Application Of Dynamic Programming Model In Inventory Management

This thesis aims to apply dynamic programming approach to formulate three main topics related to inventory management under three real world situations and then propose the corresponding optimal inventory control policies by analyzing the objective functions and computational simulations.The fist issue of the problem of inventory management in a car rental company is considered. We develop a two-stage dynamic programming model, in which we determine the vehicle transfer policy in the second stage and the optimal fleet size in the first stage. Although the objective function could be neither concave nor quasi-concave, we can find the optimal fleet size and vehicle transfer policy by solving a series of linear programming problems. A sensitivity analysis is conducted and managerial insights are drawn upon. We propose a heuristic solution based on a special case analysis, for the first-stage fleet size problem. A numerical study reveals that our heuristic solution for fleet size determination performs well. However, if the corresponding vehicle transfer policy is not appropriately determined, the overall performance can deteriorate drastically even when the fleet size is optimal. Our research not only sheds light on the optimal vehicle transfer policy and fleet size, but also underscores the importance of optimizirig vehicle transfer.The second issue considers the issue of replenish the inventory of seasonable goods, which evolves rather rapidly as time elapses. We propose a periodic-review inventory model for planning changes of inventory of seasonable goods with state-dependent demand and cost parameters. We jointly optimize product change and inventory replenishment to maximize the total expected discounted profits over the planning horizon. First, we consider a single-period model and show that the optimal product change policy is a threshold policy for the initial inventory of goods that are soon to become unseasonable. Second, we demonstrate that the corresponding optimal inventory policy follows a PKD (Purchase-Keep-Dispose) policy if the incumbent product is kept or a base-stock policy if a new seasonable product is released. Third, we propose a heuristic approach for a multi-period model. Finally, we conduct the numerical test and demonstrate the performance of our heuristics. Our research provides insights about managing seasonable goods in a dynamic environment.In the third issue, we introduce a dynamic programming model for inventory control policy under VMI system in the first step; and consider routing selection in the second stage. The system examined in this chapter consists of one supplier, one item, one vehicle and multi-locations. Firstly, as homogenous depots are considered, a (s, S) policy is proved to be optimal for the inventory strategy. Secondly, based on the previous outcome, routing selection is absorbed in the model. The two most used policies, namely, decreasing order and increasing order of routing costs, are executed in the computational study with (s,S) strategy and full capacity replenishment strategy, respectively. We found that (s,S) policy is indeed more optimal than the corresponding full capacity policy. On the other hand, in both strategies, the decreasing order visiting is the better choice. We also do the sensitivity analysis in the numerical section to find out the effectiveness of the parameter.