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