A multi-objective distributionally robust model for sustainable last mile relief network design problem
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A multi-objective distributionally robust model for sustainable last mile relief network design problem Peiyu Zhang1 · Yankui Liu2 · Guoqing Yang2,3
· Guoqing Zhang3
Accepted: 24 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Natural disasters not only inflict massive life and economic losses but also result in psychological damage to survivors, at times even causing social unrest. It is necessary to design a sustainable last mile relief network for distributing relief supplies regarding social factors, disaster relief efficiency as well as the economic cost of three perspectives in terms of sustainability. We establish a multi-objective distributionally robust optimization model for a sustainable last mile relief network problem that maximizes the equitable distribution of relief supplies and simultaneously minimizes the transportation time and operation cost. Under the partial probability information of uncertainties, such as the disaster situation, transportation time, freight, road capacity, and demand, we characterize the uncertain variables in an ambiguity set incorporating the bounds, means and the mean absolute deviations. Then, the bounds on the objective values and the safe approximations of the chance constraints are deduced under the ambiguity sets. Based on a revised multi-choice goal programming approach, we obtain a computationally tractable framework of the multi-objective model. To verify the effectiveness of the model and methods, a case study of the Banten tsunami is illustrated. The results demonstrate our proposed model can obtain a trade-off between the equitability, timeliness and economics for relief distribution in a relief network. Keywords Last mile relief network · Sustainability · Equitable distribution · Distributionally robust optimization · Multi-objective · Ambiguity set
1 Introduction Natural disasters such as earthquakes, tsunamis, hurricanes and floods threaten human lives and inflict massive economic losses (Jabbour et al. 2019). In May 2005, a magnitude 8.0
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Guoqing Yang [email protected]
1
College of Mathematics and Information Science, Hebei University, Baoding 071002, Hebei, China
2
School of Management, Hebei University, Baoding 071002, Hebei, China
3
Department of Mechanical, Automotive & Materials Engineering, University of Windsor, Windsor, ON, Canada
123
Annals of Operations Research
earthquake struck Wenchuan County in Sichuan Province. This earthquake resulted in more than 70,000 casualties and damaged the infrastructure, incurring 120 million losses. According to the statistics of Dubey et al. (2019), there have been 281 catastrophic climate-related events worldwide, with 10,733 deaths and more than 60 million affected. Therefore, we have seen some scholars make great efforts in implementing rescue operations after disasters that save lives and reduces losses. Behl and Dutta (2019) argued that nations should make rapid responses for disasters and relief networks one of the prominent ways to transfer such bad
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