Spare parts inventory management for substitute consumer products: an adaptive robust optimization approach

In this study, a multi-period spare parts inventory system providing spare parts for several consumer durable products in an assortment is investigated. An original equipment manufacturer (OEM) fulfills the after-sales service for the sold products with a repair-replacement policy. The products can substitute each other and use common and dedicated spare parts. The failure quantity of each product is uncertain and influenced by the on-market product quantity, which is governed by customer preferences and changes over the planning periods. To repair the failed products, spare parts inventory is used. The OEM aims to minimize the total inventory costs including spare parts purchase cost, holding cost, and product backorder cost. We formulate this problem as a multi-stage adaptive robust optimization model when the probability distributions of product failures are unknown. An improved partition-and-bound method is designed to solve the model. We demonstrate its relative computational advantage over the classical partition-and-bound method through numerical experiments on small- and medium-sized problem instances.