Effects of two and three variable lead time demand curves on minimizing inventory costs

This dissertation will present some techniques for a more realistic treatment of stochastic lead time demands in inventory models than has been tried in the past. It will study the effect of formulating a lead time demand model for a single item based on using three random variables instead of the traditionally used two variable case. The two variable lead time demand model is usually based on varying lead times and demands. The three variable models in this paper will be based on varying lead times, varying order sizes and varying number of orders received per period. The model will be formulated from historic data and the use of the first four moments of each variable will be used to describe the lead time demand activity. A model will be selected from the Pearson family of curves which best fits a specified criterion. Goodness of fit tests will be run to show that the three variable LTDD model is more appropriate than the two variable model. The continuous (Q, R) model of Hadley-Whitin will be used. Modifications may be necessary to accommodate the varying order size variable. An inventory model to deal with the overshoots will be discussed. The optimal ordering policy will be determined by minimizing the cost equation. The number of units short as well as the stockout probabilities will be found. This requires the use of numeric approximation techniques.; Inventory costs will be computed for both, the two and three variable model. A sensitivity study of distributional assumptions will be made. Cost ratio errors will be computed to study the effect of using a wrong model's ordering policy in a setting where the lead time demand is distributed according to another distribution. Differences will be cited. The major findings of this work will be compared to previous lead time demand research by authors who used the two variable case. This paper will also make reference to standard errors of estimate that can be encountered when using sample moments.