Authors: Jeffery K. Cochran, Nipa Phojanamongkolkij
Addresses: Department of Industrial Engineering, Arizona State University, USA. ' Department of Industrial Engineering, Northern Illinois University, USA
Abstract: Batching is an important system behaviour wherein several entities in a network are combined into a single entity in all further network flow. Total cycle time can be dramatically affected by an improper choice of batch sizes. In this paper, continuous-time Markov chains are used to represent the states corresponding to three common types of batching stations: single product batching stations with one-at-a-time arrivals, single product batching stations with bulk arrival distribution, and multiple product batching stations with one-at-a-time arrivals where a common batch-processing size is used. The associated Chapman-Kolmogorov equations are solved producing surprisingly simple steady-state predictions for the batch station|s steady-state behaviour in each case. Although the resulting formulas are useful alone, they are used to produce a supplement to queueing network analysis (QNA) that we call QNA[B]. The formulas are orders of magnitude more efficient computationally than conducting the corresponding simulation studies. They are validated by comparing discrete event simulation to QNA[B] in the redesign of an existing real-world electronic circuit board repair facility using design of experiments. The recommended process design for that system (the number of servers at the bottleneck station(s) and the batch size(s) at the batch-processing step(s)) cuts the current cycle time by approximately 70%.
Keywords: batch processing; decomposition; Markov chains; queueing network analysis; multiple products; design of experiments; circuit board repair.
International Journal of Computer Applications in Technology, 2004 Vol.20 No.4, pp.161 - 171
Published online: 10 May 2004 *Full-text access for editors Full-text access for subscribers Purchase this article Comment on this article