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A Lagrangian relaxation technique for the general assembly line balancing problem

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This paper addresses the problem of balancing assembly or fabrication lines. In order to achieve a given production rate or to optimize the use of workstations, one has to tackle the problem of balancing the production lines. It is well known that this problem belongs to the class of NP-hard problems. In this paper the polyhedron of the feasible solutions of the assembly line balancing problem is first studied. Then a Lagrangian relaxation algorithm that incorporates the set of cycle constraints in the objective function is proposed. These constraints are the complicating restrictions in the model. The relaxed problem has the interesting property that its linear programming relaxation always has integer optimal solutions. The subgradient algorithm is then used to maximize the Lagrangian dual. A heuristic is also used to find primal feasible solutions for the original line balancing integer program. These two bounds are then used to reduce the size of the branch-and-bound tree.

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References

  • Aghezzaf, E. H., Wolsey, L. A. and Magnanti, T. L. (1992) Optimizing subtrees of trees, CORE Discussion paper No.9250.

  • Arcus, A. L. (1966) COMSOAL— A computer method of sequencing operation for assembly lines. International Journal of Production Research, 4, 259–277.

    Google Scholar 

  • Artiba, A. and Tahon, C. (1992) Production planning knowledge-based system for pharmaceutical manufacturing lines. European Journal of Operations Research, 61(2), 18–29.

    Google Scholar 

  • Assche, F. V. and Herroelen, W. S. (1978) An optimal procedure for the single model deterministic assembly line balancing problem. European Journal of Operations Research, 3, 142–149.

    Google Scholar 

  • Baybars, I. (1986) Exact algorithms for simple assembly line balancing problems. Management Science, 32(8), 909–932.

    Google Scholar 

  • Elmaghraby, S. E. (1977) Activity Networks: Project Planning and Control by Network Models, Wiley, Chichester.

    Google Scholar 

  • Hackman S. T., Magazine, M. J. and Wee, T. S. (1989) Fast, effective algorithms for simple assembly line balancing problem. Operations Research, 37, 916–924.

    Google Scholar 

  • Held, M., Karp, R. M. and Shareshian, R. (1963) 'Assembly line balancing — dynamic programming with precedence constraints. Operations Research, 11, 442–459.

    Google Scholar 

  • Helgeson W. B. and Birnie, D. P. (1961) Assembly line using rancked positional weight technique. Journal of Industrial Engineering, 12, 394–398.

    Google Scholar 

  • Hoffman, T. R. (1963) Assembly line balancing with a precedence matrix. Management Science, 9, 551–562.

    Google Scholar 

  • Gröflin, H., Liebling, M. and Prodon, A. (1982) Optimal subtrees and extensions, Annals of Discourse in Mathematics, 16, 121–127.

    Google Scholar 

  • Jackson, J. R. (1956) A computing procedure for line balancing problem, Management Science, 2, 261–271.

    Google Scholar 

  • Johnson, R. V. (1981) Assembly line balancing algorithms: computation comparisons with formulation irregularities. International Journal of Production Research, 19, 277–287.

    Google Scholar 

  • Johnson, R. V. (1983) Branch and bound algorithm for assembly line balancing problems with formulation irregularities. Management Science, 29, 1309–1324.

    Google Scholar 

  • Kao, P. C. and Queyranne, M. (1982) On dynamic methods for assembly line balancing. Operations Research, 30, 375–390.

    Google Scholar 

  • Kilbridge, M. D. and Wester, L. (1961) The balance delay problem. Management Science, 8, 69–84.

    Google Scholar 

  • Mansoor, E. M. (1964) Assembly line an improvement on the rancked positional weight technique. Journal of Industrial Engineering, 15, 73–78.

    Google Scholar 

  • Mastor, A. A. (1970) An experimental investigation and comparative evaluation of production line balancing technique. Management Science, 16, 728–746.

    Google Scholar 

  • Mertens, P. (1967) Assembly line balancing by Partial Enumeration. Ablauf und Planungforschung, 8, 429–433.

    Google Scholar 

  • Nemhauser, G. L. and Wolsey, L. A. (1988) Integer and Combinatorial Optimization, Wiley, Chichester.

    Google Scholar 

  • Nivens, A. J. (1972) Assembly line balancing using best bud search. Mgmt Science, 18, 529–539.

    Google Scholar 

  • Patterson, J. H. and Albracht, J. J. (1975) Assembly line balancing: 0–1 programming with Fibonacci search. Operations Research, 23, 166–174.

    Google Scholar 

  • Queyranne, M. (1985) Bounds for assembly line balancing heuristics. Operations Research, 33, 1353–1359.

    Google Scholar 

  • Schrage, L. and Baker, K. R. (1978) Dynamic programming solution of sequencing problems with precedence constraints. Operations Research, 26, 444–459.

    Google Scholar 

  • Talbot, F. B. and Patterson, J. H. (1984) An integer programming algorithm with network cuts for solving the single model assembly line balancing problem. Management Science, 30, 85–99.

    Google Scholar 

  • Thangavelu, S. R. and Shetty, C. M. (1971) Assembly line balancing by 0–1 integer programming. AIIE Transactions, 3, 61–68.

    Google Scholar 

  • Tonge, F. M. (1961) A Heuristic Program for Assembly Line Balancing, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • White, W. W. (1961) Comments on paper by Bowman. Operations Research, 9, 274–276.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Département d'Informatique et Gestion Quantitative, Facultés Universitaires Catholiques de Mons, 151, Chaussée de Einehe, B7000, Mons, Belgium

    E. H. Aghezzaf & A. Artiba

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  1. E. H. Aghezzaf
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  2. A. Artiba
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Aghezzaf, E.H., Artiba, A. A Lagrangian relaxation technique for the general assembly line balancing problem. J Intell Manuf 6, 123–131 (1995). https://doi.org/10.1007/BF00123684

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