生產作業成本、存貨成本、交貨數量與交貨日期此四者，是從事訂單式生產的生產決策者所最關切的基本問題。本論文是在上述基本問題的考量下，針對同型態的產品，分別探討下列三種訂單式生產的最佳生產計畫模式：模式1：各時點產能未受限制之單一交貨日期的最佳生產計畫模式；模式2：各時點產能皆受限制之單一交貨日期的最佳生產計畫模式；模式3：各時點產能未受限制之兩個不同交貨日期的最佳生產計畫模式。 在追求總成本（含生產作業成本與存貨成本）為最小且能如期交貨為目標的前題下，如何藉由所考量的參數、決策變數、決策函數及基本假設，分別將該三個主題的問題各製作成一個可具體討論的數學模式來加以探討，是本論文的主要架構。 本論文對於所建構的數學模式係利用變分法以尋求其最佳解，各主要的內容分述如下：1.尋求模式1的最佳解（含最佳生產函數、最佳生產起始時點等），並展示該最佳生產計畫之生產決策屬性；2.尋求模式2的最佳解（含最佳生產函數、最佳生產起始時點、最佳全產能生產起始時點等），並展示該最佳生產計畫之生產決策屬性；3.尋求模式3的最佳解（含最佳生產函數、最佳生產起始時點、第一期交貨前最佳額外生產數量等），並展示該最佳生產計畫之生產決策屬性；4.分別探討上述三個模式之最佳解中主要參數的敏感度分析。最後，本論文綜合各章之最佳解的適用場合，進而提供一個應如何決定訂單式生產之最佳生產的決策準則，以供從事生產計畫實務之決策者在面對新訂單來臨時的決策參考。 Production operating cost, inventory cost, delivery quantity, and delivery date are four primary concerns of production decision-maker for make-to-order (MTO) problems. This study focuses on the problem of homogeneous products, and we discuss the following three optimal production plan models of MTO:Model 1: The optimal production plan model of one delivery date with un-limited production capacity at any point in time.Model 2: The optimal production plan model of one delivery date with limited production capacity at any point in time.Model 3: The optimal production plan model of two different delivery date with un-limited production capacity at any point in time.How to make the problem into a tangible mathematical model by taking into the consideration for the purpose of minimal total cost (including the production operating cost and inventory cost) and punctual delivery of products is the process of this study. For the mathematical models, we use the method of calculus of variations to look for the optimal solutions. The main content of this study are as follows:1. How to look for the optimal solution (include the optimal production function, the optimal production starting point) of Model 1. The production decision procedure of the optimal production plan is also constructed.2. How to look for the optimal solution (include the optimal production function, the optimal production starting point, the optimal full capacity production starting point) of Model 2. The production decision procedure of the optimal production plan is also constructed.3. How to explore the optimal solution (include the optimal production function, the optimal production starting point, the optimal extra quantity to be produced before the first delivery date) of Model 3. The production decision procedure of the optimal production plan is also constructed.4. The sensitivity analyses for the key parameters in the optimal solution derived from the three production plan models respectively. Finally, we combine the results derived from the three issues, and provide a production decision procedure in deciding the optimal production plan of MTO for the decision maker a decision reference in dealing with new orders.
