This paper proposes an optimal maintenance and warranty policy for the repairable second-hand product incorporating a periodic preventive maintenance strategy to slow down the deterioration of the product and derives an optimal length of non-renewing warranty period. Although a number of maintenance policies for the second-hand product have been discussed in the literature, there exist very few works dealing with the periodic preventive maintenance strategy under non-renewing warranty to obtain an optimal warranty period for the second-hand product. This work considers a non-renewing warranty policy, during which a periodic preventive maintenance is adopted to diminish the degradation process of the product and determines an optimal length of warranty period by optimizing the expected cost rate incurred to the dealer during the maintenance cycle. Since the replacement of the failed second-hand product may not be practical in general, we adopt a concept of full refund instead of replacement in this paper. By pre-setting a repair time threshold, either the refund or minimal repair is provided by the dealer depending on whether the failed second-hand product can be repaired within the repair time threshold or not. The maintenance cycle of the second-hand product starts with the purchase of the product and ends when either the refund occurs within the warranty period or the warranty expires. Given a certain cost structure charged to the dealer, we formulate the expected cost rate during the maintenance cycle of the product and determine an optimal length of warranty period minimizing the objective function. Assuming the power law process for the product’s failures and a Weibull distribution for the repair times, we present a numerical example and investigate the effects of periodic preventive maintenances and other relevant parameters on the optimal solution.

本文提出了一种针对可修复二手产品的最佳维护和保修政策，该策略结合了定期的预防性维护策略，以减缓产品的老化并得出非更新保修期的最佳长度。尽管在文献中已经讨论了许多二手产品的维护政策，但是很少有涉及非更新保修期内的定期预防性维护策略的工作来获得二手产品的最佳保修期。这项工作考虑了一项非更新的保修政策，在此政策中，应采取定期的预防性维护措施以减少产品的降级过程，并通过优化维护周期中对经销商产生的预期成本率来确定最佳的保修期限。由于一般而言，更换有故障的二手产品可能不切实际，因此本文采用全额退款的概念，而不是更换产品。通过预先设置维修时间阈值，经销商会根据是否可以在维修时间阈值内维修出现故障的二手产品来提供退款或最低限度的维修。二手产品的维护周期从购买产品开始，直到保修期内发生退款或保修到期时结束。在给经销商一定的成本结构的前提下，我们制定了产品维护周期中的预期成本比率，并确定了使目标功能最小化的最佳保修期。