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Job Shop Schedule 의 Rescheduling 과 개선방법

Job Shop Schedule 의 Rescheduling 과 개선방법. 공장자동화연구실 장양자 1998/11/05. Contents. Introduction Rescheduling method by Wu & Li, 1995 Improving Job-Shop Schedules by Chu et. al. 1998 Conclusion. Introduction. Job Shop N end products M machines Each product has its own operation sheet

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Job Shop Schedule 의 Rescheduling 과 개선방법

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  1. Job Shop Schedule의 Rescheduling과 개선방법 공장자동화연구실 장양자 1998/11/05

  2. Contents • Introduction • Rescheduling method by Wu & Li, 1995 • Improving Job-Shop Schedules by Chu et. al. 1998 • Conclusion

  3. Introduction • Job Shop • N end products • M machines • Each product has its own operation sheet • Literature Survey • Optimum schedule • Dynamic programming (Held and Karp 1962, French 1982) • Branch-and-bound (Fisher 1973)

  4. Introduction -cont’d • Literature Survey • Heuristics • Dispatching Rules • SBP • Neighborhood search heuristics (F. Werner et. al. 1995.. )

  5. A new rescheduling method for computer based scheduling systems I.J.P.R., 1995, Vol. 33, No. 8, 2097-2110 H.-H. Wu and R.-K. Li Dept. of Industrial Engineering and Management, National Chiao Tung Univ. Taiwan

  6. Introduction • After rescheduling factor occurs • Regeneration • Yamamoto & Nof(1985), Grant & Nof(1989), FACTOR(1990), Farhoodi(1990) • Net Change Rescheduling • Kanet and Sridharan(1990) • manual pairwise exchange of affected operations

  7. Scheduling Graph • Alternative representation of Gantt chart Oi,j M S T STA END POR SOR POM SOM

  8. Example SG O1,1 M1 10 100 0 110 O1,3 M1 5 30 175 210 O3,1 M1 10 60 210 280 M1 O2,1 M2 10 60 0 70 O3,2 M2 10 90 280 380 O2,3 M2 5 50 385 440 M2 O2,2 M3 10 200 175 385 O3,3 M3 10 60 475 545 O2,4 M3 5 30 440 475 O1,2 M3 5 60 110 175 M3

  9. Time Effect • SG의 구조를 변경하지 않고 공정의 시작 시간과 종료 시간만 변경 • 이러한 변경의 효과: 2개의 time-effect affected operation을 야기 -> 계속 전파 • Time effect computation(forward scheduling) - tij: time effect • STAij=MAX{END(POR)(Oij), END(POM(Oij)), STAij+tij} • ENDij=STAij+Sij+Tij

  10. Relationship Effect • Operation Insertion, Deletion, Movement • Operation Deletion • Update machine relationship • SOM(POM(Oij))=SOM(Oij) • POM(SOM(Oij))=POM(Oij) • Update sequence relationship • SOR(POR(Oij))=SOR(Oij) • POR(SOR(Oij))=POR(Oij) • Explode Starting time and Ending time those operations

  11. Relationship Effect -cont’d • Operation Insertion • Update POM and SOM for operations Oij and Oxy • Update POR and SOR of Oij • Update SOR of the operation of job i previous to Oij and POR of the operation of job i subsequent to O ij • Explode starting time and ending time

  12. How to employ the rescheduling method • Develop a series of rescheduling commands • e.g. insert a job, delete a job, move a job, split a job… • Require scenario based development

  13. Conclusion • Automated net change rescheduling function enabled • time effect and relationship effect provide functions of • identifying those operations that require revision • revising those identified affected operations • updating the starting and ending times

  14. Improving job-shop schedules through critical pairwise exchanges I.J.P.R. 1998, Vol. 36, No. 3, 683-694 C.Chu (Universite de Technologie de Troyes, Dept. GSI, France) J. -M. Proth (Institute for Systems Research, Univ. of Maryland) C. Wang (Shenyang Institute of Automation, Chinese Academy of Sciences, China)

  15. Introduction • Job Shop Scheduling Problem • Disjunctive Graph modeling 2 5 O1 O2 O3 5 4 6 3 0 3 7 4 5 5 2 4 7 0 3 5 O0 O4 O5 O6 O10 4 3 6 0 4 5 4 2 5 3 7 O8 O7 O9 6 3

  16. Introduction -cont’d • Feasible schedule • makespan=29 2 5 O1 O2 O3 4 6 3 0 4 2 4 7 0 3 5 O0 O4 O5 O6 O10 6 3 0 4 2 3 O8 O7 O9 6 3

  17. Theorem 1 The ordinary graph obtained by reversing a critical disjunctive arc in an acyclic ordinary graph is still acyclic O1 O2 O3 4 6 3 0 7 4 2 0 3 5 O0 O4 O5 O6 O10 6 3 0 4 2 3 O8 O7 O9 6 3

  18. Theorem 2 If(Oi, Oj) belongs to all the critical paths of G, then CP(G’) < CP(G) if and only if L(G,0,j)-L(G’’,0,j)+L(G,i,N+1)-L(G’’,i,N+1) > wi+wj where, G’: (Oi, Oj) -> (Oj, Oi) G’’: (Oi, Oj) deleted

  19. Heuristic Algorithm 1. Generate an initial schedule and derive its ordinary graph model 2. Compute a critical path in this ordinary graph and identify the critical disjunctive arcs 3. For each critical disjunctive arc (Oi, Oj) compute C = L(G,0,j)-L(G’’,0,j)+L(G,i,N+1)-L(G’’,i,N+1) - (wi+wj) 4. If C > 0 for at least one arc, then reverse the arc and go to 2, otherwise stop the computation

  20. Test Data • 24 test problems from OR library • http://mscmga.ms.ic.ac.uk/info.html • Imperial College Management School • J. E. Beasley

  21. Numerical Results • Data Set from Applegate and Cook(1991)

  22. Numerical ResultsAdams’: 2.31-38.18s • Another test data set- 5 groups • (10x10x10), (20x10x10), (20x15x15), (30x15x15), (40x15x15)

  23. Conclusion • show how to select the disjunctive arcs to be reversed in order to improve the makespan • Priority rules enriched by the critical pairwise exchange • simple to implement and required a very small amount of computation time

  24. References • Adams, J., Balas, E., and Zawack, D., 1988, The shifting bottleneck procedure for job shop scheduling, Mgmt Sci., 34(3), 391-401 • Calier, J., and Pinson, E., 1989, An algorithm for solving the job-shop problem, Mgmt Sci., 35(2), 164-176 • Werner, F. and Winkler, A., 1995, Insertion technique for the heuristic solution of the job shop problem, Discrete Applied Mathematics, 58, 191-211 • Panwalkar, S.S., and Iskander, W., 1977, A survey of scheduling rules, Operations Research, 25(1), 45-61 • MacCarthy, B. L. and Liu, J., 1993, Addressing the gap in scheduling research: a review of optimization and heuristic methods in production scheduling, I. J. P. R., 31, 59-79

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