隨著全球經濟的發展，各國的企業為了獲得更高的利潤必須更有效地利用有限的資源，隨著這些專案的規模逐漸成長，專安排程問題逐漸複雜化，在過去主要是利用要徑法與計劃評核術進行專案作業排程，但近年來資源限制的增加，單憑考量時程的控管而未考量有限的資源，將導致決策缺乏整體最佳化分析。因此本研究將應用網路流動技巧，並考量作業流程與資源限制及現金流量時間價值及相關作業流程，有效的以淨現值最大求解出最佳化專案排程，同時也把過去文獻求解僅求出近似解的缺點改善。
在過去的文獻中僅以確定性的觀念針對客戶端 (1)於作業完成付款(Payments at Activities' Completion Times, PAC)及(2) 全額付款(Lump-Sum Payment, LSP)從事最佳化排程，忽略隨機工期對排程的影響或雖有考量隨機工期但非預期淨現金流量計算有誤，本研究納入考量作業工期的隨機性，並以最大化淨現值為排程目標，利用數學規劃方法建構PAC及LSP兩者的數學模型。此兩種模式均為一含有額外限制的網路流動問題，可利用(CPLEX)數學規劃軟體求解。本研究以國際測試題庫(PSPLIB)所提供之專案資料，進行範例測試，兩者的測試結果均良好，顯示在PAC及LSP兩種不同付款方式下，本研究所建構的隨機模式可成為學術界及實務業者之參考。

As companies started to run business globally, scale of projects grew larger. These projects became much complex because limitation of resources increased. In the past, researchers used to conducted project scheduling by critical path method and program evaluation and review technique. However, these researches may fail to be applied to huge-scale projects due to negligence of the limitation of resources raise. As a result, In this research, integer network flow technique are applied. Cash flow, sequence of works and limitation of resources were considered as factors influencing the results of optimization.

The purpose of this research is to optimize cash flow of projects. By building two models of project payment: first, Payments at Activities' Completion Times, PAC, and second, Lump-Sum Payment, LSP. Researchers before hypothesized that the stochastic activity time does no influence to projecting scheduling, or considering the stochastic activity time ad a factor but failed to calculate the correct figures. Thus, this research utilizes network flow technique on two project payments. Two models are tested by the data referred to the Project Scheduling Problem Library(PSPLIB).

1. 朱麗穎、陳春益，「航商現金流動模式之研究」，碩士論文，國立成功大學交通管理科學研究所 (1997)。
2. 江孝頤，「隨機旅行時間下混凝土生產作業及拌合車調派決策之研究」，碩士論文，國立中央大學土木工程學系 (2008)。
3. 林士鈞，「定期貨櫃運輸船舶排程暨船期表建立之研究」，碩士論文，國立中央大學土木工程系 (2006)。
4. 許秀影等編著，專案管理基礎知識與應用實務，三版，社團法人中華專案管理學會，台北市，民國97年。
5. 張軍、陳偉能、黃韜，「運用蟻群算法優化項目調度中的折現現金流的方法」，中華人民共和國中山大學，Computer systems based on biological models (2008)。
6. 張恭文，「隨機旅行時間下拌合廠臨時性故障之混凝土生產與拌合車派遣規劃之研究」，碩士論文，國立中央大學土木工程學系 (2009)。
7. 張佩璇，「航空公司資金流動規劃模式之建立」，碩士論文，國立中央大學土木工程系 (2000)。
8. 張勻威，「自行車租賃佈署暨調度最佳之化之研究」，博士論文，國立中央大學土木工程學系 (2011)。
9. 邱明琦、陳春益、林佐鼎，「海運貨櫃排程模式之研究」，運輸計劃季刊，第三十一卷，第三期，第495-522頁 (2002)。
10. 曾貽威，「考量現金流量之專案多重資源排程最佳化之研究」，碩士論文，朝陽科技大學營建工程學系 (2001)。
11. 黃培修，「專案排程與資源調派整合模式」，碩士論文，國立成功大學土木研究所 (1999)。
12. 楊建邦、陳春益、張永昌，「動態網路應用於航現金流動問題之研究」，中華民國第四屆運輸網路研討會 (1999)。
13. 劉秋蘭，「多重作業方式及資源限制下最大淨現值專案排程模式暨求解演算法之研究」，碩士論文，國立中央大學土木工程系 (2011)。
14. 劉姿君「不同付款方式在多重作業方式及資源限制下專案排程最佳化模式之研
究」，碩士論文，國立中央大學土木工程系 (2012)。
15. 陳妙珍、顏上堯、張珮璇，「航空公司資產與負債管理模式之建立」，第四屆海峽兩岸會計與管理學術研討會論文集，武漢 (2000)。
16. 顏上堯、翁綵穗，「季節轉換間緩衝期飛航排程之研究」，運輸計劃季刊，第三十卷，第四期，第891-921頁 (2001)。
17. 鄭逸亮，「以最大-最小螞蟻系統解決多模式有限資源專案排程問題之研究」，碩士論文，國立高雄第一科技大學電腦與通訊工程系 (2007)。
18. 魏汝珊，「隨機作業時間下多重作業方式及資源限制下專案排程最佳化模式之研
究」，碩士論文，國立中央大學土木工程系 (2012)。
19. 經濟部小型企業創新研發計畫：計劃書範本。2011年5月22日，取自http://www.sbir.org.tw/SBIR/Web/Template_data.aspx?GUID=2061c7d3-9392-4ee0-9178-39d562f109b4。
20. Ballestín, F., Barrios, A. and Valls, V., “An evolutionary algorithm for the resource-constrained project scheduling problem with minimum and maximum time lags,” Journal of Scheduling, Vol. 14, No.4 , pp. 391-406 (2011).
21. Chen, W.N., Zhang, J., Chung, H.S., Huang, R.Z., and Liu, O., “Optimizing Discounted Cash Flows in Project Scheduling-An Ant Colony Optimization Approach,” IEEE Transactions on system, Vol. 40, No.1 (2010).
22. Chen, M., Yan, S., Wang, S.S., and Liu, C.L. (2015), "A generalized network flow model for the multi-mode resource constrained project scheduling problem with discounted cash flows," Engineering Optimization, Vol. 47, No.2, pp. 165-183 (SCI).
23. Hartmann, S., “Project scheduling with multiple modes - A genetic algorithm,” Annals of Operations Research, Vol. 102, No.1-4, pp. 111-135 (2001).
24. Icmeli, O., and Erenguc, S.S., “The resource constrained time cost tradeoff project scheduling problem with discounted cash flows,” Journal of Operations Management, Vol. 14, pp. 255-275 (1996).
25. Kolisch, R., Sprecher, A. and Drexl, A., “Characterization and generation of a general class of resource-constrained project scheduling problems, ” Management Science Vol. 41, pp. 1693–1703 (1995).
26. Lai, M. F. and Lo, H. K., “Ferry service network design: Optimal fleet size, routing, and scheduling,” Transportation Research Part A, Vol. 38, pp. 305-328 (2004).
27. Mika, M., Waligóra, G., and Węzglarz, J., “Simulated annealing and tabu search for multi-mode resource-constrained project scheduling with positive discounted cash flows and different payment models,” European Journal of Operational Research, Vol. 164, No.3, pp. 639-668 (2005).
28. Özdamar, L., Dündar, H., “A flexible heuristic for a multi-mode capital constrained project scheduling problem with probabilistic cash inflows,” Computers and Operations Research, Vol. 24, No.12, pp. 1187-1200 (1997).
29. Ozdamar, L. “A genetic algorithm approach to a general category project scheduling problem,” IEEE Transactions on system, Man, and Cybernetics, Part C, Vol. 29, pp. 44-59 (1999).
30. Russell, A.H., “Cash flows in networks,” Management Science, Vol.16, pp.357-373 (1970).
31. Sepil, C. And Ortac, N., “Performance of the heuristic procedures for constrained projects with progress payments,” Journal of the Operational Research Society , Vol. 48, pp.1123-1130 (1997).
32. Ulusoy, G. and Cebelli, S., “An equitable approach to the payment scheduling problem in project management,” European Journal of Operational Research, Vol. 127, pp. 262-278 (2000).
33. Ulusoy, G., Sivrikaya-S_erifo_glu, F. and S_ahin, S., “ Four payment models for the multi-mode resource constrained project scheduling problem with discounted cash flows, ” Annals of Operations Research, Vol. 102 ,pp. 237-261 (2001).
34. Wang, D. Z. W. and Lo, H. K., “Multi-fleet ferry service network design with passenger preferences for differential services,” Transportation Research Part B, Vol. 42, pp. 798-822 (2008).
35. Yang, K.K., Talbot, F.B. and Patterson, J H., “Scheduling a project to maximize its net present value: An integer programming approach,” European Journal of Operational Research, Vol. 64, pp. 188-198 (1993).
36. Yan, S., Wang, S.S., Chen, M. and Liu, J.C. (2013), “An optimal project scheduling model with lump-sum payment,” Review of Integrative Business and Economics Research, Vol. 2, No.1, pp. 399-413.
37. Yan, S. and Chen, H. L., “A scheduling model and a solution algorithm for inter-city bus carriers,” Transportation Research, Vol. 36A, pp. 805-825 (2002).
38. Yan, S. and Tseng, C.H., “A passenger demand based model for airline flight scheduling and fleet routing,” Computers and Operations Research, Vol. 29, pp. 1559-1581 (2002).
39. Yan, S., Chi, C. J. and Tang, C. H., “Inter-city Bus Routing and Timetable Setting under Stochastic Demands,” Transportation Research, Vol. 40A, pp.572-586 (2006).
40. Yan, S. and Shih, Y. L., “A Time-space network model for work team scheduling after a major disaster,” Journal of the Chinese Institute of Engineers, Vol. 30, No. 1, pp. 63-75 (2007)
41. Yan, S. and Chen, C. H., “Coordinated flight scheduling models for allied airlines,” Transportation Research Part C, Vol. 15, pp. 246-264 (2007).
42. Yan, S., Lai, W. and Chen, M., “Production scheduling and truck dispatching of ready mixed concrete,” Transportation Research, Part E, Vol. 44, No.1, pp. 164-179 (2008a).
43. Yan, S. Tang, C.H., and Fu, T.C., “An airline scheduling model and solution algorithms under stochastic demands,” European Journal of Operational Research, Vol. 190, pp. 22-39 (2008b).
44. Yan, S., Lin C.K., Chen, S.Y. “Logistical support scheduling under
stochastic travel times given an emergency repair work schedule” Computers & Industrial Engineering ,Vol. 67, pp. 20-35 (2014)