Alternative solution algorithm for winner determination problem with quantity discount of transportation service procurement

This study examines the winner determination problem (WDP) for the procurement of transportation service. The problem contains three important roles, namely, shippers, carriers, and third-party carriers. Shippers determine the service lanes that can be outsourced to carriers so that the transportation service cost may be reduced. The WDP can be formulated as a mixed integer linear programming (MILP) model. However, when solving a general MILP model, it is easy to fall into the imbalanced issue of branch-and-bound trees, such that the computational time becomes longer. This study proposes a deterministic model with a powerful and significant theoretical mechanism to conquer the imbalanced issue. Solving the proposed model can minimize the service costs subject to each lane being served by carriers and consider the quantity discount. The most important objective in this study is to identify an iterative algorithm that embeds the proposed model, which presents all alternative solutions for shippers to consider better options. Numerical experiment is also presented to confirm the usefulness of the proposed method. (C) 2019 Elsevier B.V. All rights reserved.