A multitiered supply chain network equilibrium model for disaster relief with capacitated freight service provision

Abstract

In this paper, a multitiered supply chain network equilibrium model is constructed, consisting of multiple humanitarian organizations, who seek to purchase services from multiple competing freight (logistic) service providers, for transportation of disaster relief supplies to multiple points of demand for distribution to victims. The freight service providers are faced with capacities associated with the volume of shipments that they can transport. We capture the behavior of the humanitarian organizations who individually minimize the total cost associated with payments for the freight transportation and their transaction costs. We also identify the profit-maximizing behavior of the freight service providers. The governing supply chain network equilibrium conditions are formulated as a variational inequality problem and conditions for existence given. We propose an algorithm for the computation of the equilibrium disaster relief item flows and Lagrange multipliers associated with the freight capacity constraints and provide conditions for convergence. The algorithm is then applied to several numerical examples comprising a case study focusing on an international healthcare crisis. In the case study, we explore the impacts of the addition of a freight service provider as well as that of a humanitarian organization on the profits of freight service providers and on the costs incurred by the humanitarian organizations. The theoretical and numerical results in this paper advance game theory frameworks for humanitarian operations and disaster relief, an area in which there is only a limited literature.