存貨決策一直為物流系統中重要的研究課題，但對考量不同運輸方式，其存貨控制的探討則較少受到重視，不同或非協同之存貨政策與運輸選擇模式，會對整體系統的運作效率造成明顯劣化。本研究探討之二階層配銷系統存貨政策，同時考量運輸方式對於系統的影響，倉儲中心和各零售商皆採用再訂購點暨固定訂購量存貨政策，而訂購週期皆為二的冪數乘以基期，若發生缺貨，則以遇缺補貨的方式處理，在需求為固定常數，而運輸時間具有隨機性，本研究採用正常與緊急兩種運輸方式來改善系統運作，在此緊急運輸時間的機率分布之期望值與變異數會小於正常運輸時間的機率分布之期望值與變異數，探討系統具有緊急運輸機制時，存貨決策與總成本有何改變。
　　本研究建構單位時間期望總成本表示式，總成本包含二階層配銷系統中倉儲中心向外部供應商補貨的固定訂購成本、存放商品的存貨持有成本、運送產品至倉儲中心的運輸成本，與零售商向倉儲中心訂購商品的固定訂購成本、每次產品運輸成本(包含正常與緊急運送成本)、自身存放商品的存貨持有成本和缺貨發生時產生的缺貨成本。研究主要目的為最小化單位時間期望總成本，並決定系統最佳決策變數，包含倉儲中心的再訂購點、訂購批量與各零售商的再訂購點、訂購批量和緊急運輸批量。
　　依據所建構的單位時間期望總成本表示式，本研究以多維搜尋法求得系統之最佳決策。根據演算實驗結果發現，採用緊急運輸的系統能有效降低系統總成本，統計檢定下有緊急運輸機制的系統總成本顯著小於無緊急運輸機制的系統總成本，而從演算結果歸納，兩者總成本最大差異接近百分之四十，其平均差異亦十分顯著。當緊急運輸成本較低、正常運輸時間較大，或是單位時間缺貨成本、存貨持有成本較大的情況下，採用緊急運輸機制的系統會比無緊急運輸機制的系統來得佳，雖會增加部份運輸成本，但能有效降低系統中存貨持有成本與缺貨成本。

　　We consider a two-echelon distribution system with a central warehouse and multiple retailers, where normal and emergency supply modes are used to fill the stock for each retailer. The warehouse replenishes its inventories from an outside supplier with unlimited stocks. A continuous review (s, Q) inventory policy is implemented in the system; and the order interval of each facility is a power-of-two multiple of the base-planning period. All stockouts at the retailers are backordered. Customer demand at each retailer follows a constant rate; and transportation time from the warehouse to each retailer is random. The expected value and the variance of transportation time for emergency supply mode are assumed to be smaller than those of transportation time for normal supply mode.
　　We derive the expected total relevant cost model, which includes replenishment cost, holding cost, and transportation cost at the warehouse, and replenishment cost, holding cost, shortage cost and transportation cost (normal and emergency supply) at each retailer. The expected cost is to be minimized to find the optimal inventory policy, including the base -planning period, reorder point, order quantities under normal and emergency supply modes.
　　A discrete search heuristic is developed to find the optimal inventory policy; and it is illustrated by a numerical example. Computation test, based on fractional factorial designs, has shown that the expected total system cost with emergency supply mode is significantly lower than that in the classical system with only normal supply node. The maximal cost reduction by using emergency supply is approximately 40%. When the cost for emergency supply is low, the transportation time for normal supply mode is large, or holding cost and shortage cost in each retailer are expensive, it is advantageous to implement emergency supply mode in a two-echelon distribution system.

中文部分：
1. 劉華，“兩階層配銷系統庫存問題之探討─再訂購點暨固定訂購量存貨模式發展”，國立成功大學工業管理研究所碩士論文，民國八十六年六月。
2. 黃建程，“兩階層配銷系統 (R, S) 存貨政策─倉儲中心與零售點具相異盤存週期之模式發展”，國立成功大學工業管理研究所碩士論文，民國九十一年六月。

英文部分：
3. Adlakha, V., and Kowalski, K., “On the Fixed-Charge Transportation Problem,” Omega, 27, 381-388 (1999).
4. Axster, S., “Exact Analysis of Continuous Review (R,Q) Policies in Two-Echelon Inventory System with Compound Poisson Demand,” Operations Research, 48(5), 686-696 (2000).
5. Axster, S., “A Note on Stock Replenishment and Shipment Scheduling for Vendor-Managed Inventory System,” Management Science, 47(9), 1306-1310 (2001).
6. Ballou, R.H., Business Logistics/Supply Chain Management 5th ed, Prentice Hall, New Jersey (2004).
7. Bazarra, M.S., and Shetty, C.M., Nonlinear Programming：Theory and Algorithms, Wiley, New York (1979).
8. Burns, L.D., Hall, R.W., Blumenfeld, D.E., and Daganzo, C.F., “Distribution Strategies that Minimize Transportation and Inventory Costs,” Operations Research, 33(3), 469-490 (1985).
9. Campbell, J.F., “Designing Logistics Systems by Analyzing Transportation, Inventory and Terminal Cost Tradeoffs,” Journal of Business Logistics, 11(1), 159-179 (1990).
10. etinkaya, S., and Lee, C.Y., “Stock Replenishment and Shipment Scheduling for Vendor Managed Inventory Systems,” Management Science, 46(2), 217-232 (2000).
11. etinkaya, S., and Lee, C.Y., “Optimal Outbound Dispatch Policies：Modeling Inventory and Cargo Capacity,” Naval Research Logistics, 49, 531-556 (2002).
12. etinkaya, S., and Bookbinder, J.H., “Stochastic Models for the Dispatch of Consolidated Shipments,” Transportation Research Part B, 37, 747-768 (2003).
13. etinkaya, S., Mutlu, F., and Lee, C.Y., “A Comparison of Outbound Dispatch Policies for Integrated Inventory and Transportation Decisions,” European Journal of Operational Research, 171, 1094-1112 (2006).
14. Chan, C.K., and Kingsman, B.G., “Coordination in Single-Vendor Multi-Buyer Supply Chain by Synchronizing Delivery and Production Cycles,” Transportation Research Part E, 43(2), 90-111 (2007).
15. Chen, F., “Effectiveness of (R, Q) Policies in One-Warehouse Multiretailer Systems with Deterministic Demand and Backlogging,” Naval research logistics, 47, 422-439 (2000).
16. Chiang, C., and Gutierrez, G.J., “A Periodic Review Inventory System with Two Supply Modes,” European Journal of Operational Research, 94, 527-547 (1996).
17. Dohse, E.D., and Morrison, K.R., “Using Transportation Solutions for a Facility Location Problem,” Computers & Industrial Engineering, 31(1-2), 63-66 (1996).
18. Donaldson, W.A., “The Allocation of Inventory Items to Lot Size/Reorder Level (Q, r) and Periodic Review (T, Z) Control Systems,” Operational Research Quarterly, 25(3), 481-485 (1974).
19. Forkenbrock, D.J., “Comparison of External Costs of Rail and Truck Freight Transportation,” Transportation Research Part A, 35, 321-337 (2001).
20. Forsberg, R., “Optimization of Order-up-to-S Policies for Two-Level Inventory Systems with Compound Poisson Demand,” European Journal of Operational Research, 81, 143-153 (1995).
21. Forsberg, R., “Exact Evaluation of (R, Q)-Policies for Two-Level Inventory System with Poisson Demand,” European Journal of Operational Research, 96, 130-138 (1997).
22. Galliher, H.P., Morse, P.M., and Simond, M., “Dynamics of Two Classes of Continuous-Review Inventory Systems,” Operations Research, 7(3), 362-384 (1959).
23. Gll, R., and Erkip, N., “Optimal Allocation Policies in a Two-Echelon Inventory Problem with Fixed Shipment Costs,” International Journal of Production Economics, 46-47, 311-321 (1996).
24. Hall, R.W., “Consolidation Strategy：Inventory Vehicles and Terminals” Journal of Business Logistics, 8(2), 57-73 (1987).
25. Harris, F.W., “How Many Parts to Make at Once,” Operations Research, 38(6), 947-950 (1990).
26. Huang, H.C., Chew, E.P., and Goh, K.H., “A Two-Echelon Inventory System with Transportation Capacity Constraint,” European Journal of Operational Research, 167(1), 129-143 (2005).
27. Matta, K.F., and Sinha, D., “Policy and Cost Approximations of Two-Echelon Distribution Systems with a Procurement Cost at the Higher Echelon,” IIE Transactions, 27, 638-645 (1995).
28. Mitchell, J.S.B., “98%-Effective Lot-Sizing for One-Warehouse, Multi-Retailer Inventory Systems with Backlogging,” Operations research, 35(3), 399-404 (1987).
29. Moinzadeh, K., and Nahmias, S., “A Continuous Review Model for an Inventory System with Two Supply Modes,” Management Science, 34(6), 761-773 (1988).
30. Nahmias, S., and Smith, S.A., “Optimizing Inventory Levels in a Two-Echelon Retailer System with Partial Lost Sales,” Management Science, 40(5), 582-596 (1994).
31. Ramasesh, R.V., Ord, J.K., and Hayya, J.C., “Sole versus Dual Sourcing in Stochastic Lead-Time (s, Q) Inventory Models,” Management science, 37(4), 428-443 (1991).
32. Richards, F.R., “Comments on the Distribution of Inventory Position in a Continuous -Review (s, S) Inventory System,” Operations Research, 23(2), 366-371 (1975).
33. Roundy, R., “98%-Effective Integer-Ratio Lot-Sizing for One-Warehouse, Multi -Retailer Systems,” Management science, 31(11), 1416-1430 (1985).
34. Silver, E.A., Pyke, D.F., and Peterson, R., Inventory Management and Production Planning and Scheduling 3rd ed, Wiley, New York (1998).
35. Tyworth, J.E., “Modeling Transportation–Inventory Tradeoffs in a Stochastic Setting,” Journal of Business Logistics, 13(2), 97-124 (1992).
36. van der Heijden, M.C., “Theory and Methodology：Multi-Echelon Inventory Control in Divergent Systems with Shipping Frequencies,” European Journal of Operational Research, 116, 331-351 (1999).
37. van Donselaar, K., de Kok, T., and Rutten, W., “Two Replenishment Strategies for the Lost Sales Inventory Model: A Comparison,” International Journal of Production Economics, 46-47, 285-295 (1996).
38. Vroblefski, M., Ramesh, R., and Zionts, S., “Efficient Lot-sizing under a Differential Transportation Cost Structure for Serially Distributes Warehouses,” European Journal of Operational Research, 127, 574-593 (2000).
39. Wang, J., and Kaempke, T., “Shortest Route Computation in Distribution Systems,” Computers & Operations Research, 31, 1621-1633 (2004).
40. Yan, S., and Luo, S.C., “Probabilistic Local Search Algorithms for Concave Cost Transportation Network Problems,” European Journal of Operational Research, 117, 511-521 (1999).