The Minimum Unmet Demand Stochastic Vehicle Routing Problem

In this paper, we are interested in routing vehicles to minimize unmet demand under uncertainty. Such a problem arises in situations with large demand or tight deadlines, so that routes that satisfy all demand points are difficult or impossible to obtain. An important application is the distribution of medical supplies to respond to large-scale emergencies, such as natural disasters or terrorist attacks. We consider a routing problem with uncertainty both on demand and travel time. We present a chance constrained formulation of the problem that is equivalent to a deterministic problem with modified demand and travel time parameters, under mild assumptions on the distribution of stochastic parameters. A tabu heuristic is proposed to solve this MIP and simulations are conducted to evaluate the quality of routes generated from both deterministic and chance constrained formulations. We observe that chance constrained routes can reduce the unmet demand by around 2%-6% for moderately tight deadline and total supply constraints.