ABSTRACT We study a rental firm's optimal inventory and rental allocation problem considering random inventory loss due to usage. Each product has two conditions: good and bad, both can satisfy demand. After each rental, good products have a depreciation rate to become bad, and bad products have a depreciation rate to become useless. The firm chooses its inventory before the rental season starts and decides how to allocate its good and bad products to satisfy demand in each period during the rental season. If the total inventory of the good and bad product is no greater than the demand, the firm rents out all inventory. Otherwise, the optimal rental quantities are governed by two thresholds that depend on the weighted sum of inventory of the good and bad products adjusted by the demand. Based on the two thresholds, the firm's optimal rental decision can be classified into three cases: rent the bad product first, good product first, or a mix of both products. We also analyze two priority allocation policies: Good‐First (GF) and Bad‐First (BF), and the cost difference between them and the optimal policy. When the total inventory is moderate, we propose a modified Bad‐First (MBF) policy that only optimizes the rental allocation in the last two periods and uses the BF policy for the remaining periods. Such policy performs well and significantly reduces computation complexity. Our numerical study shows that the usage‐based loss rates can have a non‐monotone impact on the initial inventories and significantly increase the firm's cost.
Li et al. (Tue,) studied this question.