Approximate Dynamic Programming for Reusable Products with Time-Dependent Rates of Return and Breakdown

A firm sells a set of products with different upfront fees. A customer arrives to request a product, and the firm makes an accept/reject decision. The accepted customer uses capacity for a random duration of time and returns it. The returned capacity is used by other customers. These products are called reusable products. This paper considers a possibility of breakdown, and it models rates of return and breakdown that depend on the rental duration. For the optimal admission control, a dynamic programming is formulated. The state variable keeps track of the number of products for each rental duration, and it is multi-dimensional. To address the computational complexity of the dynamic programming, this paper develops the approximate dynamic programming. In the numerical study, we show that the revenue gain of the dynamic programming is not significant as the initial capacity increases. However, the computational time increases exponentially. In contrast, the heuristic produces a near-optimal solution in a short time window.