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چکیده
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The problem of pricing and replenishment policy for deteriorating items in recent years has been mentioned by many researchers. In this paper, we will consider the problem where the demand rate is known, continuous and a function of price and also time. Shortages are allowed and partially backlogged, whereas the backlogging rate is variable and dependent on the waiting time for the next replenishment. The objective is to determine the optimal selling price, secondly the length of the time in which there is no inventory shortage, together with the replenishment cycle time, and order quantity such that the total profit per unit time has a maximum value. For any given selling price, we first show that a unique optimal replenishment schedule exists. Next, we demonstrate that the total profit function is concave according to the price whereas the replenishment schedule is given. Then, an algorithm is developed to find the optimal solution. Finally, a numerical example is developed to illustrate efficiency of the model and also the algorithm.
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