TWO-STAGE STOCHASTIC NONLINEAR WINNER DETERMINATION FOR LOGISTICS SERVICE PROCUREMENT AUCTIONS UNDER QUANTITY DISCOUNTS

Quantity discount is a frequently adopted scheme that has not been explicitly investigated in logistics service procurement auctions. This paper focuses on a revised winner determination problem under quantity dis-counts and demand uncertainty for a fourth-party logistics (4PL) provider in a combinatorial reverse auction. To characterize our research problem, a two-stage stochastic nonlinear programming model is constructed. Inspired by the idea of sample average approximation (SAA), the nonlinear model is reformu-lated as a deterministic mixed integer linear programming model by using a linearization technique with superior expressions. Since the reformulation has a large number of decision variables and constraints, we integrate SAA with a dual decomposition Lagrangian relaxation technique (DDLR) to develop a solution method called SAA-DDLR. Numerical experiments are conducted to illustrate the effectiveness and applicability of our model and method. Sen-sitivity analysis reveals that both the 4PL and 3PLs can benefit from the quantity discount scheme. Managerial insights are drawn for the 4PL to run a cost-effective logistics system in the presence of quantity discounts.