採購是供應鏈中最重要的面向之一。 在大多數的採購文獻中，可分為供應商選擇與訂購數量。選擇一個好的供應商不僅可以降低採購成本，還能確保商品的品質；訂購適當的量就相當於在恰當的價格下擁有較低的存貨與訂購成本。然而，現今的供應商因為產能限制往往無法滿足所有的訂單，致使購買者必須在不同的價格下向多個供應商訂購。
　　本論文以經濟訂購批量(economic ordering quantity)的傳統模型為基礎，將多產品、多供應商、有限產能與價格折扣列入考慮，提出一個供應商選擇與訂購數量的整合模式。此外，我們還提出兩階段法(the two-stage method)來求解，並與套裝軟體LINGO作比較，結果顯示兩階段法為容易找到近最佳解的方法。最後，我們利用兩階段法分別測試固定週期訂購法 (the fixed cycle approach)與獨立週期訂購法(the independent cycle approach)在該模式下的不同應用。我們發現在大多數的情況下，使用固定週期法較獨立週期法更為節省成本，特別是在高價格折扣率(price discount rate)與高限制緊度(constraint tightness)的情形下。

One of the most important aspects in supply chain is how to purchase. In most purchasing literature, the problem of purchasing can be divided into two parts: the selection of suppliers and the quantity of ordering. Choosing a good supplier can not only reduce the purchasing cost but also guarantee the quality. Ordering a right quantity is equal to have lower inventory and ordering costs under the right price. However, today suppliers can not often satisfy all demands of a purchaser because of finite capacity so that the purchaser must order from multiple suppliers in different price.
In this thesis, we use the traditional model of economic ordering quantity as the foundation and consider the multi-item, multi-supplier, finite capacity and price discount to propose a unified model for both of the supplier selection and the ordering quantity. In addition, the two-stage method is presented and compared with the software package, LINGO, to show that it is easy to find a near-optimal solution. Finally, we apply the two-stage method to test the fixed cycle approach and the independent cycle in the proposed model respectively. According to the computational results, the fixed cycle approach is more cost-effective than the independent cycle approach, especially in high price discount rate and high constraint tightness.

[1] Benton, W.C., "Quantity discount decisions under conditions of multiple items, multiple suppliers and resource limitations," International Journal of Production Research, 1953-1961 (1991).
[2] Boer, L. de, E. Labro and P. Morlacchi, "A review of methods supporting supplier selection," European Journal of Purchasing and Supply Management, 75-89 (2001).
[3] Choi, T.Y. and, J.L. Hartley, "An exploration of supplier selection practices across the supply chain," Journal of Operations Management, 14, 333-343 (1996).
[4] Das, C., “A graphical approach to price break analysis – 3,” Operational Research Society, 35(11), 995-1001 (1984).
[5] Dickson, G. W., “An analysis of supplier selection systems and decision,” Journal of Purchasing, 2(1), 5-17 (1966).
[6] Goyal, S. K. and O. K. Gupta, “A simple approach to the discount purchase problem,” Journal of the Operational Research Society, 41(12), 1169-1170 (1990)
[7] Guder, F. and J. L. Zydiak, “Non-stationary ordering policies for multi-item inventory systems subject to a single resource constraint and quantity discount,” Computers and Operations Research, 24, 61-71 (1997).
[8] Guder, F. and J. L. Zydiak, “Ordering policies for multi-item inventory systems subject to multiple resource constraints,” Computers and Operations Research, 26,583-597 (1999).
[9] Gupta, O. K. “An improved procedure for economic order quantity with all-unit price discounts,” International Journal of Operations & Production Management, 8(4), 79-83 (1987)
[10] Johnson, D.G., “A graphical approach to price break analysis,” Operational Research Quarterly, 22(3), 300-302 (1971)
[11] Liu, C., “Acquisition policies for multi-item multi-supplier systems with finite Capacity,” M.S. Thesis, Department of Industry Engineering and Engineering Management, University of Tsing Hua, Hsinchu, Taiwan (2000).
[12] Markowski, C. A. and E. P. Markowski, “An alternative criterion for the quantity discount decision,” Journal of Purchasing and Materials Management; 24(1), 31-34 (1988)
[13] Page, E. and R. J. Paul, “Multi-product inventory situation with one restriction,” Operations Research Quarterly, 27, 815-834 (1976).
[14] Pirkul, H. and O. A. Aras, “Capacitated multiple item ordering problem with quantity discounts,” IIE Transactions, 17, 206-211 (1985).
[15] Rosenblatt, M. J., “Multi-item inventory system with budgetary constraint: a comparison between the Lagrangian and the fixed cycle approach,” International Journal of Production Research, 19, 331-339 (1981).
[16] Rosenblatt, M., Y. T. Herer and I. Hefter, “An acquisition policy for a single item multi-supplier system,” Management Science, 44, 96-100 (1998).
[17] Stevenson, W.J., Production operations management, 7th Edition, McGraw-Hill companies, Inc.
[18] Weber, C.A., J.R. Current and W.C Benton, “Vendor selection criteria and methods,” European Journal of Operational Research, 50, 2-18 (1991)
[19] Wilkinson, J.G. and A. Green, “A graphical approach to price break analysis – 2,” Operational Research Quarterly, 23(3), 385-392 (1972)