Model approximation for batch flow shop scheduling with fixed batch sizes

Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these “t-step” approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.United States. Department of Homeland Security. Science and Technology Directorate (Contract HSHQDC-13-C-B0052)United States. Air Force Research Laboratory (Contract FA8750-09-2-0219)ATK Thiokol Inc

Control of manufacturing networks which contain a batch processing machine

We consider the control of a batch processing machine which is part of a larger manufacturing network of machines. Systems consisting of a batch processing machine and one or more unit-capacity machines in tandem are considered. The objective is to minimize the average time that jobs spend in the entire system. We present algorithms to determine the optimal policies for certain finite horizon, deterministic problems. We then discuss the structure of the optimal policies for infinite horizon, stochastic problems, and investigate the benefit of utilizing information about upstream and downstream unit-capacity machines in the control of the batch machine. We develop a simple heuristic scheduling policy to control the batch machine which takes into account the state of other machines in the network. Computational results demonstrate the effectiveness of our heuristic over a wide range of problem instances.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45931/1/10756_2004_Article_274353.pd

Dynamic Control of Serial-batch Processing Systems

This research explores how near-future information can be used to strategically control a batch processor in a serial-batch processor system setting. Specifically, improved control is attempted by using the upstream serial processor to provide near-future arrival information to the batch processor and further meet the re-sequencing requests to shorten critical products? arrival times to the batch processor. The objective of the research is to reduce mean cycle time and mean tardiness of the products being processed by the serial-batch processor system. This research first examines how mean cycle time performance of the batch processor can be improved by an upstream re-sequencing approach. A control strategy is developed by combining a look-ahead control approach with an upstream re-sequencing approach and is then compared with benchmark strategies through simulation. The experimental results indicate that the new control strategy effectively improves mean cycle time performance of the serial-batch processor system, especially when the number of product types is large and batch processor traffic intensity is low or medium. These conditions are often observed in typical semiconductor manufacturing environments. Next, the use of near-future information and an upstream re-sequencing approach is investigated for improving the mean tardiness performance of the serial-batch processor system. Two control strategies are devised and compared with the benchmark strategies through simulation. The experimental results show that the proposed control strategies improve the mean tardiness performance of the serial-batch processor system. Finally, the look-ahead control approaches that focus on mean cycle time and mean tardiness performances of the serial-batch processor system are embedded under a new control strategy that focuses on both performance measures simultaneously. It is demonstrated that look-ahead batching can be effectively used as a tool for controlling batch processors when multiple performance measures exist