A fuzzy two-stage capacitated continuous p-centmedian vehicle routing problem: A self-adaptive evolutionary

Document Type: Research Paper


1 Student, School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

2 University of Tehran

3 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

4 School of Industrial Engineering, Collage of Engineering, University of Tehran, Iran


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 single-objective 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 meta-heuristics 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.