Fitting Clearing Functions to Empirical Data: Simulation Optimization and Heuristic Algorithms

Clearing function (CF) models, which relate the expected output of a capacitated production resource in a planning period to some measure of its workload, have shown considerable promise for modeling workload-dependent lead times in production planning. This fundamental workload-dependent lead time problem, also known as planning circularity, is due to the fact that cycle time depends on the level of resource utilization in the system, which is determined by the allocation of products to resources made by the production planning procedure. In this thesis we focus on fitting CFs from empirical data which is the most prevalent way to model complex stochastic systems. We use a simulation model of a re-entrant bottleneck system as a surrogate for a real-world semiconductor wafer fabrication environment in order to collect empirical data and compare planning models using different CFs in terms of profit realization. We consider two CF forms: product based CF and load based CF. We apply multiple linear regression (MLR) with three stepwise selection procedures to product based CFs. For load based CFs, we develop simulation optimization and heuristic algorithms to improve the initial regression fits. We implement the load based CF form in the allocated clearing function (ACF) model and compare planning models using product based CF to one using load based CF in extensive computational experiments. We base our comparison on the profit realization in simulation using non-parametric Friedman Tests. Results indicate that the MLR models including the previous period's variables in the regression perform better in the high utilization cases. Stepwise selection procedures applied to same model do not yield significantly different results. Load based CFs perform better than Product Based CFs in terms of profit realization in simulation. Load based CFs can be further improved by using simulation optimization procedures and heuristics.