Omnichannel logistics network design with integrated customer preference for deliveries and returns

This paper proposes a mixed integer program (MIP) for the network design problem of a parcel carrier that manages online orders from omnichannel retailers. The network includes several types of facilities, such as city distribution centers, intermediary depots, parcel offices, as well as collect channel points, such as automated parcel stations (APS), stores or kiosks. The model formulation takes into account the influence of these collection points on consumer choice and the maximum distance customers are willing to walk to reach them. Realistic transportation costs are also considered, including detailed long haul costs and delivery costs in an area. The transportation costs inside an area are estimated via the Continuous Approximation proposed by Newell (1971) and Newell (1973), which results in a simpler problem than a location-routing problem, however, at the cost of losing linearity. For a special case of the problem, we propose a heuristic that, in our experimental setting, is on average 42.5 faster than the overall MIP and gives solutions within 1.02% of the optimum. Finally, we use the model to discuss the network design of a Spanish parcel carrier operating in Madrid.