A simheuristic algorithm for solving the stochastic omnichannel vehicle routing problem with pick-up and delivery

Advances in information and communication technologies have made possible the emergence of new shopping channels. The so-called ‘omnichannel’ retailing mode allows customers to shop for products online and receive them at home. This paper focuses on the omnichannel delivery concept for the retailing industry, which addresses the replenishment of a set of retail stores and the direct shipment of the products to customers within an integrated vehicle routing formulation. Due to its NP-Hardness, a constructive heuristic, which is extended into a biased-randomized heuristic and which is embedded into a multi-start procedure, is introduced for solving the large-sized instances of the problem. Next, the problem is enriched by considering a more realistic scenario in which travel times are modeled as random variables. For dealing with the stochastic version of the problem, a simheuristic algorithm is proposed. A series of computational experiments contribute to illustrate how our simheuristic can provide reliable and low-cost solutions under uncertain conditions.