An integrated location-routing problem with post-disaster relief distribution

Quick and wise decisions made regarding depot location and vehicle routing in emergency logistics play an important role in the relief of affected areas after a disaster. We address an integrated location-routing problem with post-disaster relief distribution, seeking to design an assignment system for a fleet of homogeneous rescue vehicles from a set of candidate depot locations to deliver relief supplies to affected areas after a disaster. Each affected area is associated with a soft time window, during which it is expected to receive the relief supplies. Two objective functions are involved: the penalty for time window violation, and the total operational cost comprising the depot opening cost, vehicle fixed cost, and transport cost. The overall objective to find the opened transfer depots, the number of vehicles used, and the route of each used vehicle so as to identify the approximate Pareto frontier comprising the trade-offs between the conflicting objectives. To achieve this, we develop a hybrid ant colony optimization algorithm for which we use particles as operators to more widely search for enabled depots among alternative ones and then assign clients to them so that ants can find the most effective and balanced vehicle routes for every selected depot. We conduct extensive numerical experiments to assess the performance of the developed algorithm by comparing with three algorithms. The numerical results confirm the efficacy of the developed method in terms of its computational efficiency and solution quality.