Routing and scheduling hazardous material shipments: Nash game approach

Abstract

The shipment of hazardous materials (hazmats) received considerable attention as the consequences of the incidents, including environmental pollution, economic damage, injuries, and fatalities are extremely undesirable. Previous research mainly focused on the shipment of hazmats under known link incident probabilities. Using the Nash game theory approach, this paper studies the integrated routing and scheduling hazmat shipment problem with unknown link incident probabilities. The problem is formulated as a route-based maxmin problem over the space–time expanded network proposed in this paper. This route-based problem is decomposed into a link-based linear problem so that linear programming solution methods can be adopted. To solve for solutions, this paper proposes two methods. The convergences of these methods are discussed. A numerical example is provided to illustrate the two proposed methodologies and the solution properties of the maxmin problem. The implications of these solution properties are also discussed. This approach helps find critical links over a time–space hazmat shipment network.

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