Optimal Spare Ordering Time for Preventive Replacement to Maximize the Cost Effectiveness

Abstract

This article presents a model for determining the optimal spare ordering time for preventive replacement under the cost effectiveness criterion. The spare unit for replacement is available only by order and the lead-time for delivering the spare due to regular or expedited ordering follows general distributions. To analyze the ordering policy, the failure process is modelled by a non homogeneous Poisson process. By introducing the ordering, shortage, repair, replacement cost, and the salvage value, the expected long term cost effectiveness is derived as a criterion of optimality. It is shown that, under certain conditions, the optimum spare ordering time which maximizes the expected cost effectiveness is given by a unique solution of an equation. A special case of this model is also presented and discussed. Finally, a numerical example is given for illustration of the proposed model.

Keywords:

• Cost effectiveness
• Minimal repair
• Ordering policy
• Preventive replacement
• Salvage
• Spare

Mathematics Subject Classification:

• 90B25
• 90B50

Acknowledgments

We are very grateful to the referees for their insightful comments and suggestions, which greatly improved this article significantly. All of their suggestions were incorporated directly in the text. This research was supported by the National Science Council of Taiwan, under Grant No. NSC 97-2221-E-025-004-MY3.