In this article, a multi objective model is presented to select and allocate the order to suppliers in uncertainty condition and in a multi source, multi customer and multiproduct case in a multi period state at two levels of supply chain. Objective functions considered in this study as the measures to evaluate suppliers are cost including purchase, transportation and ordering costs, timely delivering, shipment quality or wastages which are amongst major quality aspects, partial and general coverage of suppliers in respect of distance and finally suppliers weights making the products orders amount more realistic. The major limitations are price discount for products by suppliers which are calculated using signal function. In addition, suppliers weights in the fifth objective function is calculated using fuzzy Topsis technique. Lateness and wastes parameters in this model are considered as uncertain and random triangular fuzzy number. Finally the multi objective model is solved using two multi objective algorithms of Non-dominated Sorting Genetic Algorithm (NSGA-II) and Particle Swarm Optimization (PSO) and the results are analyzed using quantitative criteria Taguchi technique was used to regulate the parameters of two algorithms.
