قیمت‌گذاری و کنترل موجودی به صورت توام برای کالاهای فاسدشدنی با در نظر گرفتن هزینه کمبود به صورت پس‌افت پاره‌ای

  Determining the optimal selling price and inventory control policy for deteriorating items is one of the important issues in academic and industrial researches. In this paper, a joint pricing and inventory control model for deteriorating items is considered. The demand rate is known, continuous and functions of price and time. Shortages are allowed and partially backlogged, where the backlogging rate is variable and dependent on the waiting time for the next replenishment. The objective is to determine the optimal selling price, the length of time in which there is no inventory shortage, 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 the optimal replenishment exist and unique. Next, we prove that the total profit is a concave function of price when the replenishment schedule is given. Then, a simple algorithm is developed to find the optimal solution. Finally, we use a numerical example to illustrate the model and the algorithm .