Winner determination problem with purchase budget for transportation procurement under uncertain shipment volume

We study a winner determination problem (WDP) to help shippers in determining the winning bids proposed by carriers in a combinatorial auction for transportation service procurement. The winning carriers, together with spot market carriers which may be optional, undertake the shipper’s annual shipment tasks that are uncertain in the auction stage; completing the tasks incurs a total cost. In particular, the shipper wants to control the total cost under a prescribed purchase budget, resulting in a new problem variant—the WDP with purchase budget (B-WDP). To mitigate both the probability and magnitude of cost overrun, we introduce the Essential Riskiness Index (Zhang et al., 2019) as the decision criterion. Considering the inaccuracy in each predicted scenario/sample of shipment volumes, we allow for some perturbation around each sample and formulate a two-stage sample robust optimization model for the B-WDP. We analyze the properties of the model and, via linear decision rule and duality theory, reformulate it as a mixed-integer linear program solvable via state-of-the-art solvers. By extensive comparative studies against the traditional stochastic and robust models for the WDP, we demonstrate that our two-stage sample robust B-WDP model effectively reduces the expectation of cost overrun and the worst-case total cost. Additional sensitivity analysis confirms that our model consistently and effectively helps shippers mitigate cost overrun.