Evaluation of inventory policies with unidirectional substitutions

We propose evaluation approaches to multi-item base-stock inventory policies where unidirectional substitutions are allowed among part types. The problems in the paper are in the context of spare parts management and we identify two substitution cases: substitution of incoming demand and substitution of backlogged demand. This leads us to three unidirectional substitution policies, for each of which we develop Markovian models. As the number of part types increases, computational effort required to solve the Markovian models increases rapidly. To reduce computation burden, an approximation approach based on the decomposition of multi-dimensional state transition is used for systems with two or more part types. Numerical studies show unidirectional substitution is beneficial in cases where the substitution cost is relatively small compared with the difference in backorder cost of parts. The decomposition approach performs reasonably well.