Sequential Decision Making Schemes in Inventory and Transportation Environments

Abstract

Many mathematical models exist for the simultaneous optimization of transportation and inventory functions. A simultaneous model, while giving the lowest total cost, may not be easily implemented in a firm with decentralized transportation and inventory departments. As such, this thesis studies sequential models, where the primary department is artificially given the authority to make some set of decisions prior to the decisions made by the secondary department. Some known formulations for simultaneous models are studied in an attempt to create a sequential process for the same environment. Finally, a generalized sequential approach is developed that can be applied to any transportation and inventory model with separable costs. The generalized approach allows for the full optimization of the primary departmental costs, and then sequentially allows the optimization of the secondary departmental costs subject to a maximum allowable increase in the costs of the primary department. The analysis of this sequential approach notably reveals that when the relative deviation from the optimal cost of each department is equal, a reasonable solution with respect to total cost is attained. This balance in relative deviation is defined as the fairness point solution. Differing cost scenarios are thus tested to determine the relationship between the cost ratio among departments and the performance of the fairness point solution. The fairness point solution provides an average deviation of total cost from the total optimal cost of less than 1% in four of the seven scenarios tested. Other sequential approaches are discussed and fairness with respect to these new approaches is considered.