Optimal policies for dynamic transportation-inventory models

Abstract

This thesis studies the dynamic transportation-inventory models for a single product from which the optimal procurement quantities and the transportation modes are determined over a finite planning horizon. A basic model is proposed which is the problem of a Wangner-Whitin type. We investigate the properties of an optimal solution and the Planning Horizon Theorem from which an efficient algorithm is developed. This is extended to three different models by integrating the deteriorating effects, the quantity discounts with the disposal of the excess, or the capacity constraints. The model with the deteriorating items whose utility decreases with the passage of time is shown to be equivalent to the basic model by transformations of some variables. An actual case involving a palm oil industry is presented. For the model with the quantity discounts and the disposal of the excess, we identify the properties of an optimal solution, and present a forward algorithm for the cases of single and multiple price break points. The capacity constraints are considered on the following cases and they are: i) the number of units arriving at each period is at most one, ii) shipment can arrive by more than one mode but with only one unit for each mode, and iii) shipment can arrive by only one mode but more than one unit of the mode permitted. For each case, an algorithm is presented and a numerical example is solved to illustrate the algorithm developed.