Date of Award
Doctor of Philosophy (PhD)
Modeling Simul & Visual Engineering
Modeling and Simulation
John A. Sokolowski
Most techniques that describe and solve stochastic inventory problems rely upon the assumption of identically and independently distributed (IID) demands. Stochastic inventory formulations that fail to capture serially-correlated components in the demand lead to serious errors. This dissertation provides a robust method that approximates solutions to the stochastic inventory problem where the control review system is continuous, the demand contains autocorrelated components, and the lost sales case is considered. A simulation optimization technique based on simulated annealing (SA), pattern search (PS), and ranking and selection (R&S) is developed and used to generate near-optimal solutions. The proposed method accounts for the randomness and dependency of the demand as well as for the inherent constraints of the inventory model.
The impact of serially-correlated demand is investigated for discrete and continuous dependent input models. For the discrete dependent model, the autocorrelated demand is assumed to behave as a discrete Markov-modulated chain (DMC), while a first-order autoregressive AR(1) process is assumed for describing the continuous demand. The effects of these demand patterns combined with structural cost variations on estimating both total costs and control policy parameters were examined.
Results demonstrated that formulations that ignore the serially-correlated component performed worse than those that considered it. In this setting, the effect of holding cost and its interaction with penalty cost become stronger and more significant as the serially-correlated component increases. The growth rate in the error generated in total costs by formulations that ignore dependency components is significant and fits exponential models.
To verify the effectiveness of the proposed simulation optimization method for finding the near-optimal inventory policy at different levels of autocorrelation factors, total costs, and stockout rates were estimated. The results provide additional evidence that serially-correlated components in the demand have a relevant impact on determining inventory control policies and estimating measurement of performance.
"Methodology for Analyzing and Characterizing Error Generation in Presence of Autocorrelated Demands in Stochastic Inventory Models"
(2007). Doctor of Philosophy (PhD), Dissertation, Modeling Simul & Visual Engineering, Old Dominion University, DOI: 10.25777/fcgv-we37