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 oneechelon 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.

The flexible job shop scheduling problem (FJSP) is an extension of the classical job shop scheduling problem (JSP) which allows an operation to be processed by any machine from a given set of machines. FJSP is NP-hard and presents two major difficulties. The first is to assign each operation to a machine out of a set of capable machines; and the second deals with sequencing the assigned operations on the machines. However, it is quite difficult to obtain an optimal solution to this problem in medium and large size problems with traditional optimization approaches. In this paper, a memetic algorithm (MA) for flexible job shop scheduling with overlapping operations is proposed that solves the FJSP to minimize makespan. We also proposed a heuristic that uses the critical path method (CPM) in order to improve the results of MA and reduce the objective function. The experimental results of MA and CPM show that our approach is capable of achieving the optimal solution for small size problems and near-optimal solutions for medium and large size problems in a reasonable time.

Determining the optimal inventory control and selling price for deteriorating items is of great significance. In this paper, a joint pricing and inventory control model for deteriorating items with price-and time-dependent demand rate and time-dependent deteriorating rate with partial backlogging is considered. The objective is to determine the optimal price, the replenishment time, and economic order quantity such that the total profit per unit time is maximized. After modeling the problem, an algorithm is proposed to solve the resulted problem. We also prove that the problem statement is concave function and the optimal solution is indeed global.

This paper considers an inventory control policy for a two-echelon inventory control system with one supplier-one buyer. We consider the case of deteriorating items which lead to shortage in supply chain. Therefore, it is necessary to decrease the deterioration rate by adding some specification to the packaging of these items that is known as active packaging. Although this packaging can reduce the deteriorating rate of products, but may be increases the cost of both supplier and buyer. Because of the complexity of the mathematical model, a genetic algorithm has been developed to determine the best policy of this inventory control system.

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