Heuristic approaches for the multiperiod location-transportation problem with reuse of vehicles in emergency logistics

The coordination among the different actors in relief chains is crucial to provide effective and efficient response in emergency logistics. By recognizing this fact, we have developed two stochastic mixed-integer programming models to integrate and coordinate facility location, transportation and fleet sizing decisions in a multi-period, multi-commodity, and multi-modal context under uncertainty. One model even considers the option of reusing vehicles to cover extra routes within the same time period in an attempt to save overall resources and improve service levels. Typical uncertainty in victims׳ needs, incoming supply, inventory conditions, and roads availability are modeled through a set of scenarios representing plausible disaster impacts. To solve instances of practical size, we have devised relax-and-fix and fix-and-optimize heuristics based on decompositions by time, scenario, and stage. The proposed instances entail characteristics of the megadisaster in the Mountain Region of Rio de Janeiro State in Brazil. The results suggest that the integration of decisions in a multiperiod context and the option of reusing vehicles reduce total costs, thus improving the overall performance of the relief operations. Also, the time-decomposition fix-and-optimize heuristic outperforms the CPLEX solver in terms of elapsed times and optimality gaps, mainly in moderate-size instances. Finally, we show the importance to explicitly consider randomness instead of using simpler worst-case scenario approaches.