A Study On Two Fuzzy Joint Replenishment Models Using Differential Evolution Algorithm

Currently the joint replenishment model focused on the deterministic model, including constraints and costs are determined, and the actual operation of enterprises in general these are uncertain, so we use fuzzy theory for this situation to build a fuzzy environment under the joint replenishment model.Firstly the joint replenishment problem has been proved to be a NP-hard problem.The general derivation cannot reach the optimal solution, which needs to rely on intelligent optimization algorithms, so this thesis designs an efficient modified adaptive differential evolution algorithm (MADE) and proves its effectiveness by testing. Secondly, a fuzzy programming model is designed to minimize the sum of order cost, inventory holding cost and transportation cost by using triangular fuzzy number to represent the fuzzy capital constraints and trapezoid fuzzy number to represent the fuzzy storage capacities constraints. The improved MADE is used to solve the model and the effectiveness is confirmed by a numerical example. Simulation examples were given and comparisons were made between fuzzy resource constraint model and deterministic resource constraint model for 2400 stochastic problems. At last, a fuzzy joint replenishment programming model is designed to minimize the total cost while the minimum order cost and holding cost are regarded as fuzzy numbers. The total cost is defuzzified through the centroid and signed distance approach and the MADE is used to find the optimal solution. The total costs of joint replenishment obtained by two defuzzifying methods are compared and the principle to select the right defuzzifying method which can get a minimal total cost is provided through 16 situations.