A two-phase local search with a discrete-event heuristic for the omnichannel vehicle routing problem

This work tackles a pick up and delivery vehicle routing problem that emerges from the integration of delivery problems from two neighbouring layers of a supply chain: (i) retailer replenishment; and (ii) online customers deliveries, where online customer orders have to be picked up from retailers on route. This integration is motivated by recent developments in marketing, e.g.: the move to the omnichannel marketing paradigm, in which companies manage multiple sales channels in a seamless, unified, and integrated way. This paper proposes a novel model and an original solving approach. In order to tackle the complex capacity constraints, previous models propose to solve a delivery vehicle assignment problem before solving the associated vehicle routing problem. In contrast, our model deals with the whole routing problem by considering only the capacity feasible routing decisions. Our solving approach is based on a two-phase algorithm. In the first phase, a discrete-event constructive heuristic is employed. In the second phase, the most 'promising' solutions obtained in the previous phase are refined using a sequence of local search neighbourhoods. A series of extensive computational experiments show that our algorithm is able to identify new best-known solutions for the vast majority of problem instances. Also, for a set of small instances we obtain improved lower bounds compared to a previously proposed lower bound formulation.