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This paper presents an inventory model for deteriorating items in which shortages are allowed. It is assumed that the production rate is proportional to the demand rate and greater than demand rate. The inventory model is developed by considering four different circumstances. The optimal of the problem is obtained with the help of Mathematica 7 software. Numerical examples are given to illustrate the model for different parameters. Sensitivity analysis of the model has been developed to examine the effect of changes in the values of the different parameters for optimal inventory policy. Truncated Taylor’s series is used for finding closed form optimal solution.

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In this study, a two-warehouse inventory model with exponentially increasing trend in demand involving different deterioration rates under permissible delay in payment has been studied. Here the scheduling period is assumed to be a variable. The objective of this study is to obtain the condition when to rent a warehouse and the retailer\'s optimal replenishment policy that minimizes the total relevant cost. An effective algorithm is designed to obtain the optimal solution of the proposed model. Numerical examples are provided to illustrate the application of the model.Based on the numerical examples, we have concluded that the single warehouse model is less expensive to operate than that of two warehouse model. Sensitivity analysis has been provided and managerial implications are discussed.

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This paper deals with a deterministic inventory model for deteriorating items under the condition of permissible delay in payments with constant demand rate is a function of time which differs from before and after deterioration for a single item. Shortages are allowed and completely backlogged which is a function of time. Under these assumptions, this paper develops a retailer\'s model for obtaining an optimal cycle length and ordering quantity in deteriorating items of an inventory model. Thus, our objective is retailer\'s cost minimization problem to nd an optimal replenishment policy under various parameters. The convexity of the objective function is derived and the numerical examples are provided to support the proposed model. Sensitivity analysis of the optimal solution with respect to major parameters of the model is included and the implications are discussed.

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This paper considers the fuzzy inventory model for deteriorating items for power demand under fully backlogged conditions. We define various factors which are affecting the inventory cost by using the shortage costs. An intention of this paper is to study the inventory modelling through fuzzy environment. Inventory parameters, such as holding cost, shortage cost, purchasing cost and deterioration cost are assumed to be the trapezoidal fuzzy numbers. In addition, an efficient algorithm is developed to determine the optimal policy, and the computational effort and time are small for the proposed algorithm. It is simple to implement, and our approach is illustrated through some numerical examples to demonstrate the application and the performance of the proposed methodology.

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In the present study, the Economic Order Quantity (EOQ) model of two-warehouse deals with non-instantaneous deteriorating items, the demand rate considered as stock dependent and model affected by inflation under the pattern of time value of money over a finite planning horizon. Shortages are allowed and partially backordered depending on the waiting time for the next replenishment. The main objective of this work is to minimize the total inventory cost and finding the optimal interval and the optimal order quantity. An algorithm is designed to find the optimum solution of the proposed model. Numerical examples are given to demonstrate the results. Also, the effect of changes in the different parameters on the optimal total cost is graphically presented.

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In this paper, an EOQ model is developed for a deteriorating item with quadratic time dependent demand rate under trade credit. Mathematical models are also derived under two different situations i.e. Case I; the credit period is less than the cycle time for settling the account and Case II; the credit period is greater than or equal to the cycle time for settling the account. The numerical examples are also given to validate the proposed model. Sensitivity analysis is given to study the effect of various parameters on ordering policy and optimal total profit. Mathematica 7.1 software is used for finding optimal numerical solutions.