Abstract
To address the shortage of relief in disaster areas during the early stages after an earthquake, a location-routing problem (LRP) was studied from the perspective of fairness. A multi-objective model for the fair LRP was developed by lexicographic order object optimal method in consideration of the urgent window constraints, partial road damage, multimodal relief delivery, disaster severity, and vulnerability of each demand node when its demand is not satisfied. The goals of this model are to minimize (1) the maximum loss of demand node, (2) the total loss of demand node, and (3) the maximum time required for the demand node to receive relief. A hybrid heuristic algorithm was proposed to solve the model. Finally, the utility and fairness of the model and algorithm were demonstrated by a case study during the first day after the great Wenchuan earthquake in China.
Highlights
In recent years, earthquake disasters have caused large numbers of human casualties and property losses
The goals of the location-routing problem (LRP) model were to (1) minimize the maximum loss of demand nodes, which is the index of fair allocation of relief, (2) minimize the total loss of all nodes, which is the index of relief utility, and (3) minimize the maximum time required for demand nodes to receive relief, which is the index of efficiency of relief distribution
We define i as the loss of demand node i when its demand is unsatisfied; D is the total amount of allocated relief at all nodes; γ is the severity of the disaster, which is expressed by the earthquake intensity, degree of damage, and the disaster category; and δi is the vulnerability of demand node i when its demand is unsatisfied, which mainly depends on its location, personnel composition, extent of disaster, capability for disaster reduction, and disaster-bearing sensitivity (Ge et al [46])
Summary
Earthquake disasters have caused large numbers of human casualties and property losses. Ma et al (2014) considered a fuzzy multi-objective open LRP for relief delivery and developed a chance-constrained programming open LRP model with the objectives of minimizing the total delivery time and total system cost They designed a hybrid genetic algorithm to solve the proposed problem [13]. To restore the connectivity of post-disaster networks, Akbari and Akbari (2017) studied a multi-vehicle synchronized arc routing problem They developed an exact mixed integer programming formulation (MIP) for relief delivery, and proposed a heuristic based on an MIP-relaxation and a local search algorithm to solve this problem [27]. The experimental results show that the proposed approaches quickly solve the relief distribution program in the prescribed period after the earthquake, and take fairness and utility into consideration
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