訂單式生產係指在接到訂單後，廠商才會依照顧客的需求而開始生產商品，此時 生產決策者在承接訂單時所面臨的問題，即應以何種生產速率來從事生產、在何時生 產，才能如期交貨並使得總成本為最小。Kamien and Schwartz(1991)、陳淼勝與蔡福建 (2008)藉由數學模式的建構與分析，來探討單一交貨日期的最佳生產計畫問題；Chen and Tsai (2008)則進一步將研究推廣為二個不同交貨日期的最佳生產計畫模式。本專題 研究計畫即欲延伸此一概念，考慮多個不同交貨日期的訂單式生產計畫問題，透過數 學模式的建構，變分法與探討端點不等式限制式之角點條件的求解，尋求最佳的生產 計畫，使完成訂單合約所需的總成本為最小；此外，亦進行敏感度分析，藉以探討各 種決策變數與參數的特性，並運用電腦模擬方式進行分析，期能歸納出一個適合訂單 式生產的一般化生產計畫決策準則，幫助生產決策者在實務應用上做出較有效的決策。 Make-to-order means that a manufactory starts the production process according to customers’ requirements. Production decision-makers suffer from a problem that how to determine the production rate and starting point to achieve the minimum total cost including production operating cost and inventory cost. Kamien and Schwartz (1991) and Chen and Tsai (2008) separately studied the problem of optimal production plan with single delivery date by constructing, solving and analyzing a mathematical model. The model is further extended to the case of two different delivery dates by Chen and Tsai (2008). In this project, we intend to investigate the problem of optimal production plan with n different delivery dates. A generalization of the mathematical model will be constructed, and the optimal production plan would be obtained by using calculus of variations and discussion of corner condition about endpoint of inequality. Conditions for optimal production rate and optimal starting point will be derived, and a sensitivity analysis and simulation will also be performed to have some knowledge about the characteristics of decision variables and parameters. And a working rule for the generalized optimal production plan of make-to-order will be provided for production decision-makers in practical application.
