Meso-parametric value function approximation for dynamic customer acceptances in delivery routing

The rise of mobile communication, ample computing power, and Amazon’s training of customers has led to last-mile delivery challenges and created struggles for companies seeking to budget their limited delivery resources efficiently to generate enough revenue. In this paper, we examine the capacitated customer acceptance problem with stochastic requests (CAPSR), a problem in which a company seeks to maximize expected revenue by accepting or rejecting requests. Each accepted request generates revenue and must be routed, consuming driver time and vehicle capacity. To solve the problem, we introduce a novel method of value function approximation (VFA). Conventionally, VFAs are either parametric (P-VFAs) or non-parametric (N-VFAs). Both VFAs have advantages and shortcomings and their performances rely significantly on the structure of the underlying problem. To combine the advantages and to alleviate the shortcomings of P-VFA and N-VFA used individually, we present a novel method, meso-parametric value function approximation (M-VFA). The results of computational experiments show that the M-VFA outperforms benchmarks for the CAPSR and show M-VFA offers the advantages of the individual VFAs while alleviating their shortcomings. Most importantly, we demonstrate that simultaneous approximations lead to better outcomes than either N- and P-VFA individually or some ex-post combination.