本研究探討具有多餘產能的製造與再製造系統，以可變動生產速率進行生產的經濟批量排程問題。在無限期規劃下，單一機台在同一時間只能生產單一產品的多產品生產規劃問題稱之經濟批量排程問題。近年來因為環保意識的興起與資源再生的觀念普及，推行產品逆物流系統以執行產品的回收再製造更顯得重要，因此本研究探討加入回收再製造的可變動速率的經濟排程批量問題。由於現實生活中，並不能保證產品產出皆符合品管標準，因此本研究考慮生產系統同時具有操控與失控兩種模式。在生產過程中，機器會隨著指數分配在任意的時間由操控模式轉為失控模式，假設在操控模式下所生產的產品皆符合品管的標準，且在失控模式下的瑕疵比例為一固定且已知的常數。此生產系統可藉由維修由失控模式轉為操控模式，並分別考慮不檢驗政策與定期檢驗政策下的求解允許變動生產速率之生產系統的產品生產週期與生產量使單位期望總成本最小。於性質分析中，可以證明兩項性質(1) 在不檢驗政策下的經濟批量排程問題為一凸規劃問題；(2) 在定期檢驗政策下，無論於製造與再製造之檢驗次數與生產時間成正比，與檢驗成本成平方反比，與品質成本及維修成本成平方正比。最後，於敏感度分析得知製造與再製造整備成本、可用產品和尚不可使用回收後產品的存貨成本、需求率與回收率對總成本與共同週期時間的影響程度較大

The rise of environmental consciousness, many countries made laws to require companies to take the responsibility of waste, recycling and reuse. And in real life, facility produced products are not necessarily to conform quality control standards. So this study considers Economic Lot Scheduling Problem (ELSP) with manufacturing and remanufacturing production processes. The process has two states: “in-control” and “out-of-control”. The facility may shift at a random time to out-of-control state with exponential distribution and begin to produce a fixed fraction of nonconforming items. If the process is found to be in the out-of-control state, we can restore it to the in-control state and suppose that the restoration time is negligible. Two imperfect process models, with and without inspection and restoration, are construct to minimize the total cost per unit time. The models have the following two properties. (1) The model without inspection and restoration is shown to be convex programming problems. (2) For the model with inspection and restoration, the number of inspection during manufacturing and remanufacturing period increase as the production time, the square of quality cost and the square of restoration cost increase, and as the square of inspection cost decrease. Finally, the sensitivity analysis shows that setup cost for manufacturing and remanufacturing, holding cost for serviceable and recoverable inventory, demand rate and return rate have greater influence to the common cycle time and total cost.

中文部分
蔣其軒，「利用共同週期法求解不完美生產系統下可變動生產速率之經濟批量排程問題」，國立成功大學工業管理研究所碩士論文，2007。

王俊傑，「求解不完美系統下允許回收再製造之經濟批量排程問題」，國立成功大學工業管理研究所碩士論文，2010。

英文部分
Ben-Daya, M., & Hariga, M., Economic Lot Scheduling Problem with Imperfect Production Processes. The Journal of the Operational Research Society, 51(7), 875-881, 2000

Bomberger, Earl E., A Dynamic Programming Approach to a Lot Size Scheduling Problem. Management Science 12(11):778-784, 1966.

Brander, Pär, and Anders Segerstedt.,Economic lot scheduling problems incorporating a cost of using the production facility. International Journal of Production Research 47(13):3611 – 3624, 2009

Buzacott, J. A., and I. A. Ozkarahan., One- and two-stage scheduling of two products with distributed inserted idle time: The benefits of a controllable production rate. Naval Research Logistics Quarterly 30(4):675-696, 1983.

Chan, Hing, Sai Chung, and Tak Chan., Combining genetic approach and integer programming to solve multi-facility economic lot-scheduling problem. Journal of Intelligent Manufacturing:1-9, 2010

Dobson, Gregory., The econompc lot-sheduling problem: achieving feasiblity using time-varying lot sizes. Operations Research 35(5):764, 1987.

Elmaghraby, Salah E., The Economic Lot Scheduling Problem (ELSP): Review and Extensions. Management Science 24(6):587-598, 1978.

Eynan, A., The benefits of flexible production rates in the economic lot scheduling problem. IIE Transactions 35(11):1057, 2003.

Guide, V. Daniel R., Mark E. Kraus, and Rajesh Srivastava., Scheduling policies for remanufacturing. International Journal of Production Economics 48(2):187-204, 1997.

Hanssmann, F, ed., Operation research in production and inventory control, John Wiley & Sons, New York, 1962.

Huiqing, Ouyang, and Zhu Xiangyang., A economic lot scheduling problem for manufacturing and remanufacturing. Cybernetics and Intelligent Systems, 2008 IEEE Conference on, 2008, pp. 1171-1175, 2008.

Lin, Gary C., Dennis E. Kroll, and C. J. Lin., Determining a common production cycle time for an economic lot scheduling problem with deteriorating items. European Journal of Operational Research 173(2):669-682, 2006

Moon, I., B. C. Giri, and K. Choi., Economic Lot Scheduling Problem with Imperfect Production Processes and Setup Times. The Journal of the Operational Research Society 53(6):620-629, 2002.

Rogers, Jack., A Computational Approach to the Economic Lot Scheduling Problem. Management Science 4(3):264-291, 1958.
Silver, Edward A., Deliberately slowing down output in a family production context. International Journal of Production Research 28(1):17, 1990.

Shedon, R., The lot scheduling problem in the hierarchy of decision models. Ph.D. Dissertation. School of OR & IE, Cornell University, Ithaca, NY 14850, USA, 1986.

Tang, O., & Teunter, R., Economic Lot Scheduling Problem with Returns. Production and Operations Management, 15(4), 488-497, 2006.

Teunter, R., Lot-sizing for inventory systems with product recovery. Computers & Industrial Engineering, 46(3), 431-441, 2004.

Teunter, R., Kaparis, K., & Tang, O., Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing. European Journal of Operational Research, 191(3), 1241-1253, 2008.