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  A product life cycle is the life span of a product in which the period begins with the initial product specification and ends with the withdrawal from the market of both the product and its support. A product life cycle can be divided into several stages characterized by the revenue generated by the product. This study investigates inventory control policies in a manufacturing system for a single product during the product life cycle, which consists of four stages: introduction, growth, maturity and decline. In all inventory models a general assumption is that products have indefinitely long lives. In general, almost all items deteriorate over time. Often, the rate of deterioration is low and there is little need to consider the deterioration in the determination of the economic lot size. The objective is to derive the cycle time and optimal production lot size to minimize total costs for the product life cycle with deteriorating items. The relevant model is built, solved and some main results on the uniqueness of the solution using rigorous mathematical methods are obtained. Illustrative examples are provided to verify our findings numerically.

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We develop an inventory model to determine optimal ordering policy under permissible delay in payment by considering demand rate to be stock dependent. Mathematical models are derived under two different cases: credit period being greater than or equal to cycle time for settling the account, and credit period being less than or equal to cycle time for settling the account. The results are illustrated with numerical examples. Sensitivity analysis is given for the proposed model.

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We focus on a three-stage supply chain problem for fast moving consumer goods including a supplier, a manufacturer and customers. There are different orders over identical cycles, to be processed in production site. The problem is to find a joint cyclic schedule of raw material procurement and job scheduling minimized the total cost comprised of raw material ordering cost and holding cost, production cost, holding cost of finished products, tardiness cost and rejection cost. An integrated mixed integer programing model is proposed and optimal solution of some instances are provided by solving the model.

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In this paper, a novel scenario-based two-level inventory control model with a limited budget is formulated. The demand during the selling period is considered to follow a uniform probability distribution. In addition, it is assumed that there will be some customers who are willing to wait for their demands to be satisfied; thus a service level is considered for these customers. The aim is to find the optimal order quantities of the products and the required raw materials such that the relevant expected total profit obtained during the period is maximized. After proving the convexity of the proposed formulation, a penalty function and the Barrier method is proposed to solve the developed nonlinear stochastic programming problem. The problem is solved under different demand scenarios defined in three states of good, fair, and low. Finally, a case study in a dairy manufacturing company is provided to illustrate the application of the proposed methodology in real-world inventory control systems.