This paper presents a discounted cash-flow approach to an inventory model for deteriorating items with the two-parameter Weibull distribution. According to our proposed model, two shortages are considered: back-orders and lost-sales, in which the back-order rate is a varying function of the time when the shortage happens. In general, the demand rate is a linear function of the selling price. The objective of this model is to determine the optimal pricing policy and the optimal throughput time in such a way that the total net present value of profits is maximized in the given planning horizon. Finally, a numerical example is provided to solve the model presented using our proposed three-stage approach.

Keywords: Time-value of money, Back-order demand, Lost-sales, Present value of profits

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