The Vehicle Routing Problem with Stochastic Demand and Duration Constraints

Time considerations have been largely ignored in the study of vehicle routing problems with stochastic demands, even though they are crucial in practice. We show that tour duration limits can effectively and efficiently be incorporated in solution approaches that build fixed, or a priori, tours for such problems. We do so by assuming that each tour must be duration-feasible for all demand realizations, and determine the maximum duration of a given delivery tour by solving the optimization problem of an adversary. A computational study demonstrates the approach, and shows that enforcing tour duration limits impacts the structure of nearly-best solutions and may create the need for additional tours. However, for the instances considered, the price paid for robustness is small as the increase in total expected tour duration is modest.