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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.

Estimation of stochastic demand in physical distribution in general and efficient transport routs management in particular is emerging as a crucial factor in urban planning domain. It is particularly important in some municipalities such as Tehran where a sound demand management calls for a realistic analysis of the routing system. The methodology involved critically investigating a fuzzy least-squares linear regression approach (FLLRs) to estimate the stochastic demands in the vehicle routing problem (VRP) bearing in mind the customer's preferences order. A FLLR method is proposed in solving the VRP with stochastic demands: approximate-distance fuzzy least-squares (ADFL) estimator ADFL estimator is applied to original data taken from a case study. The SSR values of the ADFL estimator and real demand are obtained and then compared to SSR values of the nominal demand and real demand. Empirical results showed that the proposed method can be viable in solving problems under circumstances of having vague and imprecise performance ratings. The results further proved that application of the ADFL was realistic and efficient estimator to face the sto- chastic demand challenges in vehicle routing system management and solve relevant problems

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