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a b s t r a c tIn this paper, Economic Order Quantity (EOQ) based model for non-instantaneous deteriorating items with permissible delay in payments is proposed. This model aids in minimizing the total inventory cost by finding an optimal replenishment policy. In this model shortages are allowed and partially backlogged. The backlogging rate is variable and dependent on the waiting time for the next replenishment. Some useful theorems have been framed to characterize the optimal solutions. The necessary and sufficient conditions of the existence and uniqueness of the optimal solutions are also provided. An algorithm is designed to find the optimal replenishment cycle time and order quantity under various circumstances. Numerical examples are given to demonstrate the theoretical results. Sensitivity analysis of the optimal solution with respect to major parameters of the system has been carried out and the implications are discussed in detail. In the discussions, suggestions are given to minimize the total cost of the inventory system.

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