The Stochastic Vehicle Routing Problem for Minimum Unmet Demand
In this chapter, we are interested in routing vehicles to minimize unmet demand with uncertain demand and travel time parameters. 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 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 and relate it to a robust optimization approach. 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.
KeywordsTabu Search Vehicle Rout Problem Demand Point Demand Node Unmet Demand
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This research was supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE), grant number EMW-2004-GR-0112. However, any opinions, findings, and conclusions or recommendations in this document are those of the author(s) and do not necessarily reflect views of the U.S. Department of Homeland Security. Also the authors wish to thank Ilgaz Sungur, Hongzhong Jia, Harry Bowman, Richard Larson and Terry O’Sullivan for their valuable input and comments for the improvement of this chapter.
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