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A production planning problem in FMS

  • Chapter 2 Production Planning And Control
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Abstract

We present in this work a hierarchical approach for generating alternatives for production planning in a generic floor shop problem within the environment of Flexible Manufacturing Systems (hereafter, FMS). Briefly, the problem can be stated as follows: Given the resources of a FMS and the characteristics of the parts to be produced along a planning horizon, obtain the loading ordering of the parts in the FMS, the execution ordering of the operations and the processing route of each part (i.e., the working stations where each operation is to be executed), such that the production and transport costs are minimized and the modules workload is levelized. The problem is decomposed into three subproblems which are arranged in a hierarchy; a variety of models is presented, as well as the input/output relations that allow to integrate them; we also propose some algorithmic ideas to exploit the special structure of the problem. Computational experience is reported.

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References

  1. J.C. Ammons, C.B. Lofgren and L.F. McGinnis, A large-scale work station loading problem, in: Stecke, K.E. and R. Suri (eds.) (1984) 249–255.

  2. C. Abraham, B. Dietrich, S. Graves, W. Maxwell and C. Yano, A research agenda for models to plan and schedule manufacturing systems, Report RC-11329, IBM Research, Yorktown Heights, NY, 1985.

    Google Scholar 

  3. E. Balas and N. Christofides, A restricted Lagrangian approach to the traveling salesman problem, Mathematical Programming 21 (1981) 19–46.

    Google Scholar 

  4. E. Berrada and K.E. Stecke. A branch and bound approach for machine loading in Flexible Manufacturing Systems, working paper 329-b, Graduate School of Business Administration, University of Michigan, Ann Arbor, Michigan, See also: Management Science 32 (1986) 1316–1334.

    Google Scholar 

  5. C.S. Carpaneto, S. Martello and P. Toth, Linear assignment problems, School of Combinatorial Optimization, Rio de Janeiro, 1985.

    Google Scholar 

  6. E.K. Chakravarty and A. Shtub, Selecting parts and loading flexible manufacturing systems, in Stecke, K.E. and R. Suri (eds.) (1984) 284–289.

  7. A. Chatterjee, M.A. Cohen, W.L. Maxwell and L.W. Miller, Manufacturing flexibility: models and measurement, in Stecke, K.E. and R. Suri (eds.) (1984) 49–64.

  8. H. Crowder, E.L. Johnson and M. Padberg, Solving large-scale zero-one linear programming problems, Operations Research 31 (1983) 803–834.

    Google Scholar 

  9. H. Engelke, J. Grotrian, C. Scheuing, A. Schmackpfeffer, W. Schwarz, B. Solf and J. Tomann, Integrated manufacturing modeling system, IBM J. of Research and Development 29 (1985) 343–355.

    Google Scholar 

  10. L.F. Escudero, Special sets in mathematical programming, in:Applied Numerical Modeling, eds. E. Alarcon, and C. Brebbia (Pentech Press, London, 1979) 535–551.

    Google Scholar 

  11. L.F. Escudero, An integrated approach for generating production planning models in FMS, working paper, IBM GMTC, Sindelfingen, FRG, 1986.

    Google Scholar 

  12. L.F. Escudero, An (inexact) algorithm for the sequential ordering problem, European J. of Operational Research (1988, to appear).

  13. L.F. Escudero, An inexact algorithm for part input sequencing and scheduling with side constraints in FMS, Intern. J. of Flexible Manufacturing Systems (submitted for publication).

  14. A. Freville and G. Plateau, Heuristics and reduction methods for multiple constraints 0–1 linear programming problems, European J. of Operational Research 24 (1986) 206–215.

    Google Scholar 

  15. T.J. Greene and R.P. Sadowski, A mixed integer program for loading and scheduling multiple flexible manufacturing cells, European J. of Operational Research 24 (1986), 379–386.

    Google Scholar 

  16. M. Grotschel, M. Junger and G. Reinelt, A cutting plane algorithm for the linear ordering problem, Operations Research 34 (1984) 1195–1220.

    Google Scholar 

  17. M. Guignard and K. Spielberg, Propagation, penalty improvement and use of logical inequalities, Mathematics of Operations Research 25 (1977) 157–171.

    Google Scholar 

  18. T.G. Gunn, The mechanization of design and manufacturing, Scientific American 247 (1982) 870–108.

    Google Scholar 

  19. K. Hoffman and M. Padberg, LP-based combinatorial problem solving, Annals of Operations Research 5 (1986) 145–194.

    Google Scholar 

  20. IBM. 1975. MPSX/370, Mathematical Programming System Extended/370 and MIP/370, Mixed Integer Programming/370; Ref. manuals SH19-1095 and SH19-1099. Introduction to the Extended Control Language, 1978, Ref. manual SH19-1147). Newletter, 1979, SN19-1132.

  21. E.L. Johnson, M.M. Kostreva and U. Suhl, Solving 0–1 integer programming problems arising from large-scale planning models, Operations Research 33 (1985) 803–819.

    Google Scholar 

  22. R.M. Karp and J.M. Steele, Probabilistic analysis of heuristics, in:The Traveling Salesman Problem, A Guided Tour of Combinatorial Optimization, eds. E.L. Lawler, J.K. Lenstra, A.H.G. Rinnooy-Kan and B. Shmoys (Wiley, NY, 1985) 181–205.

    Google Scholar 

  23. A. Kusiak Integer programming approach to the process planning problem, Intern. J. of Advanced Manufacturing Technology 1 (1985) 73–83.

    Google Scholar 

  24. A. Kusiak and G. Finke, Modeling and solving the flexible forging module scheduling problem, Working paper 85/06, Dept. of Mechanical and Industrial Engineering, University of Manitoba, Winnipeg, Canada, 1985.

    Google Scholar 

  25. S. Martello, An enumerative algorithm for finding Hamiltonian circuits in a directed graph, ACM Transactions on Mathematical Software 9 (1983) 131–138.

    Google Scholar 

  26. C. Sandi, Solution of the machine loading problem with binary variables, in:Combinatorial Programming: Methods and Applications eds. B. Roy, (D. Reidel, Dordrecht-Holland, 1975) 371–378.

    Google Scholar 

  27. K.E. Stecke (1983), Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems, Management Sciences 29 (1983) 273–288.

    Google Scholar 

  28. K.E. Stecke A hierarchical approach to solving machine grouping and loading problems of flexible manufacturing systems, European J. of Operational Research 24 (1986) 369–378.

    Google Scholar 

  29. K.E. Stecke and T.L. Morin, Optimality of balanced workload in flexible manufacturing systems, European J. of Operational Research 20 (1985) 68–82.

    Google Scholar 

  30. K.E. Stecke, and R. Suri (eds.)Flexible Manufacturing Systems: Operations Research Models and Applications, University of Michigan, Ann Arbor, 1984.

    Google Scholar 

  31. K.E. Stecke and F.B. Talbot, Heuristic loading algorithms for flexible manufacturing systems,Proc. 7th Intern. Conf. on Production Research, Windsor, Ontario, 1983.

  32. T.J. Van Roy and L.A. Wolsey, Solving mixed integer programming problems using automatic reformulation, Operations Research 25 (1987) 45–57.

    Google Scholar 

  33. C.K. Whitney and T.S. Gaul, Sequential decision procedures for batching and balancing in FMSs, in Stecke, K.E. and R. Suri (eds.) (1984) 243–284.

  34. R.J. Wittrock, Scheduling algorithms for flexible flow lines, IBM J. of Research and Development 29 (1985) 401–412.

    Google Scholar 

  35. R.J. Wittrock, An adaptable scheduling algorithm for flexible flow lines, Report RC-11387, IBM Research Division, Yorktown Heights, NY, 1986.

    Google Scholar 

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Escudero, L.F. A production planning problem in FMS. Ann Oper Res 17, 69–103 (1989). https://doi.org/10.1007/BF02096599

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