Bi-Objective Optimization for a Location-Routing Problem with Reliability and Fuzzy Cost

Location and routing problems in emergencies are so important. This paper considers a location–routing problem with reliability by the means of considering the probability of failure occurrence. The problem has two objectives that minimizes the total cost and maximizes the reliability. Maximizing the reliability is expressed as minimizing the expected cost of the failure. In this problem, three kinds of failures are considered, which are: failure of centers, routes and vehicles. Since travel costs is dependent on manyzparameters and hence it is not possible to estimate exactly so they are considered as fuzzy number using linguistic variables. At first, mathematical formulation of the problem is presented, and then because the problem is the NP-hard therefore, meta-heuristics algorithms are used to solve the model. Additionally, a bi-objective discrete firefly algorithm is providedand then in order to evaluate the performance of the algorithm, several test problems are implemented and compared with the NSGA-II. The results show that the biobjective discrete firefly algorithm has a better DM measure; however, it is only suitable for small to medium-sized problems due to the MID measure and it loses its efficiency in larger sizes.