本文假設需求函數與購買成本皆隨時間波動，並證明了最佳生產排程存在且唯一。另外，我們亦證明了存貨系統的總成本是補貨次數的凸函數，因此，尋找最佳補貨次數可簡化為尋找區域極小值。我們進一步提供尋找最佳補貨次數的精確起始值，且描述需求和購買成本對生產週期和經濟生產量的影響。最後，舉例說明模式的求解過程並證明理論結果。 In this paper, we assume that not only the demand function but also the unit purchase cost is fluctuating with time. We then prove that the optimal production schedule not only exists but is also unique. In addition, we also show that the total cost associated with the proposed inventory system is a convex function of the number of replenishments. Consequently, the search for the optimal number of replenishments is simplified to find a local minimum. We further provide an accurate starting value for searching the optimal replenishment number. Next, we characterize the influences of both demand and unit purchase cost over the length of production run time and the economic production quantity. Finally, a numerical example is provided not only to illustrate the proposed algorithms but also to verify the theoretical results.
