Winner determination for logistics service procurement auctions under disruption risks and quantity discounts

摘要

Disruption risks and quantity discounts have not been explicitly studied in traditional winner determination problems. This paper investigates an innovative winner determination problem with accidental disruptions and quantity discounts for a fourth party logistics provider in a logistics service procurement auction. An effective hybrid strategy that integrates a fortification policy with an outside option policy is developed to mitigate possible disruptions. Integrating the hybrid strategy with a piecewise-linear discount function, a stochastic nonlinear winner determination model is constructed. Utilizing a linearization technique, such a nonlinear winner determination model can be reformulated as a mixed integer linear program. To obtain nearly optimal solutions, a scenario-based approximation method is developed, including a reduced scenario technique and a dual decomposition Lagrangian relaxation technique. Numerical experiments are conducted to illustrate the effectiveness and applicability of the proposed model and method. When the discount parameter decreases or the disruption probability increases, the fortification policy becomes more important for the logistics system. An interesting result indicates that both the auctioneer and bidders may benefit from considering the discount policy. Managerial implications are drawn for fourth party logistics providers to run a reliable logistics system in a cost-effective way.