Shaolong Hu, Chuanfeng Han, Zhijie Sasha Dong, Lingpeng Meng

“Transportation Research Part B” 123 (2019) 64–87

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The authors develop a multi-stage stochastic programming model for disaster relief distribution with consideration of multiple types of vehicles, fluctuation of rental, and the state of road network and propose a progressive hedging algorithm (PHA) for solving the model in large-scale size. Based on a real-world case of Yaan earthquake in China, numerical experiments are presented to study the applicability of the proposed model and demonstrate the effectiveness of the proposed PHA. Useful managerial insights are provided by conducting numerical analysis.

About the author

Shaolong Hu:School of Economics and Management, Tongji University;Texas State University
Chuanfeng Han: professor, School of Economics and Management,Tongji University. The main research directions are management system and system engineering, public security and social governance, industrial economy and regional development.
Zhijie Sasha Dong:Texas State University
Lingpeng Meng:China Institute of FTZ Supply Chain, Shanghai Maritime University

Keywords

Emergency logistics; Transportation; Uncertain and dynamic road capacity; Multi-stage stochastic programming; Progressive hedging algorithm

Brief introduction

Large amounts of relief supplies are required in the aftermath of a major disaster. Satisfying victims’ needs is crucial to the success of disaster relief operations, as a lack of relief supplies may cause suffering and life loss for victims. Relief supplies are usually insufficient due to damages to local inventory and markets. Therefore, procuring relief supplies from distant locations, and transporting them to the disaster-affected areas within a given time frame is of great importance. There are two challenges in relief distribution of current common disaster practice: (1) The number of vehicles and costs for using them vary. (2) The state of road network also vary. Motivated by the significance of developing relief distribution plans, this paper studies a relief distribution problem with consideration of multiple types of vehicles, fluctuation of rental, and the state of road network to quickly respond to natural disasters.

Relief supplies are transported to the disaster region and stored in selected temporary warehouses. Then, the “last mile distribution” has to be carried out according to the differential demands of disaster-affected locations. Motivated by the relief practice, the authors consider relief distribution as a transshipment problem. The transshipment problem is formulated as a multi-stage stochastic programming model with consideration of multiple types of vehicles, fluctuation of vehicle rental cost, and the state of road network. A scenario-based approach is applied to represent the uncertain and dynamic road capacity, wherein a scenario tree is employed to demonstrate the decision process of multi-stage relief distribution. As the multi-stage stochastic programming models are difficult to be solved and time-consuming even for small-sized instances, this study proposes a progressive hedging algorithm for solving the proposed model. Based on real-world case data, numerical experiments are performed to study the applicability of our model and explore its managerial implications for disaster relief distribution. An appropriate distribution plan can be especially beneficial in terms of saving costs, utilizing road network, and satisfying victims’ needs.

Based on the results of the numerical analysis, several practical implications are identified in this study: (1) The larger the quantity of initial supplies reserved in areas that are prone to earthquakes, the more time- and cost-efficiencies can be gained by relief distribution operations. (2) The expansion of fleet size should guarantee that increasing a vehicle can bring a large marginal decrease in penalty cost and total cost. (3) Relief agencies should focus on being cost-efficient in long distance transportation by negotiating for low transportation fees. They should focus on the reliability of local distribution by preparing backup distribution plans.