Robust Vehicle Routing under Uncertainty of Customer Demand

Abstract

This paper discusses a version of the vehicle routing problem with stochastic demand (VRPSD). In this problem, a customer's demand is characterized by a known probability distribution and the customer's actual demand is only revealed when the vehicle reaches the customer location. In such a problem, two approaches are proposed. The objective of the first approach is to find a route sequence that minimizes the expected travel cost. This approach has good performance stochastically; however, when it is applied an upper bound on the travel cost cannot be guaranteed. The second approach is a robust approach implemented through chance-constrained programming. The objective is to find a route sequence that is robust with respect to uncertain demands and, at the same time, minimize the travel cost. When the probability that the vehicle's route is executed as planned is high, the route is said to be robust. In chance-constrained programming, the maximum allowable probability of route failure can be specified by the planner. The chance-constrained approach may have a higher travel cost than the first approach; however, it can guarantee a boundary for worst case performance. In this paper, we employ the chance-constrained approach as a robust method. We formulate VRPSD as a set-covering problem and solve the problem using column generation. We propose an efficient method for designing the route sequences that enable the maximum allowable probability of route failure to be specified.