genetic algorithm and hybrid method to minimize total distribution cost in multi-level supply chain

in this paper, the distribution network for multi-level supply chain has been studied. products produced in factories are sent to customers through warehouses and distribution centers based on specific demands. warehouses as holding inventory facilities are located close to factories and the distribution centers are placed in the most accessible locations for services near customers. each item is sent from factories to customers through warehouses and distribution centers. therefore, a model was designed to minimize the total distribution costs in a multi-level supply chain network. the main goal of this paper is offering a model to determine a replenishment program, to determine the values of inventory distributed to reduce the cost of lost sales, and also to determine delivery routes to reduce transport costs and determine the values stored to reduce the holding costs. a mixed integer programming for the suggested model is formulated. therefore, the objective function of this model is to minimize the total costs of distribution network including holding cost, lost sale cost, replenishment cost and transportation costs. the model shows that the problem is np-hard and thus cannot be solved by lingo for large size problems. hence, two meta-heuristics methods for solving the model have been used. in the first part, we have used the genetic algorithm that according to the specification of the suggested model was programmed to earn high quality solution in short run time. secondly we have used a hybrid algorithm that simultaneously takes advantage of genetic and simulation annealing algorithms. for the hybrid algorithm, the initial solution was earned through the implementation of genetic algorithms and then this solution was improved using simulated annealing algorithm. computational results indicate the superiority of the hybrid algorithm for small and medium size problems but for larger problems it is recommended to use the genetic algorithm alone.