AN INTEGRATED PRODUCTION-\INVENTORY POLICY IN A TWO-LAYER SUPPLY CHAIN FOR A DETERIORATING ITEM WITH QUANTITY DISCOUNT

Effective coordination in a supply chain plays a vital role in improving its efficiency. This becomes more critical when it comes to deteriorating materials and products in order to reduce a huge amount of waste or demand fluctuations. Integrated management can effectively reduce the total cost including waste costs, holding costs, shipping, and delivering costs and increase the income, especially when the price or even the demand is affected by the freshness. In this article, an integrated production-inventory system for a perishable product in a two-echelon supply chain, including a producer and multi-retailers, is considered. The quality of raw material and finished product varies at the holding interval and the price is an age-dependent function. Volume discounts are available. The shortage is not allowed. The rates of production and demand are considered determined and fixed. The numbers of deliveries to retailers are not essentially equal. The objective is to determine the number of raw material deliveries to the producer and the number of deliveries from the producer to each retailer in a production cycle in a way that total profit is maximized. This combination of assumptions has not been considered in the literature yet. A nonlinear mixed-integer programming model is developed for the problem. Because of the complexity of the problem, a metaheuristic algorithm is employed to solve the numerical examples. An example is solved and sensitivity analysis is done using a genetic algorithm. The results show that the optimal number of orders and also the economic order sizes change corresponding to the rate of deterioration such that the higher the rate of deterioration, the larger the number of orders and the lower the size of each order. The profit almost increases significantly in the presence of volume discounts in all cases and also increases when a different number of delivers per each cycle for different retailers is possible.