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The Design of Cellular Manufacturing System

The Design of Cellular Manufacturing System. 2000. 06. 01 제조통합자동화 실험실 변 명 희. Contents. Paper: CF method Critical review “ A Comparison of cellular manufacturing research presumptions with practice ”. Classification of the CF methods. CF 의 input, consideration

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The Design of Cellular Manufacturing System

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  1. The Design of Cellular Manufacturing System 2000. 06. 01 제조통합자동화 실험실 변 명 희 MAI Lab Seminar

  2. Contents • Paper: CF method • Critical review • “A Comparison of cellular manufacturing research presumptions with practice” MAI Lab Seminar

  3. Classification of the CF methods • CF의 input, consideration • Parts, machines, machine capacity, routing… • CF의 performance measure • Inter-cell transfer, Diagonal voids • machine utilization balance • CF의 method Cell Formation Techniques Cluster Analysis Graph Partitioning Artificial Intelligence Mathematical Programming MAI Lab Seminar

  4. Stepwise decomposition approaches for large scale cell formation problems Ja-Shen Chen, Sunderesh S. Heragu Dept. of Business Administration, Yuan-Ze Univ., Taiwan Dept. of Decision Science and Eng. Sys., USA EJOR 113(1999) 64-79 MAI Lab Seminar

  5. Introduction • Three steps in cellular manufacturing systems • Cell formation • Machine layout • Cell layout • Incorporating three critical aspects • Alternate routings • resource underutilization • Practical constraints-machine capa., cell size, machine특성 • Stepwise decomposition approach to solve large scale cell formation problems MAI Lab Seminar

  6. The cell formation model • Decision variables Operation time of part i in machine j # of part i machine j is required for part i Total available time of machine j MAI Lab Seminar

  7. Model(continue) Underutilization cost Model I volume i: part j: machine k: cell Inter-cell movement cost Inter-cell cost Operation # s,t는 같이 위치하면 안 된다. s,t는 같이 위치해야 한다. MAI Lab Seminar

  8. Model reformulate Nonlinear linear Model Ia MAI Lab Seminar

  9. Benders decomposition structure • 1. Primal problem • Integer variable 을 fixing 시킨 문제 • 2. Dual problem • From primal problem • 3. Benders master problem • Fixed 되었던 변수로 이루어진 problem Dual로 UB, Master로 LB를 구한다 MAI Lab Seminar

  10. Primal 과 Dual의 관계 Primal Dual   MAI Lab Seminar

  11. Solution Technique(1/3) Primal problem(Model P)- fixing the value of yjk MAI Lab Seminar

  12. Solution Technique(2/3) Dual problem(Model D) MAI Lab Seminar

  13. Solution Technique(3/3) Master problem(Model M) yjk에 관련되는 constraints Benders cut MAI Lab Seminar

  14. Benders decomposition Algorithm1 • Step0: Set LB=-, UB=+ , yj1=1 j and yjk=0 j,k1 • Step1: Solve Model D. If the current optimal solution value ž<UB, set UB= ž. If LB UB, stop. We have opt. Solution of the original mixed-integer problem. Otherwise go to Step2. • Step2: Update Model M by adding a new cst(23), solve the model and obtain opt. Solution z* and opt. values for integer variables yjk. Set LB=z* and update the yjk variables in the dual problem. Go to Step1. MAI Lab Seminar

  15. Stepwise decomposition approach • 반복적으로 Benders decomposition 사용 • Integer variable 수 : j * k • Machine 수는 조절이 불가능하지만, cell은 가능하다. • Approach1: 초기의 cell의 크기를 2로 놓는다. • Approach2: Heuristic을 이용하여 초기의 문제를 적절한 수의 cell로 decomposition한다. MAI Lab Seminar

  16. Example of approach • 155 parts, 19 machine types • Machine capacity 고려한 machine 수=21개 • First decomposition step • 117 parts, 13 machines/ 38 parts, 8 machines • 특징 : 모든 part는 machine 1or 2를 처음에 거친다. • M1,2를 제외하고 계속 decomposition 진행 M3, M4, M6 M5,M7,M8,M9,M10,M11 M1 M2 M12,M13 M13,M14,M15 M15,M18 MAI Lab Seminar M16,M17,M19

  17. A Comparison of CM research presumptions with practice Robert F. Marsh1, Scott M. Shafer2, Jack R. Meredith2 1: University of Wisconsin-Milwaukee, USA 2: Wake Forest University, USA IJPR(1999), VOL. 37, NO. 14 MAI Lab Seminar

  18. Introductions • Research of CM is rich • CM literature has made a significant shift away from application to theory • Biased on sophisticated cell formation procedures • Something to do in this paper • Identifying the consistency b/w CM as envisioned by researchers and CM as used in practice • 10 presumptions & practices of 14firms MAI Lab Seminar

  19. Introductions MAI Lab Seminar

  20. Research presumptions compared to practice • Pre.1: CM consists of dissimilar equipment types and similar part families. • Pre.2: CM planning is performed comprehensively rather than incrementally. 대부분 sequential planning • Pre.3: Aggregate measures are more appropriate than individual cells/part families aggregate measure는 다른 용도로 사용된다. MAI Lab Seminar

  21. Compared to practices • Pre. 4: Identification of part families and machine groups is a complex problem. human and organizational elements more difficult than technical element • stopping rule, a guideline when CF should cease. • Pre. 5: more efficient when cells are independent. • Pre. 6: Cell efficiency and other advantages decrease for cells with a large # of workers or machines •cell size: # of machines or # of workers MAI Lab Seminar

  22. Compared to practices • Pre. 7: remainder cell의 필요성 • Pre. 8: Equipment duplication is the best alternative for accommodating parts requiring equipment residing in more than one cell cost 때문에 remainder cell을 선택 • Pre. 9: Cell workloads must be balanced.  machine utilization imbalances  labor utilization을 통해 가능할 수 있다. MAI Lab Seminar

  23. Compared to Practices • Pre. 10: A common CM disadvantage is a loss of flexibility. which flexibility????  routing flexibility  flexibility definition : the ability to increase volume or change mix without constraint MAI Lab Seminar

  24. Conclusions • Incremental cell formation • Cell-level measures of performance • Stopping rules • Trade-offs of inter-cellular transfers and cell size • Cell system as a collection of workers and machines MAI Lab Seminar

  25. References • Ching-Yuen Chan, Fat-Wing Lam, Chee-Pui Lee, “Consideration for using cellular manufacturing”, Journal of Materials Processing Technology, 96, 182-187(1999) • C.Caux, R. Bruniaus, H. Pierreval, “Cell formation with alternative process plans and machine capacity constraints: A new combined approach”, IJPE, 64, 279-284(2000) • Hassan M. Selin, Ronald G. Askin, Asoo J. Vakharia, “Cell formation in GT: review, evaluation and directions for future research”, Computers ind. Engng, 34, 3-20(1998) • Willam T. Akright, Dennis E. Kroll, “Cell formation performance measures determining when to change an existing layout”, Computers ind. Engng, 34, 159-171(1998) MAI Lab Seminar

  26. Reference • Richard Kipp Martin, “ Large scale linear and integer optimization : a unified approach”, Kluwer Academic Publisher, 1999 MAI Lab Seminar

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