Freight Service Provision for Disaster Relief: A Competitive Network Model with Computations

In this paper, we develop a competitive freight service provision network model for disaster relief. A humanitarian relief organization is interested in determining its most cost-effective deliveries of needed supplies in a crisis setting. Multiple freight service providers are engaged in competition to acquire the business of carrying the supplies in the amounts desired to the destinations. We describe the objective functions faced by the various decisionmakers and their underlying constraints, and present the optimality conditions. We then define the freight service provision network equilibrium for disaster relief and formulate it as a variational inequality problem. We provide qualitative results for the equilibrium product shipment pattern in terms of existence and uniqueness. For completeness, we also construct a new cooperative system-optimization model and discuss the price of anarchy relating the two models, along with additional theoretical results. In addition, we propose algorithmic schemes that take advantage of the underlying network structure of the problem. We present a case study on the shipment of personal protection equipment (PPE) supplies in the context of the Ebola humanitarian healthcare crisis in west Africa. The computational results in this paper yield insights on the equilibrium shipment and price patterns in the freight service provision sector for humanitarian operations in terms of enhanced or reduced competition, as well as increases in demand.