Holdout transshipment policy in two-location inventory systems
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In two-location inventory systems, unidirectional transshipment policies are considered when an item is not routinely stocked at a location in the system. Unlike the past research in this area which has concentrated on the simple transshipment policies of complete pooling or no pooling, the research presented in this thesis endeavors to develop an understanding of a more general class of transshipment policy. The research considers two major approaches: a decomposition approach, in which the two-location system is decomposed into a system with independent locations, and Markov decision process approach. For the decomposition approach, the transshipment policy is restricted to the class of holdout transshipment policy. The first attempt to develop a decomposition approach assumes that transshipment between the locations occurs at a constant rate in order to decompose the system into two independent locations with constant demand rates. The second attempt modifies the assumption of constant rate of transshipment to take account of local inventory levels to decompose the system into two independent locations with non-constant demand rates. In the final attempt, the assumption of constant rate of transshipment is further modified to model more closely the location providing transshipments. Again the system is decomposed into two independent locations with non-constant demand rates. For each attempt, standard techniques are applied to derive explicit expressions for the average cost rate, and an iterative solution method is developed to find an optimal holdout transshipment policy. Computational results show that these approaches can provide some insights into the performance of the original system. A semi-Markov decision model of the system is developed under the assumption of exponential lead time rather than fixed lead time. This model is later extended to the case of phase-type distribution for lead time. The semi-Markov decision process allows more general transshipment policies, but is computationally more demanding. Implicit expressions for the average cost rate are derived from the optimality equation for dynamic programming models. Computational results illustrate insights into the management of the two-location system that can be gained from this approach.