A Fuzzy Two-Stage Capacitated Continuous Pcentmedian Vehicle Routing Problem: A Selfadaptive Evolutionary

In this paper, a two-stage continuous p-center and p-median (namely p-centmedian) problem is developed. in the first step, a location problem is studied to compare the differences between the p-center and p-median by considering facility disruption. p-center problems are common in emergency situations with aim of minimizing the maximum distance between the facilities and costumers, while p-median problem aim is to minimize the total spent distance. moreover, an integer linear programming is developed to deal with a time-window multi-depot capacitated vehicle routing problem in order to optimize the flows between facilities. this paper compares the mentioned p-center and p-median effects along with the vehicle routing problem as a two-step integrate problem. since both steps are np-hard, to deal with the problem in both stages a possibilistic programming, fuzzy singleobjective programming is developed and solved by an efficient algorithm, namely self-adaptive differential evolution algorithm. considering demand as a fuzzy parameter is an important factor and makes the problem more realistic, this feature is more considerable in emergency situations such as p-center problems. to improve the performance of results, the taguchi method is used. in order to validate the results of the mentioned algorithms of small-sized test problems are compared with gams, also other valid metaheuristics are developed to be compared with the proposed algorithm in large-sized problems. the results show the capability of algorithm to generate near-optimal solutions. also, the results demonstrate the p-median problem is more volatile against variation in the parameters while the p-center problem is more expensive.