Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios

On the Difficulty of Pricing Routes for Stochastic Vehicle Routing Problems Many approaches exist for dealing with the uncertainty in the vehicle routing problem with stochastic demands (VRPSD), but the most popular approach models the VRPSD as a two-stage stochastic program where a recourse policy prescribes actions that handle when the realized demands exceed the vehicle capacity. Similarly to other VRP variants, some state-of-the-art algorithms for the VRPSD use set-partitioning formulations that generate variables (routes) via a pricing problem. All of these algorithms, however, have strong assumptions on the probability distribution of customer demands, a simplification that might not be realistic in some applications. In “Hardness of Pricing Routes for Two-Stage Stochastic Vehicle Routing Problems with Scenarios,” Ota and Fukasawa examine the challenges associated with solving the pricing problem of the VRPSD when the customer demands are given by scenarios. They demonstrate that the VRPSD pricing problem is strongly NP-hard for a wide variety of recourse policies and route relaxations. This highlights the difficulty of developing efficient pricing algorithms for the VRPSD with scenario-based demand models.