A Distributionally Robust Chance-Constrained Model for Humanitarian Relief Network Design

36 Pages Posted: 24 Sep 2021 Last revised: 8 Apr 2022

See all articles by Zhenlong Jiang

Zhenlong Jiang

George Mason University - The Volgenau School of Information Technology and Engineering

Ran Ji

George Mason University

Sasha Dong

affiliation not provided to SSRN

Date Written: September 14, 2021

Abstract

We propose a novel two-stage distributionally robust joint chance-constrained (DRJCC) model to design a resilient humanitarian relief network with uncertainties in demand and unit allocation cost of relief items in the post-disaster environment. This model determines the locations of the supply facilities with pre-positioning inventory levels and the transportation plans. We investigate the problem under two types of ambiguity sets: moment-based ambiguity and Wasserstein ambiguity. For moment-based ambiguity, we reformulate the problem into a mixed-integer conic program and solve it efficiently via a sequential optimization procedure by finding the optimal scaling parameters iteratively. For Wasserstein ambiguity, we reformulate the problem into a mixed-integer linear program. We conduct comprehensive numerical experiments to assess the computational efficiency of the proposed reformulation and algorithmic framework, and evaluate the reliability of the generated network by the proposed model. Through a case study in the Gulf Coast area, we demonstrate that the DRJCC model under Wasserstein ambiguity achieves a better trade-off between cost and network reliability in out-of-sample tests than the moment-based DRJCC model and the classical stochastic programming model.

Keywords: Distributionally Robust Optimization, Chance-Constrained Programming, Humanitarian Relief Network, Network Reliability

JEL Classification: Q54

Suggested Citation

Jiang, Zhenlong and Ji, Ran and Dong, Sasha, A Distributionally Robust Chance-Constrained Model for Humanitarian Relief Network Design (September 14, 2021). Available at SSRN: https://ssrn.com/abstract=3929286 or http://dx.doi.org/10.2139/ssrn.3929286

Zhenlong Jiang

George Mason University - The Volgenau School of Information Technology and Engineering ( email )

Fairfax, VA
United States

Ran Ji (Contact Author)

George Mason University ( email )

Fairfax, VA
United States

Sasha Dong

affiliation not provided to SSRN

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