ON SOME STATISTICAL PROBLEMS IN INVENTORY SYSTEMS ASSOCIATED WITH MODELING THE LEAD TIME DEMAND.

摘要

This dissertation contains a number of varied, yet closely related, results that are relevant to the construction of mathematical and statistical models of inventory systems. Its primary focus is on the sensitivity of some specific inventory models to errors in certain modeling assumptions. Motivation for this research is provided through the development of analytical expressions that show that the deterministic economic order quantity can be quite sensitive to errors in the forecast of the demand rate whenever the lead time is non-zero. Similar results are provided for the stochastic case by means of a carefully designed experiment that shows that the specific form or "shape" of the distribution chosen to represent the stochastic behavior of the lead time demand can have a significant impact on a minimum cost (Q,R) policy. Together, these results refute the "conventional wisdom" that inventory models are generally insensitive to errors in model specification or parameter estimation. Considerable attention is also given to the postulation of a "robust" model for the lead time demand distribution (LTDD). This discussion culminates with the introduction of a new probability distribution, based on a hyperbolic cosine transformation of normal random variables, that appears to be well-suited for modeling the LTDD. Furthermore, it is concluded that the two- and three-parameter versions of the lognormal and inverse Gaussian distributions can also be considered as viable candidates to model the LTDD in a wide variety of inventory systems. A number of new algorithms for computing optimal (Q,R) policies are also introduced. These significantly reduce both the amount and complexity of computation required by the standard iterative method. Two additional sets of analytical results are chronicled in this work. The first allows the LTDD to be characterized (by its first four moments) on the basis of information about the distributions of the lead time and demand rate. The second expresses the linear loss functions (LLF's) for a number of probability distributions whose LLF's are not readily available in the inventory control literature. Complete and intuitive proofs of these results are included.