Cycle-time quantile estimation in discrete event simulation.
Book Description: In today’s business environment, the ability to generate accurate customer delivery dates is crucial. While estimates of mean cycle-time are often readily available, using them to generate estimates of delivery dates ignores inherent variability in the cycle-time distribution and can result in reduced on time delivery. Estimates of cycle-time quantiles, on the other hand, provide a complete picture of the cycle-time distribution and allow customer delivery dates to be quoted with levels of confidence comfortable to the decision maker. Obtaining cycle-time quantile estimates from discrete-event simulation (DES) models of manufacturing systems, however, is a difficult task. Techniques often call for excessive data storage, are tedious to implement, or require the quantiles of interest to be known a priori. A quantile estimation technique that provides high accuracy, low variability, and which is easy to implement would be extremely useful. This work proposes such a method, based on the first four terms of the Cornish-Fisher expansion, for generating steady-state cycle time quantile estimates from DES models of manufacturing systems. The CFE-based quantile estimation technique has the advantages of requiring very low data storage and enabling the generation of multiple quantile estimates from a single set of simulation runs. Additionally, it is shown to generate precise and accurate quantile estimates for a wide variety of cycle-time distributions, particularly when First-In-First-Out (FIFO) dispatching policies are employed at all workstations. When non-FIFO dispatching rules are employed in a system, however, the cycle-time distribution becomes heavily skewed and the kurtosis increases significantly. In such cases, the accuracy of the CFE-based approach is shown to degrade. A power transformation for use in combination with the CFE is proposed to combat these accuracy problems. Results show that the combination of the CFE with the transformation generates a cycle-time quantile estimation technique with high accuracy for non-FIFO systems. Finally, an approach for using the quantile estimates obtained from DES models with ranking and selection procedures for selection of the best system amongst a set of alternative systems is presented. The approach is shown to work in conjunction with standard ranking and selection procedures while not requiring unreasonable simulation effort.
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