Abstract

We propose evaluation approaches to multi-item base-stock inventory policies where unidirectional substitutions are allowed. The problems in the paper are in the context of spare parts management and we identify two substitution cases: substitution upon demand arrivals and substitution upon order deliveries. 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 spare part types. Numerical studies show unidirectional substitution improves various system performance measures such as the average inventory level, the average backlogged demand, and the fill rate. The proposed decomposition approach reduces the computation required to compute the performance measures and the approximation errors seems to be quite small.

Keywords: Inventory; Unidirectional substitution; Spare part; Markovian model; Decomposition approach

Article Outline

1. Introduction

2. Policies of substitution

3. The exact models

3.1. Substitution upon demand arrivals only

3.2. Substitution upon demand arrivals and order deliveries

3.3. Substitution upon demand arrivals and limited backlogged demands

4. The decomposition model

4.1. The two-part system

4.2. The N-part system

5. Numerical studies

5.1. Impact of target inventory levels in a two-part system

5.2. Comparison of the three policies in a two-part system

5.3. Accuracy of the decomposition models

5.4. Benefit of substitution

6. Conclusions and future studies

Appendix A. Proof of Theorem 1

References