Linearization technique with superior expressions for centralized planning problem with discount policy - Yang, Fang; Huang, Yao-Huei (Physica A, 2020)
This paper studies a centralized planning problem (CPP), which is a variant of the winner determination problem (WDP) in transportation service procurement. The WDP contains one shipper with multiple depots, and multiple carriers. Traditionally, the shipper solves the WDP to obtain winning carriers for serving lanes. In this paper, the shipper specifically considers J possible locations, and then only p locations can be selected as depots. These carriers provided the best quantity discount are able to obtain the best chance of being winners for serving lanes. This study proposes a mixed-integer nonlinear programming (MINP) model for the CPP. The non-convex property of the MINP makes the model difficult to find an exact global optimal solution efficiently and effectively. To overcome the difficulty, the MINP model can be converted into a mixed-integer linear programming (MILP) model to obtain an optimal solution by utilizing the proposed linearization technique with superior expressions. Numerical experiments also show the usefulness of the proposed model, and indicate that moderately sized realistic instances can be solved efficiently and effectively.