Optimizing a hybrid vendor-managed inventory and transportation problem with fuzzy demand: An improved particle swarm optimization algorithm

Vendor-managed inventory (VMI) is a popular policy in supply chain management (SCM) to decrease bullwhip effect. Since the transportation cost plays an important role in VMI and because the demands are often fuzzy, this paper develops a VMI model in a multi-retailer single-vendor SCM under the consignment stock policy. The aim is to find optimal retailers' order quantities so that the total inventory and transportation cost are minimized while several constraints are satisfied. Because of the NP-hardness of the problem, an algorithm based on particle swarm optimization (PSO) is proposed to find a near optimum solution, where the centroid defuzzification method is employed for defuzzification. Since there is no benchmark available in the literature, another meta-heuristic, namely genetic algorithm (GA), is presented in order to verify the solution obtained by PSO. Besides, to make PSO faster in finding a solution, it is improved by a local search. The parameters of both algorithms are calibrated using the Taguchi method to have better quality solutions. At the end, conclusions are made and future research is recommended.