Investigating Zone Pricing in a Location-Routing Problem Using a Variable Neighborhood Search Algorithm

In this paper, we assume a firm tries to determine the optimal price, vehicle route and location of the depot in each zone to maximise its profit. Therefore, in this paper zone pricing is studied which contributes to the literature of location-routing problems (LRP). Zone pricing is one of the most important pricing policies that are prevalently used by many companies. The proposed problem is very applicable in the product distribution, such as fruit. The problem is formulated by two models consisting of a node and flow based model. The resulting nonlinear mixed integer models are approximated by a piecewise linearization method and the performance of them is compared. To cope with real-world cases, a variable neighborhood search (VNS) algorithm is developed and implemented in some instances. Three different combinations of local search are defined and the performance of them is compared with each other and two proposed models. The results of the computational study confirm that the suggested algorithm solves large instances efficiently compared to the proposed mathematical models. Moreover, the results show that the flow based model uses less computational time in comparison with the node based model.