No. 15, pp Bermon, S. and Hood, S. J., 1999, Capacity optimization planning system, Interfaces, Vol. 29 No. 5, pp Chen, C. S., Mestry, S., Damodaran, P. and Wang, C., 2009, The capacity planning problem in make-to-order enterprises, Mathematical and Computer Modelling, Vol. 50, pp Chen, J. C., Chen, C. W., Lin C. J. and Rau, H., 2005, Capacity planning with capability for multiple semiconductor manufacturing fabs, International Journal of Computers and Industrial Engineering, Vol. 48, No. 4, pp Chen J. C., Chen C. W., Dai, J. Y. and Tyan, J. C., 2004, Dynamic state-dependent dispatching for wafer fab, International Journal of Production Research, Vol. 42, No. 21, pp Chen, J. C., Chen, K. H., Wu, J. J. and Chen, C. W., 2008, A study of the flexible job shop scheduling problem with parallel machines and reentrant process, International Journal Advanced Manufacturing Technology, Vol. 39, No. 3-4, pp Chen, K. H., 2006, A study on the integrated operation scheduling for weapon production systems, Department of Industrial Engineering, Chung-Yuan Christian University, Ph. D Dissertation. 8. Chou, Y. C., Cheng, C. T., Yang, F. C. and Liang, Y. Y., 2007, Evaluating alternative capacity strategies in semiconductor

11 56 International Journal of Electronic Business Management, Vol. 9, No. 1 (2011) manufacturing under uncertain demand and price scenarios, International Journal of Production Economics, Vol. 105, No. 2, pp Corti, D., Pozzetti, A. and Zorzini, M., 2006, A capacity-driven approach to establish reliable due dates in a MTO environment, International Journal of Production Economics, Vol. 104, pp Hung, Y. F. and Leachman, R. C., 1996, A production planning methodology for semiconductor manufacturing based on iterative simulation and linear programming calculations, IEEE Transactions on Semiconductor Manufacturing, Vol. 9, No. 2, pp Jiang, J. C., Chen, K. H. and Wee, H. M., 2008, A dynamic scheduling model of parallel-machine group for weapon production, International Journal of Advanced Manufacturing Technology, Vol. 36, No , pp Jiang, J. C., Chen, K. H., Wee, H. M., Lin, C. H. and Hsieh, H. H., 2006, Development of a heuristic production planning framework base on forward/backward approach, Proceeding of Society of Manufacturing Engineers, pp Li, S. and Tirupati, D., 1995, Technology choice with stochastic demands and dynamic capacity allocation: A two-product analysis, Journal of Operations Management, Vol. 12, No.3-4, pp Schönsleben, P., 2003, Integral logistics management: Planning & control of comprehensive business processes, St. Lucie Press, Boca Raton, London. 15. Swaminathan, J. M., 2000, Tool capacity planning for semiconductor fabrication facilities under demand uncertainty, European Journal of Operational Research, Vol. 120, No. 3, pp Wortman, J. C., Euwe, M. J., Taal, M. and Wiers, V. C. S., 1996, A review of capacity planning techniques within standard software package, Production Planning and Control, Vol. 7, No. 2, pp ABOUT THE AUTHORS James C. Chen is a Professor in the Department of Industrial Management at National Taiwan University of Science and Technology, Taiwan. Prior to his current position, he was Professor in the Department of Industrial and Systems Engineering at Chung Yuan Christian University and a researcher at Industrial Technology Research Institute, Taiwan. He received a B.S. in Industrial Engineering from National Tsing-Hua University, Taiwan, an M.S. in Manufacturing Systems Engineering, and a Ph.D. in Industrial Engineering, both from the University of Wisconsin- Madison. He has published academic articles in European Journal of Operational Research, International Journal of Production Research, International Journal of Management Science (Omega), Computers and Industrial Engineering, Production Planning and Control, and International Journal of Advanced Manufacturing Technology. Dr. Chen has been working on several projects with wafer fabs, IC packaging plants, IC final test plants, and TFT-LCD fabs in Taiwan. His current research interests include capacity planning and state-dependent scheduling. Dr. Chen was awarded IBM Manufacturing Research Graduate Fellowship Kou-Huang Chen is an Assistant Professor in the Department of Industrial Engineering and Management, China University of Science and Technology. He received his Ph.D. degree in Industrial Engineering, at Chung-Yuan Christian University in His current research and teaching interests are in the general area of Project Management and International Quality Management. In particular, he is interested in Manufacturing Planning System, Supply Chain Management, Advanced Planning and Scheduling. Chien-Hsin Lin is a Ph.D candidate of Industrial Engineering and Systems Engineering, Chung-Yuan Christian University. Also, he is a senior specialist in Chemical Systems Research Division, Chung-Shan Institute of Science & Technology, Armaments Bureau, M.N.D. His research interests are Simulation, Planning and Scheduling. Chia-Wen Chen is a post doctoral in the Department of Industrial and Information Management, National Cheng Kung University. She received her Ph.D. degree in Industrial Engineering, at Chung-Yuan Christian University in Her current research interests are in the general area of Simulation, Planning and Scheduling. In particular, she is interested in Supply Chain Management, Advanced Planning and Scheduling. Chia-Lin Yang received his MS degree from Industrial Engineering, at Chung-Yuan Christian University in His research interests are Simulation, Planning and Scheduling. (Received November 2009, revised January 2010, accepted March 2010)

12 J. C. Chen et al.: A Study of a Heuristic Capacity Planning Algorithm for Weapon Production System 57 以 啟 發 式 演 算 法 運 用 於 武 器 生 產 系 統 產 能 規 劃 之 研 究 陳 建 良 1 陳 國 晃 2* 林 建 鑫 3,5 陳 佳 雯 4 5 楊 家 霖 1 台 灣 科 技 大 學 工 業 管 理 系 所 台 北 市 大 安 區 基 隆 路 4 段 43 號 2 中 華 科 技 大 學 工 業 工 程 與 管 理 系 台 北 市 南 港 區 研 究 院 路 三 段 245 號 3 軍 備 局 中 山 科 學 研 究 院 第 四 研 究 所 桃 園 縣 龍 潭 鄉 佳 安 村 6 鄰 中 正 路 佳 安 段 481 號 4 成 功 大 學 工 業 與 資 訊 管 理 學 系 台 南 市 大 學 路 1 號 5 中 原 大 學 工 業 與 系 統 工 程 學 系 桃 園 縣 中 壢 市 中 北 路 200 號 摘 要 本 研 究 發 展 一 產 能 規 劃 啟 發 式 演 算 法, 以 因 應 少 量 多 樣 製 程 複 雜 且 設 計 變 動 頻 繁 及 不 確 定 訂 單 之 武 器 生 產 系 統 作 業 環 境, 其 功 能 具 有 分 配 訂 單 至 各 生 產 資 源 決 定 各 訂 單 最 適 之 投 料 時 點 以 及 評 估 工 廠 所 有 機 具 設 備 之 預 期 負 荷 等 因 此, 工 廠 管 理 者 可 以 針 對 產 能 不 足 之 瓶 頸 機 具 採 取 行 動, 進 而 修 正 生 產 計 畫 本 演 算 法 程 式 建 構 於 Microsoft Visual Basic 上, 並 以 實 際 武 器 生 產 工 廠 所 獲 數 據 進 行 模 擬 評 估 此 程 式 之 效 果 及 效 率, 模 擬 結 果 優 於 現 行 手 動 作 業 方 式, 並 已 成 功 應 用 於 武 器 生 產 系 統 之 產 能 規 劃 關 鍵 詞 : 武 器 生 產 系 統 啟 發 式 演 算 法 產 能 規 劃 (* 聯 絡 人 :[email protected])