Control of a Batch Processing Machine Serving Compatible Job Families

We consider the control of a single batch processing machine with random arrivals, random processing times, and compatible job families (jobs from different families may be processed together in the same batch, with the processing time distribution of the entire batch determined by the job family in the batch having the greatest expected processing time). The objective is to minimize the long-run average time that jobs spend in the system. We present properties possessed by the optimal policies and discuss the structure of these policies. We next develop a simple heuristic scheduling policy to control the machine. Simulation results are provided to demonstrate the effectiveness of our heuristic over a wide range of problem instances.     

Control of an Assembly System with Processing Time and Subassembly-Type Uncertainty

We address the problem of controlling an assembly system in which the processing times as well as the types of subassemblies are stochastic. The quality (or performance) of the final part depends on the characteristics of the subassemblies to be assembled, which are not constant. Furthermore, the processing time of a subassembly is random. We analyze the trade-off between the increase in the potential value of parts gained by delaying the assembly operation and the inventory costs caused by this delay. We also consider the effects of processing time uncertainty. Our problem is motivated by the assembly of passive and active plates in flat panel display manufacturing. We formulate the optimal control problem as a Markov decision process. However, the optimal policy is very complex, and we therefore develop simple heuristic policies. We report the results of a simulation study that tests the performance of our heuristics. The computational results indicate that the heuristics are effective for a wide variety of cases.     

Estimating job waiting times in production systems with cross-trained setup crews

We model a production system with multiple machines, each serving a variety of jobs. The machines require setups to switch from one job to another. Setup operations are performed by a limited number of setup crews who are cross-trained to perform all setup operations. We develop an approximation model that takes into account the effect of delays caused by unavailability of the setup crews, and obtain average job waiting times in the system. A numerical study demonstrates that our approximation performs very well. Our study also provides insights into the importance of explicitly modeling the effects of cross-trained setup crews on performance measures, and whether and when the cross-training of setup crews improves system performance.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute 'approximately optimal' base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

CONWIP ASSEMBLY WITH DETERMINISTIC PROCESSING AND RANDOM OUTAGES

We develop structural results and an approximation for the throughput of an assembly system fed by multi-station fabrication lines where releases are governed by the CONWIP protocol and all machines have deterministic processing times but are subject to random outages. This formulation is motivated by a printed circuit board manufacturing process.

We demonstrate that while throughput of such systems is nondecreasing in machine speed, there are cases where throughput declines when mean time between failures (MTBF) increases or mean time to repair (MTTR) decreases. Using the concept of "deterministic steady state," which describes the behavior of the system in die absence of failures, we derive a simple, closed-form approximation for throughput. Comparisons with simulation show that this approximation is robust over a wide range of conditions. Finally, we observe that throughput tends to be higher when the bottleneck is located in fabrication rather than assembly.     

ECONOMIC PRODUCTION QUOTAS FOR PULL MANUFACTURING SYSTEMS

We consider the problem of using “safety capacity” to ensure due date integrity in a pull manufacturing system and quantify the basic tradeoff between lost revenue opportunity and overtime costs. In this context, we address the question of when it is economically attractive to use “under capacity scheduling” and the problem of setting economic production quotas.

We develop four models for addressing the quota setting problem. The first three assume that quota shortfalls cannot be carried over to the next regular time production period. Models 1 and 3 assume that these shortages are made up on overtime and incur fixed or fixed plus variable costs. Model 2 does not use a capacity buffer and treats shortages as lost sales. Finally, Model 4 assumes that shortages can be backlogged to the next regular time production period at a cost. For this model, we compute both an optimal quota and an overtime “trigger,” which represents the minimum shortage for which overtime is used. We give computational results that illustrate and contrast the various models.     

Integrated maintenance and production control of a deteriorating production system

We consider a make-to-stock production/inventory system consisting of a single deteriorating machine which produces a single item. We formulate the integrated decisions of maintenance and production using a Markov Decision Process. The optimal dynamic policy is shown to have a rather complex structure which leads us to consider more implementable policies. We present a double-threshold policy and derive exact and approximate methods for evaluating the performance of this policy and computing its optimal parameters. A detailed numerical study demonstrates that the proposed policy and our approximate method for computing its parameters perform extremely well. Finally, we show that policies which do not address maintenance and production control decisions in an integrated manner can perform rather badly.     

Author Index for 2002

Authors Index

Author Index for 2002     

Release policies for assembly systems

We consider a production system consisting of several fabrication lines feeding an assembly machine. The machines in the fabrication lines and at assembly are assumed to have general processing time distributions. Releases to the system are governed by the kanban release mechanism. We first derive a heuristic for the throughput of this system by replacing the assembly system under kanban release by an equivalent system under CONWIP release and by making use of an approximation for the throughput of a CONWIP assembly system (Duenyas, 1992). Comparisons with simulation show that this heuristic is robust over a wide range of conditions.

We also address the issue of which release mechanism is more effective in obtaining a desired throughput level with the minimum possible work-in-process inventory level in the system. We present both analytical and simulation results to demonstrate that the CONWIP release policy seems to be a more effective release policy for assembly systems.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute approximately optimal base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.