本研究探討商品在展售期間，當需求為隨機不確定時，其最佳特別訂購量與在此期間第二次最適折扣價格之共同決策問題。商品之展售期為事先確定已知，且展售期初之銷售價格為固定，但在展售期中之一預定時點必須決定其第二次折扣價格，以促銷剩餘商品。由於展售期間甚短，故不考慮補貨，即商品缺貨視為銷售損失；在展售結束後，剩餘未售出之商品將以固定之運輸成本送回廠商，以提供正常之銷售。在商品售價與需求成反向函數關係下，本研究探討其最佳訂購數量與最適價格政策，使展售期間期望總利潤極大化。

模式中考慮之商品相關成本包含：商品購買成本、期初與期末商品之運輸成本及兩階段價格政策下之存貨持有成本與缺貨成本，並在期望總利潤極大化的目標下，決定展售期間商品之期初最佳訂購數量與第二階段最適價格政策。本研究根據隨機理論，針對第一階段與第二階段存貨系統之運作進行分析，分別建立其收入與各相關成本之精確與近似期望數學表示式，進而建構商品展售之期望總利潤模式，作為後續理論分析與最佳決策制定之基礎。

經由實驗發現，本研究之期望總利潤估計模式與模擬結果之誤差甚小，顯示近似品質良好。故據此數學模式，發展一快速之黃金分割搜尋法，在期望總利潤最大化下，求得在已知特定兩階段銷售價格下之最佳特別訂購數量，並進一步同時決定第二次折扣價格之最適決策。後續演算實驗發現，商品單位購買成本、第一階段銷售價格與兩階段推行時間的長短對於商品展售之期望總利潤有著關鍵性的影響，降低第一階段銷售價格與增加第二階段的促銷期間皆能使總利潤獲得改善，故展售政策參數的設定應根據行銷策略與利潤管理作系統化的考量與訂定。實驗中亦觀察到，在最適決策下，缺貨大部分發生於第二階段，故以行銷手法降低第二階段之缺貨成本，可大幅減少因缺貨所造成的損失。

The optimal procurement quantity model with a secondary price-discount has been studied in this thesis. Specifically, an on-sale item under stochastic demand is considered, where on-sale period and initial sale price are known before hand. The on-sale duration is partitioned into two parts: initial on-sale period with the known sale price and the second on-sale period, where the price is to be determined. The objective is to determine the optimal procurement quantity and the secondary price to maximize the expected total profit during the sale period.

The expected total profit is the difference of the expected total revenue and the expected total relevant cost. The considered costs include item purchase cost, ordering cost, shipment costs for initial procurement and restocking, inventory cost and shortage cost at both stages. An expected profit model is developed, where both exact and approximate analyses are used to estimate the costs and the revenue.

The simulation experiment has demonstrated that the estimations of expected total profit from the proposed model and simulation result yield no significant difference. A golden section search algorithm is developed to find the optimal procurement quantity and the secondary price discount. The computational experiment reveals that the change of item purchase cost, sale price in first stage and the duration of the second on-sale period have significant impacts on the expected total profit. A lower on-sale price at first stage and longer duration of second stage all increase the expected total profit. On the other hand, a higher sale price at first stage leads to a higher secondary on-sale price and a lower procurement quantity, due to reduced demand. On the contrary, a shorter second on-sale period will lead to a lower secondary on-sale price, to stimulate the demand.

一、中文部分
簡信惠，民國八十七年。在隨機需求下特價商品之最佳訂購量與最適售價決策模式，國立成功大學工業管理學系碩士論文。

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