專案是一個有生命週期概念的管理活動。專案業者為因應全球化競爭環境，需更有效的專案管理技術執行其管理活動，以追求最大利潤，進而極大化股東的財富。然而，隨著專案規模擴大，資源限制增加，專案排程問題牽涉的相關因素逐漸複雜。有鑑於此，過去文獻考量資源限制、不同作業方式及淨現值等因素，建立決策模式並分別依不同假設發展求解演算法，然而，過去文獻所發展的啟發解法所求得的結果大多為近似解，難以確定其為最佳解或與最佳解之誤差。最近有研究應用網路流動技巧，在考量現金流量時間價值及相關作業流程與資源限制下，有效地求解出最大淨現值下之最佳化專案排程，改善過去文獻所求之解僅為近似解的缺點。然而，該研究僅針對客戶端於作業完成時付款(payments at activities’ completion times, PAC)方式，實務上可應用範圍較小。
因此，本研究針對(1)相同間隔時間付款(Payments at Equal Time Intervals, ETI)、(2)按進度付款( Progress Payments, PP) 、(3)全額付款(Lump-Sum Payment, LSP)等不同客戶端付款方式之最大淨現值專案排程問題，考量現金流量時間價值及相關作業流程與資源限制下，利用數學規劃方法及時序網路流動技巧，分別構建各種數學規劃模式，以幫助決策者面對不同的付款方式下有效地規劃專案作業排程。此等模式為一含額外限制整數網路流動問題，本研究以最佳化軟體(CPLEX)求解。為測試本研究模式的實用求解績效，本研究以國際測試題庫(PSPLIB)所提供的專案資訊，進行範例研究，測試結果良好，顯示出本研究之不同付款模式可提供給學術及實務業者做為參考。

The project scheduling problem is sensitive to the time period. Due to the fact that the global industrial environment has rapidly grown nowadays, to maximize the profit, the enterprises in the market must adopt appropriate project management method to perform the project schedule. However, because the project size rapidly increases, with the shortage of environmental resources, factors involving in project scheduling are becoming more and more complicated than before. Although, in the past, there have been many studies where solution algorithms have been employed/developed to solve the problem which considers the limited resources, multiple modes and the net present value, the solutions obtained are approximate rather than optimal solutions. As a result, the optimality of the obtained solution is difficult to evaluate. It should be mentioned that there has been study where the network flow technique is applied to optimally solve the multi-mode resource constrained project scheduling problem with discounted cash flows (MRCPSPDCF), with the payment at activity completion time (PAC) pattern. Although its solution performance is good but it just focuses on the PAC pattern.
In this study, to increase the usefulness of model in payment pattern, the three different payment patterns, Payments at Equal Time Intervals (ETI), Progress Payments (PP), and Lump-Sum Payment (LSP) are considered to construct the MRCPSPDCF model. The proposed model will be expected to help enterprises efficiently solve the MRCPSPDCF for different payment patterns. The model is formulated as an integer network flow problem with side constraints. We employ the CPLEX mathematical programming solver, to solve the problem. To evaluate the performance of the proposed model, numerical tests regarding the project scheduling problem library (PSPLIB) are performed. The test results show that the model could be useful references for academics and practicals.

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