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 revised winner determination problem under quantity discounts and demand uncertainty for fourth-party (4PL) provider combinatorial reverse auction. To characterize our research problem, two-stage stochastic nonlinear programming model constructed. Inspired by the idea of sample average approximation (SAA), reformulated as deterministic mixed integer linear using linearization technique with superior expressions. Since reformulation large number decision variables constraints, we integrate SAA dual decomposition Lagrangian relaxation (DDLR) to develop solution method called SAA-DDLR. Numerical experiments are conducted illustrate effectiveness applicability method. Sensitivity analysis reveals both 4PL 3PLs can benefit from scheme. Managerial insights drawn run cost-effective system presence discounts.