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研究生:朱碩智
研究生(外文):Shou-Chih Chu
論文名稱:資源受限之專案排程下的資源配置與排程問題
論文名稱(外文):The Resource-Constrained Project Scheduling Problems with Resource Allocation and Scheduling
指導教授:陳明德陳明德引用關係
學位類別:碩士
校院名稱:國立中正大學
系所名稱:企業管理所
學門:商業及管理學門
學類:企業管理學類
論文種類:學術論文
畢業學年度:93
語文別:英文
論文頁數:55
中文關鍵詞:專案排程資源受限之專案排程資源分配資源排程整數規劃
外文關鍵詞:RCPSPResource allocationResource schedulingInteger Programming
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在專案排程問題中ㄧ般均假設「資源無限」的情況下,以最短的時間完成ㄧ個專案。但「資源無限」的假設並不符合釵h現實的情況,如資源只有特定的可使用量。因此,資源的限制就會明顯的影響專案排程的結果,也因此產生了「資源受限之專案排程(Resource-Constrained Project Scheduling Problems, RCPSP)」的問題。傳統的RCPSP問題僅探討在資源的限制之下,如何最佳化專案排程目標,對於詳細的資源分派或資源排程的問題,卻未曾在過去的文獻中仔細探討。
實務上,專案經理往往必須同時對專案的活動與可利用資源進行排程以獲得最佳的排程目標。因此,本篇論文旨在提出ㄧ可同時針對專案活動與專案可利用資源進行排程的解決方法,以幫助專案經理能有效率的安排專案的運行與資源的使用。這也正是本篇論文與過去「資源受限之專案排程問題」相關研究最大的不同之處。
本研究提出一數學模型以協助管理者規劃專案活動與相關之資源分派的最佳化。此一整數規劃數學模型(Integer Programming Model, IP Model)經過數個假設性專案的數據檢測其在解決資源分派/資源排程問題上的適用性,均證明能以極有效的方式得到最佳化的結果。並希冀對實務界的專案管理人員有顯著的幫助。
The most general definition of the project scheduling problem is that of assigning scarce resources to competing activities over a given time horizon to obtain the best possible system performance. The objective of the traditional RCPSP problems is to schedule the project activities subject to resource limitations. However, the resource allocating and scheduling problems have not been addressed.
In practice, a project manager might need to schedule the project and allocate/schedule the available resources to each activity simultaneously. Therefore, this research intends to bridge the gap between them and propose a solution approach to project managers. This is the major difference between this thesis and the existing papers that mainly deal with the typical RCPSP problems only.
This study attempts to propose a mathematical-based model to assist in project managers for allocating and scheduling resources as well as project activities in a more efficient way. The developed IP model are verified and tested through a number of case projects with different number of activities and resources. Hope it do help to project managers in practice.
中 文 摘 要......................................................................................................................... i
ABSTRACT ........................................................................................................................... ii
致 謝.................................................................................................................................... iii
List of Contents.................................................................................................................... iv
List of Figures...................................................................................................................... vi
List of Tables....................................................................................................................... vii
================================================================
CHAPTER I INTRODUCTION .......................................................................................... 1
1.1 Research Background and Motivation ............................................................................. 1
1.2 Research Objectives ....................................................................................................... 3
1.3 Overview of This Thesis................................................................................................... 4
CHAPTER I I LITERATURES REVIEW ............................................................................ 6
2.1 Project scheduling problem ............................................................................................. 6
2.2 Fundamentals of resource-constrained project scheduling problem ................................... 10
CHAPTER III MODEL FORMULATION........................................................................... 13
3.1 Notations: .......................................................................................................................13
3.2 Preliminary analysis ......................................................................................................... 14
3.3 Decision variable............................................................................................................. 15
3.4 The objective ................................................................................................................. 15
3.5 The Constraints............................................................................................................... 17
Each job must be done.......................................................................................................... 17
Precedence relationship constraint ........................................................................................ 17
Parallel relationship constraint ............................................................................................... 17
3.6 The entire model............................................................................................................. 19
3.7 An example......................................................................................................................19
CHAPTER IV EXPERIMENTS and DISCUSSIONS.......................................................... 22
4.1 Case projects with 5 ≤ J ............................................................................................... 22
Case 1: (4×3) project ........................................................................................................... 22
Case 2: (4×4) project ........................................................................................................... 24
Case 3: (5×2) project ........................................................................................................... 25
Case 4: (5×3) project .......................................................................................................... 26
Case 5: (5×4) project ........................................................................................................... 27
Summary ............................................................................................................................. 29
4.2 Case projects with 6 to 10 activities................................................................................. 29
Case 6 and 7: (7×2) project and (7×4) project...................................................................... 29
Case 8: (8×4) project .......................................................................................................... 32
4.3 Case projects with over 10 activities................................................................................ 35
CHAPTER V CONCLUSIONS and RECOMMENDATIONS......................................... 38
5.1 Conclusions .................................................................................................................. 38
5.2 Recommendations ......................................................................................................... 39
References.......................................................................................................................... 41
Appendix............................................................................................................................ 43
1.Ahn, T., and S. S. Erenguc, 1998, “The Resource Constrained Project Scheduling Problem with Multiple Crashable Modes: A Heuristic Procedure” European Journal of Operational Research, Volume 107, Issue 2, pp.250-259.
2.Bandellomi, M., M. Tucci, and R. Rinaldi, 1994, “Optimal resource leveling using non-serial dynamic programming” European Journal of Operational Research, Volume 78, pp.167-177.
3.Brucker, P., and K. Sigrid, 2000, “A Linear Programming and Constraint Propagation-based lower bound for the RCPSP” European Journal of Operational Research, Volume 127, pp.355-362.
4.Böttcher, J., A. Drexl, R. Kolisch, and F. Salewski, 1999, “Project scheduling under partially renewable resource constraints” Management Science, Volume 45, Issue 4, pp.543-559.
5.Elmaghraby, S. E., 1995, “Activity nets: A guided tour through some recent developments” European Journal of Operational Research, Volume 82, Issue 3, pp.383-408.
6.Etgar, R., A. Shtub, and L. J. LeBlanc, 1995, “Scheduling projects to maximize net present value-the case of time-dependent, contingent cash flows” European Journal of Operational Research, Volume 96, pp.90-96.
7.Icemli, O., and W. O. Rom, 1996, “Solving the Resource Constrained Project Scheduling Problem with Optimization Subroutine Library” Computers & Operations Research, Volume 23, Issue 8, pp801-817.
8.Kempf, K., R. Uzsoy, S. Smith, and K. Gary, 2000, “Evaluation and comparison of production schedules”, Computers in Industry, Volume Vol. 42, pp. 203-220.
9.Kolisch, R., and R. Padman, 2001, “An integrated survey of deterministic project scheduling” Omega, The International Journal of Management Science, Volume 29, pp.249-272.
10.Kolisch, R., and A. Sprecher, 1996, “PSPLIB - A project scheduling problem library” European Journal of Operational Research, Volume 96, pp.205-216.
11.Nudtasomboon, N., and S. U. Randhawa, 1997, “Resource-constrained project scheduling with renewable and non-renewable resources and time-resource tradeoffs” Computers & Industrial Engineering Volume 32, Issue 1, pp. 227-242.
12.Schwindt, C., 1999, “Minimizing earliness-tardiness costs of resource-constrained projects” Operations Research Proceedings
13.Sprecher, A., R. Kolisch, and A. Drexl 1995, “Semi-active, active, and non-delay schedules for the resource-constrained project scheduling problem” European Journal of Operational Research, Volume volume 80, issue 1, pp 94-102.
14.Sprecher, A., and A. Drexl, 1998, “Multi-mode resource-constrained project scheduling by a simple, general and powerful sequencing algorithm” European Journal of Operational Research, Volume volume 107, issue 2, pp.431-450.
15.Talbot, F.B., 1982, “Resource-constrained project scheduling with time-resource tradeoffs: the non-preemptive case” Management Science, Volume 28, Issue 10, pp.1197-1210.
16.郭詩豪, 2004, 6 “於時間區間配置下有限資源專案排程問題最佳化之研究-以混合整數線性規劃求解”, 國立成奶j學, 工業與資訊管理學系碩士班, 碩士論文.
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