近年來，因為科技的快速發展，導致產品的生命週期變得更短。而當一產品在市場中被淘汰時，其原因可以歸咎於不只是物理上的損壞，還有功能上的不足。因此，產品回收就有其再利用的價值。現今，基於延伸生產者責任到回收處理的要求，遵行回收立法對於一家公司是必要的，且顧客對於消費型態逐漸由傳統的銷售轉變為功能式產品銷售，而租賃就是功能式銷售中的一環。租賃提供一個商業的經營模式來處理回收產品的不確定性數量、品質和回收時間，亦可以幫助產品的原始設備製造商來執行顧客關係管理。
在本論文中，我們提出了一個數學模型，以解決閉迴路供應鏈系統下之多產品的訂價以及多產品、多期和共用零件的再利用規劃。所提出的租賃分析模型稱作確定性租賃模型，其被分成兩個階段做求解。第一階段的租賃模型是以整數非線性規劃的形式下作訂價，第二階段的租賃模型是以整數線性規劃的形式下作生產規劃。
第一階段的目的是決定出租賃產品的最佳價格和最佳需求量，第二階段的目的是求得在產能限制下的最佳生產規劃。此研究所提出的模型可用來支援決策者在租賃系統下，根據不同的零件特性來規劃不同產品再利用或升級之最佳零件組合。
因為對於一家公司來說，預測的需求仍然存在著不確定性。為了處理這樣不確定下的需求問題，我們提出租賃在閉迴路供應鏈系統之穩健性模型，稱作穩健性租賃模型，其提供穩健性的決策在各零件的生產量和採購量，以至於未來面臨到不同的情境，也可以有效地運用有限之產能。最後，並且以數值範例和其敏感度分析來說明與驗證所提出模型的適用性。規劃的結果是最佳的生產方案，其貢獻於達到最大的成本減省和有效地利用每一個零件。

In recent years, the life cycle of products has become much shorter because of the rapid technological development. When the products are out of market, it can be attributed to not only the physical deterioration, but also the functional obsolescence. Therefore, product recovery remains valuable. Nowadays, take-back legislation based on extended producer responsibility is critical to a company. Moreover, the business models have gradually changed from traditional product-selling to functional sales. Leasing is an example of functional sales that provides an alternative business strategy to cope with the uncertainty in quantity, quality, and time for the returned products. Leasing also helps Original Equipment Manufacturer (OEM) perform Customer Relation Management (CRM).
In this study, we propose a mathematical model to solve the reutilization planning problem under a Closed-loop Supply Chain (CLSC) system which includes multiple products with components commonality in multiple periods. An analytical leasing model, namely Deterministic Leasing Model (Deterministic-LM), is divided into two phases. The first phase of leasing model is pricing model in the form of Integer Non-linear Program (INLP), and the second phase of leasing model is production planning model in the form of Integer Linear Program (ILP).
The goals of the first phase are to determine the optimal leasing prices and the optimal quantity for the leased products at different leasing periods, and the goal of the second phase is to determine the optimal production planning under the production capacity constraints. According to different characteristics of the components, the model can be used to support the manager's decision regarding the optimal combinations of components from different products for reuse and upgrade possibilities.
Because demand forecasting has been an uncertainty for a company in order to cope such uncertainty, we propose a robust model of leasing in a closed-loop supply chain system, namely Robust Leasing Model (Robust-LM), which provides a robust decision on the volumes of processed components and procured components such that the limited capacity can be efficiently utilized. Finally, numerical results are presented to illustrate the procedure and the validity of the proposed model with the sensitivity analysis. The result of planning is an optimal production scheme which contributes to achieving high cost savings and effective reuse along the multiple times of components.

1. Aras, N., Gullu R., Yurulmez S., “Optimal Inventory and Pricing Policies for Remanufacturable Leased Products.” International Journal of Production Economics, Vol. 133, pp. 262-271, 2011.
2. Bass, F. M., “A New Product Growth for Model Consumer Durables.” Management Science, Vol. 15, No. 5, pp. 215-227, 1969.
3. Boustani, A., Sahni, S., Graves, S. C., Gutowski, T. G., “Appliance Remanufacturing and Life Cycle Energy and Economic Saving.” Paper presented at the International Symposium on Sustainable Systems and Technology, May 17-19, Arlington County, Virginia, USA, 2010.
4. Chien, C., F., Zheng, J. N., “Mini–max Regret Strategy for Robust Capacity Expansion Decisions in Semiconductor Manufacturing.” Journal of Intelligent Manufacturing, Vol. 23, No. 6, pp. 2151-2159, 2012.
5. Denizel, M., Ferguson, M., Souza, G. C., “Multiperiod Remanufacturing Planning with Uncertain Quality of Inputs.” IEEE Transaction on Engineering Management, Vol. 57, No. 3, pp. 394-404, 2010.
6. European Union, “Directive 2002/96/EC of the European Parliament and of the Council on Waste Electrical and Electronic Equipment”, 2003.
7. Geyer, R., Van Wassenhove, L. N., Atasu A., “The Economic of Remanufacturing Under Limited Component Durability and Finite Product Life Cycle.” Management Science, Vol. 53, No. 1, pp. 88-100, 2007.
8. Guide Jr., V.D.R., Van Wassenhove, L. N., “The Evolution of Closed-Loop Supply Chain Research.” Operations Research, Vol. 57, No. 1, pp. 10-18, 2009.
9. Guo, J., Liang, C., “Models for Recycling and Production Policy for a Closed-Loop System.” Journal of Quality, Vol. 18, No. 4, pp. 303-314, 2011.
10. Jung, K. S., Hwang, H., “Competition and Cooperation in a Remanufacturing System with Take-back Requirement.” Journal of Intelligent Manufacturing, Vol. 22, No. 3, pp. 427-433, 2009.
11. Linton, J., Yeomans, J., Yoogalingam, R., “Recovery and Reclamation of Durable goods : A Study of Television CRTs.” Resources Conservation & Recycling, Vol. 43, No.4, pp. 337-352, 2005.
12. Matsuda, A., Shimomura, Y., “Upgrade Planning for Upgradeable Product Design.” Paper presented at the Third International Symposium on Environmentally Conscious Design and Inverse Manufacturing, Tokyo, December 8-11, 2003.
13. Meixell, M., J., Wu, S. D., “Scenario Analysis of Demand in a Technology Market Using Leading Indicators.” IEEE Transaction on Semiconductor Manufacturing, Vol. 14, No. 1, 2001.
14. Mitra, S., Webster, S., “Competition in Remanufacturing and the Effects of Government Subsides.” International Journal of Production Economics, Vol. 111, No. 2, pp. 287-298, 2008.
15. Mulvey, J. M., Vaanderbei, R. J., Zenios, S. A., “Robust Optimization of Large-Scale System.” Operations Research, Vol. 43, No. 2, pp. 264-281, 1995.
16. Östlin, J., Sundin, E., Biӧrkman, M., “Product Life-Cycle Implications for Remanufacturing Strategies.” Journal of Cleaner Production, Vol. 17, No.11, pp. 999-1009, 2009.
17. Östlin, J., Sundin, E., Biӧrkman, M., “Importance of Closed-Loop Supply Chain Relationships for Product Remanufacturing.” International Journal of Production Economics, Vol. 115, No. 2, pp. 336-348, 2008.
18. Östlin, J., “Material and Process Complexity - Implications for Remanufacturing.” Paper presented at the Fourth International Symposium on Environmentally Conscious Design and Inverse Manufacturing, pp. 154-161, December 12-14, Tokyo, Japan, 2005.
19. Ramani, K., Ramanujan, D., Bernstein, W. Z., Zhao, F., Sutherlamd, J., Handwerker, C., Choi, J. K., Kim, H., Thurston, D., “Integrated Sustainable Life Cycle Design: a Review.” Journal of Mechanical Design, Vol. 132, No. 9, 091004, pp.1-15, 2010.
20. Reich-Weiser, C., Vijayaraghavan, A., Dornfeld, D., “Metrics for Sustainable Manufacturing.” Paper presented at the 2008 Internaional Manufacturing Science and Engineering Conference, October 7-10, Evanston, Illinois, USA, 2008.
21. Savaskan, R., Bhattacharya, S., Van Wassenhove, L. N., “Closed-Loop Supply Chain Models with Product Remanufacturing.” Management Science, Vol. 50, No. 2, pp. 239-252, 2004.
22. Sundin, E., Bras, B., “Making Functional Sales Environmentally and Economically Beneficial through Product Remanufacturing.” Journal of Cleaner Production, Vol. 13, No. 9, pp. 913-925, 2005.
23. Sutherland, J. S., Adler, D. P., Haapala, K. R., Kumar, V., “A Comparison of Manufacturing and Remanufacturing Energy Intensities with Application to Diesel Engine Production.” CIRP Annals – Manufacturing Technology, Vol. 57, No. 1, pp. 5-8, 2008.
24. Teunter, R. H., Flapper, S. D. P., “Optimal Core Acquisition and Remanufacturing Policies under Uncertain Core Quality Fractions.” European Journal of Operational Research, Vol. 210, No. 2, pp. 241-248, 2011.
25. Van Wassenhove, L. N., Zikopoulos, C., “On the Effect of Quality Overestimation in Remanufacturing.” International Journal of Production Research, Vol. 48, No. 15, pp. 5263-5280, 2010.
26. Wang, H. F., Kuo, T. Y., “Fuzzy Inference to Scenario Generation for Uncertain Demand of a Production System.” National Tsing Hua University Thesis, 2013.
27. Wang, H. F., Huang, Y. S., “A Two-Stage Robust Programming Approach to Demand-Driven Disassembly Planning for a Closed-loop Supply Chain System.” International Journal of Production Research, Vol. 51, No 8, pp. 2414-2432, 2013.
28. Wu, Y., “Robust Optimization Applied to Uncertain Production Loading Problem with Import Quota Limits under the Global Supply Chain Management Environment.” International Journal of Production Research, Vol. 44, No. 5, pp. 849-882, 2006.
29. Xing, K., Lee, L., “Modelling and Evaluation of Product Fitness for Service Life Extension.” Journal of Engineering Design, Vol. 20, No. 3, pp. 243-263, 2009.
30. Xing, K., Belusko, M., “Design for Upgradability Algorithm: Configuring Durable Products for Competitive Reutilizaion.” Journal of Mechanical Design, Vol. 130, No. 11, 111102, pp.1-14, 2008.
31. Yu, C. S., Li, H. L., “A Robust Optimization Model for Stochastic Logistic Problems.” International Journal of Production Economics, Vol. 64, No. 1-3, pp. 385-397, 2000.