Estimating the marginal cost to deliver to individual customers

This paper proposes a scenario sampling-based framework to estimate the expected incremental routing cost required so as to incorporate a target customer into an inherently stochastic supply chain network. Inspired from a real-life setting arising in the distribution of industrial gases, we demonstrate our framework and elucidate the quality of the marginal cost estimates it can provide by sampling instances of the multi-depot vehicle routing problems with inter-depot routes. In order to solve such rich routing problems exactly, we also develop a tailored branch-price-and-cut algorithm, which is shown to be able to solve to optimality instances of up to 70 customers within reasonable time, outperforming existing state-of-the-art methods. Our computational studies further provide insights to the effect that various factors related to the target customer and/or the overall network structure can generally have on the marginal routing costs.