Fuzzy MCDM for weight of object’s phrase in location routing problem

•A new analytical model for determining the relative weights of evaluation criteria.•Selection of locations for plants and central depots (CD), to minimize total network cost.•A two phase heuristic simulated annealing is presented as solution methodology.

This study is divided in two parts. In first Phase, we come up with a new analytical model for determining the relative weights of evaluation criteria using trapezium fuzzy numbers in decision making problems, and then in the second part, the previous part integrated with the presented LRP. The LRP is a three layer location-routing problem consisting of plants, depots, and customers. In this network, products are transferred from plants to depots and from there to customers, phrases of objective function have weights, located at the pre-determined locations, customers demand their requirements stochastically. The goal is to select locations for plants and central depots (CD), among sets of potential locations, allocate customers to DCs, find routes from DCs to customers, to minimize total network cost. A two phase heuristic simulated annealing is presented as solution methodology. Test problem is designed and solved by the developed algorithm to evaluate the presented solution approach. Results show that the integrated decision leads to saving on the network cost.