The present study reviews different studies on inventory control of deteriorating items in chain supply published over the period 1963- 2013. The study investigates supply chain of the items in terms of various perspectives. Finally, the summary of the studies is shown in two tables for one-echelon and multi-echelon supply chain including the main information and assumptions of each paper. In the mentioned tables, the papers were classified in terms of the type of demand rate, deterioration rate, solution procedure and findings. It can be said that no analysis on the results was done in the present study and it can be only used as a good reference in the study field for other researchers.

In this article, a multi-echelon supply chain for growing and deteriorating items, where the grower has a lot of live newborn items (growing) is discussed. The grower transfers the matured inventory to the processor in each shipment. The processor begins to process the stock as a ready-sale product in the market. The processor also delivers the processed inventory to the retailer in each shipment in the non-processing period of his cycle length. Then the processor offers trade credit to the retailer and makes the retailer agree to share a portion of his profit with him. The product’s life cycle when in the hand of the retailer is certain and it expires after some time t. Carbon emission during processing is considered while packing and preserving the livestock for sale. Depending on these assumptions, there are six possibilities to discuss profit values. Sensitivity analysis was also brought to verify the optimal determined values. The profit-sharing sharing method’s outcome benefits the processor and the retailer more.