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研究生:盧寶后
研究生(外文):Baw-Ho Lu
論文名稱:具機器可用時間與機器合適度限制之平行機台排程問題
論文名稱(外文):Parallel Machine Scheduling with Machine Availability and Eligibility Constraints
指導教授:沈國基沈國基引用關係
指導教授(外文):Gwo-Ji Sheen
學位類別:碩士
校院名稱:國立中央大學
系所名稱:工業管理研究所
學門:商業及管理學門
學類:其他商業及管理學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:61
外文關鍵詞:Schedulingbranch and boundnetwork flowspar
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In this paper we consider the problem of scheduling n non-preemptive jobs on m identical machines with availability and eligibility constraints for minimizing the maximum lateness. That is, each machine is not continuously available at all time and each job is only allows to be processed on specified machines. Each availability interval of machines has a specific service level, and each job has to be processed at availability intervals with the service level specified or higher one.
We develop a branch-and-bound algorithm to solve this scheduling problem optimally. Firstly, we propose an algorithm based on the Least Flexible Job First/ Earliest Due Date First (LFJ/EDD) rule to find the upper bound. Network flow technique is used to model the scheduling problem of the preemptive jobs into a series of base problem that is equivalent to a maximum flow problem. Then, we propose a polynomial time algorithm that combines a maximum flow algorithm and binary search procedure to solve this scheduling problem optimally and use this result as our lower bound.
Computational experiments are proposed to compare the validity with complete branching method and to test the efficiency of proposed branch and bound algorithm. According to the result of computational experiment, we find that the run time of our algorithm is acceptable.
Table of Content


Abstract i
Table of Content ii
List of Tables iv
List of Figures v

Chapter 1 Introduction 1

1.1 Background and Motivation 1
1.2 Problem Description 4
1.3 Research Objectives 5
1.4 Research Methodology and Framework 5
1.4.1 Research Methodology 5
1.4.2 Research Framework 6

Chapter 2 Literature Review 8

2.1 Machine Availability Constraint 8
2.2 Machine Eligibility Constraint 12

Chapter 3 Branch and Bound Algorithm 15

3.1 Notation 15
3.2 Bounding Scheme 17
3.2.1 Upper Bound 18
3.2.2 Lower Bound 22
3.3 Branching Scheme 42
3.3.1 Node Representation 42
3.3.2 The branching process 42
3.3.3 The Proposed Branch and Bound Algorithm for the Problem 45

Chapter 4 Computational Analysis 48

4.1 Test Generation 48
4.2 Validation of the Branch and Bound Algorithm 49
4.3 Evaluation of the Branch and Bound Algorithm 50
4.3.1 Comparing with complete branching method 51
4.3.2 The Performance of the Branch and Bound Algorithm 53

Chapter 5 Conclusion 57
5.1 Research Contribution 57
5.2 Limitation Research 58
5.3 Further Research 58

References 59
[1]Blazewicz, J., M. Drozdowski, P. Formanowicz, W. Kubiak, and G.. Schmidt (2000), “Scheduling preemptable tasks on parallel processors with limited availability,” Parallel Computing, 26, 1195-1211.
[2]Blazewicz, J., P. Dell’Olmo, M. Drozdowski, and P. Maczka (2003), “Scheduling multiprocessor tasks on parallel processors with limited availability,” European Journal of Operational Research, 149, 377-389.
[3]Centeno, G., and R. L. Armacost (1997), “Parallel machine scheduling with release time and machine eligibility restrictions,” Computers & Industrial Engineering, 33(1-2), 273-276.
[4]Centeno, G., and R.L. Armacost (2004), “Minimizing makespan on parallel machines with release time and machine eligibility restrictions,” International Journal of Production Research, 42(6), 1243-1256.
[5]Ecker, K., G. Schmidt, J. Weglarz, and J. Blazewicz (1994), Scheduling in Computer and Manufacturing Systems (2th ed.), Springer-Verlag, Berlin.
[6]Federgruen, A., and H. Groenevelt (1986), “Preemptive scheduling of uniform machined by ordinary network flow techniques,” Management Science, 32(3), 341-349.
[7]Hwang, H.C., and S.Y. Chang (1998), “Parallel machines scheduling with machine shutdowns,” Computers & Mathematics with Applications, 36(3), 21-31.
[8]Hwang, H.C., S.Y. Chang, and K. Lee (2004), “Parallel machine scheduling under a grade of service provision,” Computers & Operation Research, 31, 2055-2061.
[9]Kellerer, H. (1998), “Algorithm for multiprocessor scheduling with machine release time,” IIE Transactions, 30, 991-999.
[10]Lee, C.Y. (1991), “Parallel machines scheduling with nonsimultaneous machine available time,” Discrete Applied Mathematics, 30, 53-61.
[11]Lee, C.Y. (1996), “Machine scheduling with an availability constraint,” Journal of Global Optimization, 9, 395-416.
[12]Lee, C.Y., Y. He, and G. Tang (2000), “A note on parallel machine scheduling with non-simultaneous machine available time,” Discrete Applied Mathematics, 100, 133-135.
[13]Lin, Y., and W. Li (2004), “Parallel machine scheduling of machine-dependent jobs with unit-length,” European Journal of Operational Research, 156, 261-266.
[14]Liu, Z., and E. Sanlaville (1995), “Preemptive scheduling with variable profile, precedence constraints and due dates,” Discrete Applied Mathematics, 58, 253-280.
[15]Liu, Z., and E. Sanlaville (1994), Profile scheduling of list algorithm, In: Chretienne, P. et al. (Eds.), Scheduling Theory and its Applications, NY: Wiley, p.91-110.
[16]Pinedo, M. (2002), Scheduling: Theory, Algorithm and System (2th ed.), Prentice Hall, Englewood Cliffs, NJ.
[17]Sanlaville, E. (1995), “Nearly online scheduling of preemptive independent tasks,” Discrete Applied Mathematics, 57, 229-241.
[18]Schmidt, G. (1988), “Scheduling independent tasks with deadlines on semi-identical processors,” Journal of the Operational Research Society, 39, 271-277.
[19]Schmidt, G. (2000), “Scheduling with limited machine availability,” European Journal of Operational Research, 121, 1-15.
[20]Ullman, J.D. (1975), “NP-complete scheduling problems,” Journal of Computer and System Sciences, 10, 384-393.
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