Service level constraints and total order quantity commitments in inventory models

This thesis deals with single-item stochastic inventory models with service level constraints and total order quantity commitments.;There are two schools of thought on how to deal with shortages when establishing inventory control systems. The first point of view is to assign explicit cost to shortage situations, though these costs are largely intangible. The alternative point of view is to impose a service level constraint (SLC): the service specification requires that the level of stockout must be bounded in some sense. While the service level approach is more frequently implemented than the shortage cost approach, the rigorous theoretical framework for this approach has been largely missing. It is our aim in the first part of this thesis to provide a comprehensive analysis of service level constraints in inventory models and to present both theoretical and computational results.;For the SLC models, we address theoretical issues such as the classification of SLCs, definitions for major service levels, and optimality of (s,S) policies under different SLCs. We also derive and test exact and efficient algorithms for computing optimal (s,S) policies subject to these SLCs.;Classical inventory models generally assume that both the timing and size of procurement are entirely controlled by the buyer, that is, new inventory can be ordered at any time and in any quantity. However, there exist numerous other buyer-supplier arrangements. In the second part of the thesis we address one such arrangement of particular importance: total order quantity commitment (TOQC). Under the TOQC contract that has been negotiated between the buyer firm and the supplier, the former agrees to an obligation to procure a certain quantity of an item from the latter over a predetermined contract period (inventory beyond the committed quantity can be procured maybe at a different price). We address the issue of how to determine the optimal decision on how much to commit and when and how much to order during the contract period.;For the full-cost model with the TOQC, known stockout cost and zero setup cost, we establish the optimality of "dual" order-up-to-level policy. The computation of the optimal parameters proves to be quite difficult. Moreover, in practice, the TOQC contract often contains an option for the buyer to adjust the initially committed quantity before a specified time. With this additional feature, the full-cost model is hard to deal with both analytically and computationally. After introducing service level constraints to substitute for the shortage cost, we are able to obtain simple form of optimal ordering policies and simple procedures for computing the optimal contract parameters.