An M/M/C/K queueing system in an inventory routing problem considering congestion and response time for post-disaster humanitarian relief: a case study

Due to the randomness and unpredictability of many disasters, it is essential to be prepared to face difficult conditions after a disaster to reduce human casualties and meet the needs of the people. After the disaster, one of the most essential measures is to deliver relief supplies to those affected by the disaster. Therefore, this paper aims to assign demand points to the warehouses as well as routing their related relief vehicles after a disaster considering convergence in the border warehouses.

This research proposes a multi-objective, multi-commodity and multi-period queueing-inventory-routing problem in which a queuing system has been applied to reduce the congestion in the borders of the affected zones. To show the validity of the proposed model, a small-size problem has been solved using exact methods. Moreover, to deal with the complexity of the problem, a metaheuristic algorithm has been utilized to solve the large dimensions of the problem. Finally, various sensitivity analyses have been performed to determine the effects of different parameters on the optimal response.

According to the results, the proposed model can optimize the objective functions simultaneously, in which decision-makers can determine their priority according to the condition by using the sensitivity analysis results.

The focus of the research is on delivering relief items to the affected people on time and at the lowest cost, in addition to preventing long queues at the entrances to the affected areas.