Optimal Overhaul-Replacement Policies for a Repairable Machine Sold with Warranty

Abstract

This research deals with an overhaul-replacement policy for a repairable machine sold with a free replacement warranty (FRW), which will be used for a finite horizon T and evaluated at fixed interval s. At each evaluation point, the buyer considers three alternative decisions, i.e. (1) keep the machine, (2) overhaul it, or (3) replace it with a new identical one. If the machine fails during the warranty period, this is rectified at no cost to the buyer. Any failure occurring before and after the expiry of the warranty is restored by minimal repair. An overhaul-replacement policy was formulated using a dynamic programming approach. The results show that overhaul rejuvenation may extend the machine life cycle and delay the replacement decision. In contrast, the warranty stimulates early machine replacement and in so doing increases the replacement frequency for a certain range of replacement costs. This implies that in order to minimize the total ownership costs over T, the buyer needs to consider the minimal repair cost reduction due to the rejuvenation effect of an overhaul as well as the warranty benefit due to replacement. Numerical examples are presented for both illustrating the optimal policy and describing the behavior of the optimal solution.