An inventory model for non-instantaneous deterioration items in a two -echelon Supply chain

Most of the inventory control models assume that items can be stored indefinitely to meet the future demands. However, certain types of commodities either deteriorate or become obsolete in the course of time and hence are unstable. In this study, a mathematical model is presented for a two-echelon supply chain including a buyer and a producer for an inventory integrated system with non-instantaneous of items that demand is probable and follows a normal distribution. Since, the rate of deterioration describes the condition deterioration the goods and regarding the relation between time and deterioration rate is probable rather than the fixed rate of deterioration. In reality, considering the shortages is necessary in both forms of backlogging and lost sales. Therefore, both kinds of shortages are used in the model.
The main goal of this model is determining the optimal ordering policy so that the total cost of supply chain is minimized. The proposed model is solved for some problems by Lingo software. The validity of model is determined by sensitive analysis and the problem is known a NP-hard one, hence a genetic algorithm has been used in order to solve the model problem. The rates of deterioration and confidence level sensitivity analysis have been applied to analyze effect of some important parameters affecting on optimal solution of the inventory model.
Finally, the optimal value of the expected cost of supply chain under integrated and non-integrated decision-making has been determined and compared. The results show the efficiency of algorithm .