A REPLACEMENT PROBLEM WITH TRADE-IN

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  • Hatoyama Yukio
    Department of Management Science and Engineering, Tokyo Institute of Technology

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  • 下取りを考慮した取替問題

Abstract

Consider the following replacement problem with trade-in. Suppose a system must operate for T time periods. There is an essential component of the system whose failure results in the failure of the system. There are n alternative types of components. The failure distribution for type i component is assumed to be exponential with rate λ_i. If type i component is replaced by type j component, replacement cost C(i, j) is incurred. The dependency of the replacement cost on the failed component as well as a new component to replace the old one implies that the failed component has some trade-in value or salvage value. The problem is to determine an optimal policy for the purchase of a new type of component supposing type i component has just failed with t time periods remaining. Some properties of the optimal policy are discussed under the assumption that C(i, j) has some cost structure such as a submodular function. In particular if C(i, j) is additive, an explicit form of an optimal policy is derived. The model is then extended to multi-component coherent systems where it is shown that for most of the cases the results obtained for single-component system can be directly applicable.

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