A Mean-Variance Disaster Relief Supply Chain Network Model for Risk Reduction with Stochastic Link Costs, Time Targets, and Demand Uncertainty

Abstract: In this paper, we develop a mean-variance disaster relief supply chain network model with stochastic link costs and time targets for delivery of the relief supplies at the demand points, under demand uncertainty. The humanitarian organization seeks to minimize its expected total operational costs and the total risk in operations with an individual weight assigned to its valuation of the risk, as well as the minimization of expected costs of shortages and surpluses and tardiness penalties associated with the target time goals at the demand points. The risk is captured through the variance of the total operational costs, which is relevant to the reporting of the proper use of funds to stakeholders, including donors. The time goal targets associated with the demand points enable prioritization as to the timely delivery of relief supplies. The framework handles both the pre-positioning of relief supplies, whether local or nonlocal, as well as the procurement (local or nonlocal), transport, and distribution of supplies post-disaster. The time element is captured through link time completion functions as the relief supplies progress along paths in the supply chain network. Each path consists of a series of directed links, from the origin node, which represents the humanitarian organization, to the destination nodes, which are the demand points for the relief supplies. We propose an algorithm, which yields closed form expressions for the variables at each iteration, and demonstrate the efficacy of the framework through a series of illustrative numerical examples, in which trade-offs between local versus nonlocal procurement, postand pre-disaster, are investigated. The numerical examples include a case study on hurricanes hitting Mexico.