EFFECT OF ACTIVITY SCHEDULINGS AND INVENTORY CONTROL: AN EXPERIMENTAL INVESTIGATION FOR PC ASSEMBLY

282 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3, pp. 282-294 (2003) EFFECT OF ACTIVITY SCHEDULINGS AND INVENTORY CONTROL: AN EXPERIMENTAL INVESTIGATION FOR PC ASSEMBLY Abhyuday A. Desai and Yung-Nien Yang * Department of Industrial Engineering Texas Tech University, Lubbock, TX 79409, USA Hamid R. Parsaei Department of Industrial Engineering University of Houston, Houston ABSTRACT This paper investigates three scheduling algorithms and three inventory control policies to evaluate their effect on the system performance measures using computer simulation. The model chosen is a flow-shop type, computer assembly plant. Analysis is conducted on two scheduling measures (summation of process time and tardiness) and two inventory control measures (ordering cost and holding cost). The scheduling algorithms used are Shortest Processing Time, Genetic Algorithm and Simulated Annealing. The aim of the applied algorithms was to minimize the sum of flow times. Since it is known that SPT minimizes sum of flow times, it provides a benchmark for comparing the efficiency of genetic algorithm and simulated annealing search methods. EOQ, MRP and JIT are used as inventory control methods. An experimental design for the comparison is presented to evaluate which combination of control methods produces the best results under the designed scenario. Keywords: genetic algorithms, simulated annealing, economic ordering quantity, material requirement planning, just-in-time 1. INTRODUCTION At present, various inventory control algorithms are applied in industry. Choice of an inventory control method affects the system performance measures such as the ordering cost, holding cost and shortage cost. Manufacturers choose methods depending upon their manufacturing model. For example, make-by-order assembly plants choose the Just-in-Time technique for controlling plant inventory. Another aspect of manufacturing is the choice of the scheduling method. Scheduling problems are known to be NP-hard. As a result, the correct choice of the scheduling method is a major factor that decides the performance of the plant. Factors such as the utilization of the plant facility, make span and tardiness are depending on the scheduling method employed. Various approaches have been used to solve scheduling problems. Heuristics have been an important tool used since the problem is NP-hard. These approaches aim to find the near-optimal solution in real time. Based upon local research, some modern heuristic techniques for combinatorial problems have been successfully used for scheduling problems, in recent years, including Simulated Annealing and Genetic Algorithms. Inventory control and scheduling are the most important aspects in the current production environment, especially in this networked era. Improvement of communication cannot prevent mistakes from inventory or scheduling but shorten the chance to make corrections. Therefore, the study of interaction between these two factors is a vital issue for traditional and virtual manufacturing environments. Also, the ready information in virtual manufacturing environments makes the integrated consideration possible and reasonable. This paper studies this interaction between the inventory control method and the scheduling technique employed. 2. LITERATURE REVIEW 2.1 Inventory Control Methods The traditional methods of inventory control use EOQ models. However, the basic EOQ model * Corresponding author: yung-nien.yang@coe.ttu.edu

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 283 was based on the assumption that demand is constant, no shortage is considered and the lead-time is zero or constant. These assumptions are not faced in real life applications. The EOQ model does not take into consideration the demand pattern of the end product before determining the inventory levels of parts and materials. This is another major shortcoming of this model. The Material Requirement Planning (MRP) model determines the demand of a product using orders obtained from the sales department. Inventory levels are then calculated using these figures and the cost inputs from the purchasing department. It is basically a push-type inventory control system. The other popular model is the just-in-time model (JIT) that is a pull type of inventory control. This model takes into consideration various uncertainties in the industry such as machine failures, demand fluctuations, stochastic set-up times, and random yields. 2.1.1 Economic Ordering Quantity (EOQ) The EOQ model is the basic model for inventory control in production companies. It is very simple to execute, however, it is based on unrealistic assumptions. The demand is assumed to be constant. Such unrealistic assumptions make EOQ not very attractive in current industrial settings. Besides the basic model, there are many extensions to the simple EOQ models. For example, Reorder lead-time, allowing a lead-time between placing an order and receiving it, this introduces the problem of when to reorder (typically at some stock level called the reorder level); Stockouts, allowing stockouts (often called shortages) i.e. no stock currently available to meet orders. Often replenishment is not received all at once. It is the EPQ (economic production quantity) extension. For example, if the replenishment comes from another part of the same factory then items may be received as they are produced; Buffer (safety) stock, some stock kept back to be used only when necessary to prevent stockouts; and Probabilistic demand, instead of a constant depletion (demand) for stock, allow probability distributions [1]. 2.1.2 Just-in-Time (JIT) System Just-in-time system, which is a pull-type inventory control system, is one of the most popular new technologies adopted. It originally referred to the production of goods to meet customer demand exactly, in time, quality and quantity, whether the customer is the final purchaser of the product or another process further along the production line. It has now come to mean producing with minimum waste. Waste is taken in its most general sense and includes time and resources as well as materials [9]. Most research efforts to date have focused on descriptions of JIT philosophy. There were conceptual and experimental studies, mathematical models and simulations in many cases. Golhar and Stamm [7] presented a complete review of JIT systems. These research efforts indicate that the JIT technique is a highly effective method for controlling the flow of inventory on shop floors as it reduces the inventory level to a bare minimum and thus reduces production costs. 2.1.3 Material Requirement Planning (MRP) MRP is a set of procedures for converting forecast demand for a manufactured product into a schedule for obtaining components, subassemblies, and raw materials. The purpose of MRP, from a logistics viewpoint, is to avoid, as much as possible, carrying these items in inventory. The MRP approach emphasizes on a realistic master production schedule (MPS) to coordinate the production stages in terms of volume of production that prevents the creation of extraordinary intrastage slack. MRP also stresses on calculating dependent demand and prevents the creation of superfluous interstage slack due to unbalanced lot sizing of matched set of parts. The only safety stocks, which are allowed in such an approach, are stocks at the MPS level. MRP decides the following two factors: timing (when to order) and quantity (how much to order). With respect to the timing decision orders are made as late as possible, but never allowing a stockout. This is a driving principle in MRP, never order before one needs to, never allow to stockout [11]. Thus MRP effectively reduces the cost of production by minimizing the inventory levels. 2.2 Scheduling Methods The traditional methods of scheduling the jobshop production used heuristics. The most commonly used scheduling algorithms were: Shortest Processing Time (SPT), Earliest Due Date (EDD), Most Remaining Operations (MRO), Truncated SPT (TSPT), etc. However these algorithms consider the static nature of the job-shop. This limitation led to the development of new heuristic approaches like the simulated annealing. In actual fact, the simulated annealing is a variation of hill climbing. Genetic algorithms are also being studied since they can provide the basis for the tool that provides optimal schedules in near real-time. Genetic algorithms use a binary representation scheme for coding job schedules into chromosomes. These chromosomes are then reproduced, followed by crossover and then

284 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) mutation to search for optimal solutions. The efficiency of the genetic algorithms is found to be very high. 2.2.1 Genetic Algorithm The application of genetic algorithm (GA) to scheduling problems has interested many researchers as GA's seem to offer the ability to cope with the difficult search spaces involved in optimizing schedules, and have been applied to other combinatorial problems such as the traveling salesman problem with some success [13]. Biegel and Davern [2] described applications of GA to the job shop-scheduling (JSS) problem. They provided an elementary n-task, one processor (machine) problem to demonstrate the GA methodology in the JSS problem arena. Lee and Kim [10] developed a parallel genetic algorithm for a job-scheduling problem on a single machine. The objective of the scheduling was to minimize the total weighted earliness and tardiness penalties from a common due date. A binary represented scheme was employed for coding job schedules into chromosomes. Parallel sub-populations were constructed by considering only jobs that can be processed first in the schedule. The efficiency of the parallel genetic algorithm was illustrated to be considerably high [6]. 2.2.2 Shortest Processing Time The SPT is the simplest heuristic scheduling method. It selects the job, which has the shortest processing time, to be processed first. In the single machine environment with ready time at 0 for all jobs, this algorithm is optimal in minimizing the mean flow time, the mean number of jobs in the system, the mean waiting time of the jobs, the maximum waiting time, and the mean lateness and mean flow time. Other heuristic methods have also been successfully employed based on the similar principle. 2.2.3 Simulated Annealing Simulated annealing (SA) has been successfully used for job-shop scheduling in recent years. It simulates the annealing procedure used in metallurgy. Catoni devised a simulated annealing procedure to deal with a large variety of scheduling problems [3]. He concluded that simulated annealing is very efficient for solving job-shop problems. Chang and Hsu [4] described a heuristic method based on the simulated annealing (SA) approach, to solve parallel processor scheduling problems. The jobs to be scheduled on parallel processors had dependence relationships and the goal was to minimize the make span. They studied various parameter settings, such as the initial schedule, perturbation scheme and annealing schedule in SA approach, and their effect on the performance measure (i.e., the make span). They compared the SA approach to the traditional heuristic methods such as the longest processing time first (LPT), and the critical path first (CP) procedures. The experimental results showed that the SA approach performed much better than heuristic approaches and provided very competitive solutions when compared to optimal solutions generated from the Branch and Bound approach. 2.3 Inventory Control and Scheduling Rule Selection It is known that the inventory and scheduling control are both important topics and the interaction between them should be studied in order to have efficient integration in manufacturing. Recently, He and Kusiak [8] carried out a study of production planning and scheduling in a virtual manufacturing set-up. The problem encountered was of assigning tasks to each partner company in the virtual corporation and scheduling the production based on the strength of each of them. The solution developed was found to be useful in design and scheduling of products by suggesting appropriate product structures. The choice of inventory control technique in our study was based on factors such as usage, simplicity, etc. It can be seen that EOQ is the most basic model used for inventory control. Though it is not feasible and advisable for complex systems, it is the most fundamental inventory control policy and many complex heuristic models are modified models of EOQ policy. MRP and JIT are very useful in minimizing inventory levels in industries. Most of the current research is also focused on these two control policies as can be seen from the literature review. Hence the three inventory control policies have been selected for evaluation in this study. An analysis of job shop performance for different scheduling rules was evaluated using computer simulation by Randhawa and Zeng [12]. They used fourteen different scheduling rules and six performance measures in the analysis. According to the study, the simple operation-time-based rules produced the best combination of results for the performance measures evaluated. Therefore, besides the extension and interaction of inventory control policies, the scheduling rules selected in this study for evaluation, are also based on operation times and not on other factors such as due dates or priority. However, the performance of other factors, such as due dates, was compared to evaluate whether any effect was brought over due to interaction of scheduling and inventory control techniques.

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 285 The performance measure selected for this study was summation of flow times. SPT minimizes the average flow time. Since it provides a benchmark for comparison with other search algorithms, it was selected as a scheduling algorithm. Simulated annealing is arguably the best heuristic method currently available. Genetic algorithms are fast becoming popular in scheduling algorithms. Therefore these three scheduling control algorithms are selected for analysis. Both genetic algorithm and simulated annealing algorithm were developed such as to minimize the average flow time. Thus all three algorithms aim at obtaining scheduling with the minimum average flow time. The effects of using these inventory control and scheduling algorithms is presented later in the paper. For study purpose, a flow-shop computer assembly plant is being used for simulation. The study model is presented in the next section. 3. STUDY MODEL The model being studied in this paper is a PC assembly type flow-shop layout. The plant assembles 3 PC models. One production line with seven workstations is used to assemble all three models. The product models pass through workstations sequentially in mixed product bases. Those models are 1) Club America, 2) Compu Add, and 3) DC 486. The Club America model requires 26 assembly operations and the total assembly time is 11.253 minutes. Workstation 6 requires the longest time for assembly, with the time required being 2.089 minutes. Considering an eight-hour shift, i.e. 480 minutes of production time, available daily, total number of units produced per day is 230 units. The Compu Add model requires 27 assembly operations. Total assembly time is 13.797 minutes. Workstation 3 has major assembly work, which requires 3.085 minutes. The total number of units that can be produced per day is 156 units. The DC 486 model requires 24 assembly operations and workstation 2 requires 3.30 minutes for assembly. Hence the total number of DC 486 models that can be produced are 145 units. Figure 1 shows the operation tasks and assignments to workstations of the first product model Club America. Based on the above factory model, a single production line with three product models are mixed produced in the same line, with three-production scenarios were selected. The scenarios are high production rate (or market demand) as 92 % of the production capacity, medium production rate as 75 % of the production capacity, and low production as 55 % of the production capacity. These flow-shop assembly operations were simulated over a six-month period horizon and three types of product orders were randomly fed into the system to study the inventory and scheduling control changes. As described in section 2.3, three inventory control methods and three scheduling control algorithms were selected. The studied model is P = f D, I, S,) (1) i ( j k l P is performance index and i is from 1 to 4 which represents: ordering cost, inventory cost, tardiness, and sum of flow times. D is demand rate and j is from 1 to 3, which represents: high demand (92 % of capacity), medium demand (75 % of capacity), and low demand (55 % of capacity). I is inventory control method and k is from 1 to 3, which represents: EOQ, MRP, and JIT. S is scheduling algorithm and l is from 1 to 3, which represents: SPT, GA, and SA. The purpose is to determine which inventory control combined with a particular scheduling technique gives a better result. The definitions of performance indexes are shown in Table 1 as well as a few assumptions that were made in this simulation. 4. DESCRIPTION OF SCHEDULING ALGORITHMS 4.1 Shortest Processing Time Shortest processing time (SPT) schedule arranges orders in the ascending order of processing times. It is used to minimize the average completion time, average lateness, average waiting time, and average flow time. The following example is provided to explain its working: Example: Job# J1 J2 J3 J4 J5 J6 Processing time 7 3 5 9 4 2 The SPT algorithm will result in the following sequence: J6 J2 J5 J3 J1 J4 4.2 Genetic Algorithm Genetic algorithms simulate the process of information transfer in natural organisms. Information is transferred through chromosomes in natural systems. Nature reproduces only those streams of chromosomes that it deems best for the survival of the organism. Mixing this reproduced stream, referred to as a cross over, then produces new streams. Some of these streams are better than the original streams from which they were produced. These better streams survive and inferior streams perish. This process of generating superior quality organisms, which are better suited for survival, is well suited for solving combinatorial optimization problems such as job shop scheduling.

286 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) Operation tasks Op. No. Operation No. of units Time (m sec) 1 Load upper case 1(upper case) 89 2 Assemble motherboard 1(motherboard) 258 3 Screw motherboard 6(m.b screws) 195 4 Insert fan cable 1(fan cable) 191 5 Insert RAM 8(RAM) 23 6 Assemble cable 1(cable) 311 7 Assemble network card 1(network card) 411 8 Assemble drive A 1(drive A) 119 9 Assemble hard drive 1(hard drive) 137 10 Assemble I/O 1(I/O device) 567 11 Screw drive A 1(drive A screws) 280 12 Screw hard drive 1(hard drive screws) 280 13 Assemble VDO card 1(VDO card) 296 14 Assemble drive B 1(drive B) 72 15 Assemble control card 1(control card) 267 16 Screw drive B 2(drive B screws) 180 17 Insert frontal case 1(frontal case) 685 18 Insert cable from frontal case to board 1(cable) 335 19 Assemble Power supply (PW) 1(power supply) 118 20 Insert cable from disk drives to board 1(cable) 400 21 Screw PW 4(PW screws) 194 22 Insert flat cable 1(flat cable) 400 23 Insert PW cable 1(PW cable) 731 24 Insert flat cable 1(flat cable) 400 25 Assemble outer case 1(outer case) 227 26 Screw outer case 5(outer case screws) 313 Figure 1. Operation tasks and assignments to workstations for Club America computer Table 1. Performance index definition and simulation assumptions Performance Index Definition Ordering Cost (OC) Fixed ordering cost + Variable ordering cost Fixed ordering cost = $10 per order 1 Variable ordering cost = Ordering quantity * Cost per unit 2 Holding cost (HC) Annual interest rate 3 * Inventory on hand Tardiness (TD) Sum of Flow Time (FT) Sum of Time units of delay for all delayed orders/total number of orders Sum of Completion times for all orders. Assumptions 1. Minimizing the make span for all three scheduling control algorithms 2. Components required for the assembly of the three computer models are ordered from the same vendor and so the ordering costs are the same 3. There are no breakdowns of the assembly workstations 4. The orders for the next six-month period are known before hand and there are no additional orders Note: 1 The costs of placing orders are assumed to be fixed at $10. 2 The costs of units chose were the current prices of the components in market. 3 The annual interest rate was taken as 5%.

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 287 In this study, random orders were generated with each order given a number. Given these orders, 6 new schedules were generated randomly. For each schedule, the sum of flow time value was computed and the schedules with the best values (i.e. lesser values) were mixed to produce new streams. Infeasible schedules are usually generated in this since some orders were repeated in the schedule. To bring feasibility into the schedules, orders that were repeated twice were simply replaced with orders that did not occur in the schedule. Five hundred iterations were carried out of this process of reproduction and cross over. After this, mutations were carried out and again 500 iterations were carried out. This total process of reproduction, crossover and mutation was carried out for 200 iterations. For around 60 orders, total time required to find out the near-optimal schedule was on average 4 seconds. An example is given below to illustrate the working of the genetic algorithm used in this study. Example: Suppose we have two randomly generated schedules as follows: J1 J3 J5 J2 J4 J6 J6 J1 J5 J3 J4 J2 A site for crossover is randomly selected by generating a random number. For this example, if the site was chosen as 3, then following crossover takes place. J1 J3 J5 J3 J4 J2 J6 J1 J5 J2 J4 J6 It can be seen that this produces infeasible schedules. For the first schedule, Job 3 is scheduled twice. For second schedule, Job 6 is scheduled twice. To obtain a feasible solution, procedures such as PMX, X (crossover) are available. However, a different and simplified method was used in this study. Whenever a repeated job was observed, it was replaced with a non-observed job schedule. Thus, in the first schedule, job 3 that is in the 4th position is replaced with Job 6. Similarly, in schedule 2, Job 6, which is in the 6 th position, is replaced with job 3. Thus the feasible schedules that are obtained are as follows: J1 J3 J5 J6 J4 J2 J6 J1 J5 J2 J4 J3 The sum of flow time is calculated for the new schedules, and depending upon their goodness (i.e. low sum of flow time) they are again reproduced and further crossover is carried out. Mutations are carried out after 300 such iterations. 4.3 Simulated Annealing (SA) Simulated annealing simulates the process of annealing used in metallurgy to reduce the brittleness of metals and alloys. In this process, first the solid particles are heated so that they have high energy and move freely, then they are cooled slowly so as to achieve an equilibrium state. The SA process used in this study to carry out the scheduling is as follows: First a random schedule is generated and an initial temperature is selected. A neighbor schedule is formed by making a slight difference in the random schedule. The new schedule is selected immediately if it is better than the original schedule. Otherwise it is selected with a probabilistic approach. The temperature is lowered with the process carried on until the temperature becomes zero. The best schedule obtained during all these iterations is selected as the best schedule. An example is given below: Example: Suppose we have a randomly generated schedule as follows: J1 J3 J5 J2 J4 J6 A site on the schedule is randomly selected. Say it is 3. Then, any two jobs on either side of site are switched. This produces a new schedule in the neighborhood of the original schedule. Suppose the new schedule is: J1 J4 J5 J2 J3 J6 For the new schedule, the objective function value is calculated. If this value is better than the original value, then this schedule is immediately selected as the best schedule, and the current schedule is changed to this new schedule. If the objective function for the new schedule is not better than the original schedule, then it may still be accepted as the current schedule according to the probability given by: (change in objective function/(-t)) Probability = exp where t is the simulation temperature. This method called as the Metropolis method is generally used for combinatorial problems. Thus the procedure can be summarized as follows: 1) Generate an initial schedule S. 2) Let the initial best schedule S* = S. 3) Compute the objective function value of S as f(s). 4) Compute the initial temperature T 0 5) While the stop criterion is not satisfied: a) Repeat Markov chain length (M) times: i) Select random neighbor S to the current schedule S ii) Let (f) = f(s ) f(s). iii) If (f) < 0, then: S = S If f(s) < f(s*), then S* = S iv) If (f) > 0, then: Generate a random number r from uniform(0,1) (change in objective function/(-t)) If r < exp then S = S b) Reduce temperature T. 6) Return the best schedule S*

288 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) 5. EXPERIMENT As shown in Table 1, four performance indexes were studied in this project. First, the control scenario and demand rate (D), is evaluated so that the null and alternative hypothesis are: H o : OC H = OC M = OC L H o : HC H = HC M = HC L H o : TD H = TD M = TD L H o : FT H = FT M = FT L H 1 : OC H OC M OC L H 1 : HC H HC M HC L H 1 : TD H TD M TD L H 1 : FT H FT M FT L Where the INDEX H is the mean value during the 6-month of high demand rate (such as the OC H is the mean value of 30 simulated repetitions of the total-ordering-cost in 6 month period) and so on. This can evaluate which performance index is sensitive to the demanding rate, regardless of the scheduling and inventory control method. Ninety (30 repetitions and 3 scenarios of utilization) computer simulations were performed and the performance data was collected from the simulations (shown in Table 2). Second, the statistical tests such as t-tests and f- tests were performed to evaluate the performance of scheduling and inventory policy in each scenario so that the null and alternatives hypothesis are: H o : OC EOQ = OC MRP = OC JIT H o : HC SPT&EOQ = HC SPT&MRP = HC GA&EOQ = HC GA&MRP = HC SA&EOQ = HC SA&MRP = HC JIT&SPT/GA/SA H o : TD SPT = TD GA = TD SA H o : FT SPT = FT GA = FT SA H 1 : OC EOQ OC MRP OC JIT H 1 : HC SPT&EOQ HC SPT&MRP HC GA&EOQ HC GA&MRP HC SA&EOQ HC SA&MRP HC JIT&SPT/GA/SA H 1 : TD SPT TD GA TD SA H 1 : FT SPT FT GA FT SA The results are given in the next section. 5.1 Results 5.1.1 Statistical Data Collection The following results were obtained from the study. Thirty repetitions were made. The above values given are the mean and standard deviation values obtained after 30 repetitions. For each utilization scenario, three sums of flow time values were obtained. After 30 repetitions, average of these values was found to give the average sum of flow time value for SPT, GA and SA. Thirty repetitions were performed for each utilization scenario, such as High, and. The following points are noted: i) The sum of flow time for SPT will be the same under all three inventory-control policies. The same follows for GA and SA. This is because sum of flow time does not depend on inventory control policies. The above is also true for tardiness. Hence, in the above table, only scheduling policies are mentioned under flow time and scheduling methods under tardiness. ii) The ordering cost for EOQ will be the same under all three scheduling policies. The same goes for MRP and JIT. This is because ordering cost does not depend on the schedule, but depends on inventory control policy. Therefore only the inventory control policy is mentioned under ordering cost. The modified inventory control policy, such as MRP with EOQ order quantity, will be explored in later study. iii) The holding cost will be same for JIT under all three scheduling methods. This happens because only the amount of inventory that is required to complete the order that is to be processed next is ordered. For example, say for a particular order, the amount of inventory that will be ordered to complete that order and the amount of time that inventory will stay in the system is the same whether it is scheduled first or last in the schedule. Hence the inventory cost will remain the same, although this is not true for other inventory control policies, such as MRP and EOQ. The results from the table indicate the following: 1) Mean values of flow time for SPT are lower than mean values of flow time for GA and SA. 2) Mean values of ordering cost for EOQ are lower than mean values of ordering cost for MRP that is in turn lower than JIT. 3) Mean values for holding cost for JIT are lower than that of MRP which are in turn lower than EOQ. Respect holding costs of EOQ for SPT, GA and SA do not show much difference. Mean tardiness values do not show much difference or significant pattern. 5.1.2 Scenario Analysis Comparison of Mean Values Null Hypothesis H 0 : No significant difference in mean values of high, medium, and low demand rate populations. The statistic analyses are performed to evaluate whether the differences noticed in mean values are significantly different in high demand (92 % of capacity), medium demand (75 % of capacity), and low demand (55 % of capacity). In order to compare the different scenario, the values are normalized by the utilization values (i.e. 0.92, 0.75 and 0.55 respectively) for the respective utilization types. The normalized performance values are shown in Table 2- b.

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 289 Table 2. Performance index data FT Average SPT m: 3235.00; σ: 195.14 m: 2182.00; σ: 178.20 m: 1212.70; σ: 136.70 m: 2209.90; σ: 170.01 GA m: 3883.27; σ: 399.30 m: 2565.50; σ: 279.80 m: 1312.13; σ: 192.50 m: 2586.96; σ: 290.50 SA m: 3921.32; σ: 339.10 m: 2497.78; σ: 537.50 m: 1335.23; σ: 380.30 m: 2584.30; σ: 18.70 Average m: 3679.60; σ: 311.01 m: 2414.60; σ: 331.30 m: 1286.50; σ: 236.20 m: 2465.90: σ: 292.84 TD Average SPT m: 18.84; σ: 3.93 m: 11.44; σ: 2.78 m: 7.56; σ: 3.56 m: 12.61; σ: 3.43 GA m: 19.57; σ: 3.09 m: 14.17; σ: 3.37 m: 7.41; σ: 3.69 m: 13.71; σ: 3.38 SA m: 19.42; σ: 2.82 m: 14.20; σ: 3.47 m: 7.42; σ: 2.82 m: 13.68; σ: 3.06 Average m: 19.27; σ: 3.28 m: 13.27; σ: 3.20 m: 7.46; σ: 3.38 m: 13.33; σ: 3.28 OC Average EOQ m: 10353.63; σ: 331.40 m: 8387.20; σ: 315.41 m: 6014.53; σ: 275.90 m: 8251.70; σ: 307.60 MRP m: 10618.63; σ: 346.00 m: 8646.30; σ: 324.31 m: 6318.17; σ: 275.49 m: 8527.60; σ: 321.20 JIT m: 10641.83; σ: 331.00 m: 8667.20; σ: 299.24 m: 6386.88; σ: 298.30 m: 8565.30; σ: 309.50 Average m: 10537.80; σ: 336.13 m: 8567.00; σ: 313.00 m: 6239.60; σ: 283.10 m: 8481.00; σ: 311.00 HC Average SPT & EOQ m: 2871033.6; σ: 16369 m: 2328030; σ: 16232 m: 1741397; σ: 15236.7 m: 2313145.8; σ: 15945.6 SPT & MRP m: 2634099.3; σ: 39691 m: 1866170; σ: 51365 m: 1217764.7; σ: 44586.7 m: 1909256.5; σ: 45214 GA & EOQ m: 2873377.6; σ: 12087 m: 2375800; σ: 84233 m: 1719935.7; σ: 11581 m: 2323036.5; σ: 35967 GA & MRP m: 2652786.3; σ: 39784 m: 1885730; σ: 45499 m: 1213866.12; σ: 28452.4 m: 1917460.67; σ: 37911.6 SA & EOQ m: 2846929.3; σ: 13672 m: 2348770; σ: 11352 m: 1738166.38; σ: 10787.7 m: 2311288.3; σ: 11937 SA & MRP m: 2643871.3; σ: 38772 m: 1899830; σ: 34788 m: 1221066.34; σ: 14159.8 m: 1921589.5; σ: 29239 JIT with SPT, GA & SA m: 691397.4; σ: 6898.8 m: 565083; σ: 6085.4 m: 438959.22; σ: 4956.5 m: 565146.3; σ: 5979.69 Average m: 2066254; σ: 20119.1 m: 1599941.1; σ: 29080 m: 1129890.2; σ: 15518 m: 1598695; σ: 21572.4 Table 2-b. Normalized performance index data FT Average SPT m: 3516.00; σ: 212.11 m: 2909.33; σ: 237.60 m:2204.91; σ: 248.55 m: 2876.85; σ: 232.75 GA m: 4220.95; σ: 434.02 m: 3420.67; σ: 373.07 m: 2385.69; σ: 350.00 m: 3342.43; σ: 385.70 SA m: 4262.30; σ: 368.59 m: 3330.37; σ: 716.67 m: 2427.69; σ: 691.45 m: 3340.12; σ: 592.23 Average m: 3999.85; σ: 338.24 m: 3220.12; σ: 442.44 m: 2339.43; σ: 430.00 m: 3186.47; σ: 403.56 TD Average SPT m: 20.48; σ: 4.27 m: 15.25; σ: 3.70 m: 13.75; σ: 6.47 m: 16.49; σ: 4.82 GA m: 21.27; σ: 3.36 m: 18.89; σ: 4.49 m: 13.47; σ: 6.70 m: 17.88; σ: 4.85 SA m: 21.11; σ: 3.07 m: 18.93; σ: 4.63 m: 13.49; σ: 5.13 m: 17.84; σ: 4.27 Average m: 20.95; σ: 3.56 m: 17.69; σ: 4.28 m: 13.57; σ: 6.10 m: 17.41; σ: 4.65 OC Average EOQ m: 11253.9; σ: 360.2 m: 11182.9; σ: 420.5 m: 10935.5; σ: 501.6 m: 11124.1; σ: 427.5 MRP m: 11542.0; σ: 376.1 m: 11528.4; σ: 432.4 m: 11487.6; σ: 500.9 m: 11519.3; σ: 436.5 JIT m: 11567.2; σ: 359.8 m: 11556.3; σ: 399.0 m: 11612.5; σ: 542.4 m: 11578.6; σ: 433.7 Average m:11454.4; σ: 365.4 m: 11422.5; σ: 417.3 m: 11345.2 σ: 515.0 m: 11407.4; σ: 432.5 HC Average SPT & EOQ m: 3120689; σ: 17792 m: 3104040; σ:21642 m: 3166176; σ: 27703 m: 3130302; σ: 22379 SPT & MRP m: 2863151; σ: 43142 m: 2488227; σ:68487 m: 2214118; σ: 81067 m: 2521832; σ: 64232 GA & EOQ m:3123237; σ: 13138 m: 3167733; σ: 112310 m: 3127156; σ: 21056 m: 3139375; σ: 48835 GA & MRP m: 2883463; σ:43243 m: 2514307; σ: 60665 m: 2207029; σ: 51731 m: 2534933; σ: 51880 SA & EOQ m: 3094488; σ: 14860 m: 3131693; σ: 15136 m: 3160303; σ: 19614 m: 3128828; σ: 16537 SA & MRP m: 2873773; σ: 42143 m: 2533107; σ: 46384 m: 2220121; σ: 25745 m: 2542333; σ: 38090 JIT with SPT, m: 751518; σ: 7499 m: 753444; σ: 8114 m: 798108; σ: 9012 m: 767690; σ: 8208 GA & SA Average m: 2672903; σ: 2608934 m: 2527507; σ: 47534 m: 2413287; σ: 33704 m: 2537899; σ: 35737

290 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) The plot for normalized performance indexes are shown in Figure 2. The t-tests and f-test show significant differences in sum of flow time and tardiness in three demand scenarios; the only test shown statistic insignificant is the tardiness value in low and medium demand rate using SPT scheduling method (TD m : m = 15.25, σ = 4.94; TD L : m = 13.74, σ = 11.77; T = 1.24 < T 0.025, 29, 29 =). The test also conform significant differences in ordering cost and holding cost in three demand scenarios. The above results indicate the following: The plot for normalized performance indexes are shown in Figure 2. The t-tests and f-test show significant differences in sum of flow time and tardiness in three demand scenarios; the only test shown statistic insignificant is the tardiness value in low and medium demand rate using SPT scheduling method (TD m : m = 15.25, σ = 4.94; TD L : m = 13.74, σ = 11.77; T = 1.24 < T 0.025, 29, 29 =). The test also conform significant differences in ordering cost and holding cost in three demand scenarios. The above results indicate the following: 1) The factory-loading rate (demand rate) significant affects the flowtime for all three scheduling methods; the higher loading rate, the longer time to finish customer orders. On other words, more waiting time is required. 2) Tardiness is affected by the demand rate such that it confirms the result of longer flowtime in high demand rate. The SPT algorithm generates similar tardiness levels in both low and medium demand rate (statistic insignificant); but it still result significant increasing in tardiness when the demand rate increasing to high demand. 3) Ordering costs of high, medium, and low demand rate have no significant different. 4) Holding costs for each combination of inventory control and scheduling methods are significantly different for high, medium, and low demand rate. 5.1.3 Scheduling Algorithm and Inventory Control Method Analysis (Univariate Analysis) Comparison of Mean Values Null Hypothesis H 0 : No significant difference in mean values of different scheduling and inventory control method. The t-tests below are performed to evaluate whether the differences noticed in mean values are significantly different. For example, the first t-test was performed on the mean values sum of flow time for SPT and GA. The mean value of sum of flow time for High utilization for SPT and GA are 3235.00 and 3883.27 minutes respectively. The t-test performed indicated that the difference was significant. 5000 Normalized Sum of Flow Time 22 Normalized Tardiness 4000 20 3000 SPT 18 SPT 2000 1000 GA SA 16 14 GA SA 0 12 11700 11400 11100 10800 10500 Normalized Ordering Cost EOQ MRP JIT 3.5 3.0 2.5 2.0 1.5 1.0 0.5 M illions Normalized Holding Cost SPT & EOQ SPT & M RP GA & EOQ GA & M RP SA & EOQ SA & M RP JIT with SPT, GA & SA Figure 2. Normalized performance index compariso

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 291 Variable Comparison High Utilization t value FT TD OC HC SPT and GA SPT and SA GA and SA SPT and GA SPT and SA GA and SA EOQ and MRP EOQ and JIT MRP and JIT For SPT: EOQ and MRP EOQ and JIT MRP and JIT For GA: EOQ and MRP EOQ and JIT MRP and JIT For SA: EOQ and MRP EOQ and JIT MRP and JIT Table 3: T-tests- univariate analysis of mean values 60.85 (Reject) 73.17 (Reject) 3.03 (Reject) 6.09 (Reject) 5.00 (Reject) 1.49 (Accept) 23.07 (Reject) 25.67 (Reject) 2.02 (Reject) 230 (Reject) 4468 (Reject) 2011 (Reject) 221 (Reject) 6540 (Reject) 2026 (Reject) 206 (Reject) 5871 (Reject) 2068 (Reject) Utilization t value 48.22 (Reject) 23.26 (Reject) 4.66 (Reject) 26.07 (Reject) 25.89 (Reject) 0.25 (Accept) 23.89 (Reject) 26.86 (Reject) 1.98 (Accept) 357 (Reject) 857 (Reject) 1049 (Reject) 214 (Reject) 894 (Reject) 1200 (Reject) 511 (Reject) 5777 (Reject) 1576 (Reject) Utilization t value 17.57 (Reject) 12.65 (Reject) 2.26 (Reject) 1.22 (Accept) 1.28 (Accept) 0.08 (Accept) 32.49 (Reject) 38.22 (Reject) 7.05 (Reject) 463 (Reject) 2838 (Reject) 724 (Reject) 687 (Reject) 4241 (Reject) 1119 (Reject) 1211 (Reject) 4565 (Reject) 2174 (Reject) t-distribution value T 0.025, 29, 29 It should be noted that holding costs are the same for JIT inventory policy for all three scheduling policies. The above results indicate the following: 5) Flowtime mean value of SPT is significantly different than that of GA and SA. Flowtime values of GA and SA are also significantly different. 6) Tardiness values do not show significant difference while in low utilization (loading) rate regardless the scheduling method. During the medium and high loading rates, the GA and SA have similar tardiness performance. 7) Ordering costs of EOQ, MRP and JIT are significantly different; except the comparison of MRP and JIT methods in medium utilization rate. 8) Holding costs are significantly different for each inventory control measure. 5.1.4 General Linear Model (Multivariate Analysis) Comparison of Mean Values Null Hypothesis H 0 : No significant difference in mean values of different scheduling and inventory control method. The f-test is performed to determine whether there is significant difference between values of different populations. For example, the flow times of SPT, GA and SA for high utilization were checked for significant difference. The f-statistic (Table 4) shows significant difference and hence the null hypothesis (no significant difference in populations) is rejected. Based on the above statistic analysis, some observations are summarized as following: a) Under the single objective (shortest sum of flow times) case, the SPT algorithm performance is superior than GA & SA. Note that the objective here was only minimizing the sum of flow times. This study validates the point that SPT minimizes the sum of flow times. GA performed slightly better than SA. However, the results are dependant on the algorithms that were used. Better algorithms may give different results than were obtained here. Although the demand rate is a significant factor, no interaction between scheduling method and demand rate is observed (see Figure 3). b) Inventory (holding) Cost (HC) can be decreased by a JIT and MRP approach regardless of the scheduling algorithm. JIT emerged as the best inventory control technique. However, it is noted that only holding and ordering cost were considered in the system as inventory control performance measures. In reality, it is difficult and costly to operate a JIT type of inventory control system.

292 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) Table 4: F-tests- multivariable analysis of mean values Variable Pr > F statistic Conclusion Sum of Flow Time (SPT Vs. GA Vs. SA) High Tardiness (SPT Vs. GA Vs. SA) High Ordering Costs (EOQ Vs. MRP Vs. JIT) High Holding Cost For SPT (EOQ Vs. MRP Vs. JIT) High For GA (EOQ Vs. MRP Vs. JIT) High For SA (EOQ Vs. MRP Vs. JIT) High 0.24 0.65 0.78 0.0132 Accept H 0 Accept H 0 Accept H 0 Sum of Flow Time Chart Tardiness 3600 18 3000 2400 1800 SPT GA SA 14 10 SPT GA SA 1200 6 Ordering Cost 2.9 Holding Cost SPT & EOQ 10500 2.4 SPT & MRP 9000 7500 EOQ MRP JIT 1.9 1.4 GA & EOQ GA & MRP SA & EOQ 0.9 SA & MRP 6000 0.4 JIT with SPT, GA & SA Figure 3. Performance index comparison

Abhyuday A. Desai et al.: Effect of Activity Schedulings and Inventory Control 293 c) Order Tardiness (TD) presents a relatively insignificant pattern in the result of this study result such that no strong deviation or difference was fund. It can be improved by adding minimization of TD as an objective in the objective function in GA & SA (but not in case of SPT). This objective function, which considers multiple objectives, is termed the Utility Function [5]. This study supports the theory that SPT schedule does not affect tardiness (which is true in our study when the demand rate was moving from low to median). d) Ordering cost has lower value while using EOQ method. However, it also results higher holding cost regardless scheduling method. The holding cost present three patterns: high holding cost with EOQ model, median holding expense while applying MRP, and low holding cost using JIT. The holding cost pattern shown in Figure 3 exposes an important research topic: how to decrease the holding cost while the factoryloading rate (demand rate) are increasing. e) Overall, in this study the combination of SPT with JIT produced the best results that have short flowtime, less tardiness, and low holding cost. f) Facility configuration change and scheduling and inventory variation can be applied for a detailed system study. The setup here was a simple single assembly line flow-shop type model. However, such a setting will rarely be encountered in industrial settings. More realistic set-ups include multiple assembly lines, and multiple servers within a workstation, etc. Setting up JIT in complex industrial production lines is a difficult task. 6. CONCLUSIONS & FUTURE RESEARCH A computer simulation and the experiment design for the effect of activity scheduling and inventory control is presented in this article. This study attempted to obtain more information on the interaction between scheduling control and inventory control since one of the functions of virtual manufacturing is to optimize the system performance before the actual events occurred. The results can provide the guideline for future improvement of the total system integration, especially in the integration of supply chain and production system. It is known that SPT minimizes the sum of flow time; hence it produced better results than GA and SA under this study. However, in real-life situations where there are multiple objectives such as average flow time, due dates, etc. to satisfy, SPT can not be used to schedule the orders. This calls for scheduling techniques such as search heuristics that satisfy multiple objectives simultaneously. This area of multi-criteria scheduling, more specifically that of Intelligent Scheduling, is the focus of our future research. Our future research will consist of following: c) More realistic assembly setup, with multiple assembly lines and multiple servers within workstations. d) Complex inventory control policy. e) Multi-criteria objective scheduling, considering goals such as due dates, customer priority, and processing times. f) Active interaction between user and scheduler for deciding priority between goals. REFERENCES 1. Beasley, J. E., OR-note, Online, Internet, Available, http://mscmga.ms.ic.ac.uk/jeb/or/invent.html. 2. Biegel, J. E. and J. J. Davern, Genetic algorithms and job shop scheduling, Computers & Industrial Engineering, 19, 81-91 (1990). 3. Catoni, O., Solving scheduling problems by simulated annealing, SIAM Journal on Control and Optimization, 36, 1539-1575 (1998). 4. Chang, P. and R. Hsu, A simulated annealing approach to parallel processor scheduling problems with precedence relations, Journal of the Chinese Institute of Engineers, 17, 485-497 (1994). 5. Gilkinson, J.C., L. C. 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294 Journal of the Chinese Institute of Industrial Engineers, Vol. 20 No. 3 (2003) Conference on Control 96, University of Exeter, England (1996). ABOUT THE AUTHOR Abhyuday Desai received the MS degree in Industrial Engineering from the Department of Industrial Engineering at Texas Tech University. He is currently a doctoral student in Operations Research at Texas Tech University and his research interests are in simulation methodology and its applications in scheduling, inventory control and automation. Yung-Nien Yang is an Assistant Professor and the Supervisor of Automation and Robotic Laboratory of the Department of Industrial Engineering at Texas Tech University. He is interested in Intelligent System, Computer Aided Planning and Scheduling, Information Automation and Integration, CAM/CIM Integration, and Production System Analysis and Simulation. Hamid R. Parsaei, Ph.D., P.E. is Professor and Chairman of Department of Industrial Engineering at the University of Houston. Dr. Parsaei also serves as the Director of the Texas Manufacturing Assistance Center-Gulf Coast Region. His research interests include, Computer Aided Process Planning, Cellular Manufacturing, and Economic Analysis. Dr. Parsaei is a Fellow of the Institute of Industrial Engineers.