A New Dantzig-Wolfe Reformulation and Branch-and-Price Algorithm for the Capacitated Lot-Sizing Problem with Setup Times

Published Online:https://doi.org/10.1287/opre.1070.0404

References

  • Barany I., Van Roy T. J., Wolsey L. A. Strong formulations for multi-item capacitated lot sizing. Management Sci. (1984) 30(10):1255–1261LinkGoogle Scholar
  • Barnhart C., Johnson E. L., Nemhauser G. L., Savelsbergh M. W. P., Vance P. H. Branch-and-price: Column generation for solving huge integer programs. Oper. Res. (1998) 46(3):316–329LinkGoogle Scholar
  • Belvaux G., Wolsey L. A. BC-PROD: A specialized branch-and-cut system for lot-sizing problems. Management Sci. (2000) 46(5):724–738LinkGoogle Scholar
  • Belvaux G., Wolsey L. A. Modelling practical lot-sizing problems as mixed integer programs. Management Sci. (2001) 47(7):993–1007LinkGoogle Scholar
  • Bitran G. R., Matsuo H. The multi-item capacitated lot size problem: Error bounds of Manne's formulations. Management Sci. (1986) 32(3):350–359LinkGoogle Scholar
  • Cattrysse D., Maes J., Van Wassenhove L. N. Set partitioning and column generation heuristics for capacitated dynamic lotsizing. Eur. J. Oper. Res. (1990) 46:38–47CrossrefGoogle Scholar
  • Dantzig G. B., Wolfe P. Decomposition principle for linear programs. Oper. Res. (1960) 8:101–111LinkGoogle Scholar
  • Degraeve Z., Jans R. A new Dantzig-Wolfe reformulation and branch-and-price algorithm for the capacitated lot sizing problem with set up times. (2003) ERIM Report Series ERS-2003-010-LIS, Erasmus University, Rotterdam, The NetherlandsGoogle Scholar
  • Degraeve Z., Peeters M. Optimal integer solutions to industrial cutting stock problems: Part 2, Benchmark results. INFORMS J. Comput. (2003) 15(1):58–81LinkGoogle Scholar
  • Dzielinski B. P., Gomory R. E. Optimal programming of lot sizes, inventory, and labor allocations. Management Sci. (1965) 11(9):874–890LinkGoogle Scholar
  • Eppen G. D., Martin R. K. Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper. Res. (1987) 35(6):832–848LinkGoogle Scholar
  • Florian M., Klein M. Deterministic production planning with concave costs and capacity constraints. Management Sci. (1971) 18(1):12–20LinkGoogle Scholar
  • Geoffrion A. M. Lagrangean relaxation for integer programming. Math. Programming Stud. (1974) 2:82–113CrossrefGoogle Scholar
  • Gopalakrishnan M., Ding K., Bourjolly J.-M., Mohan S. A tabu-search heuristic for the capacitated lot-sizing problem with set-up carryover. Management Sci. (2001) 47(6):851–863LinkGoogle Scholar
  • Huisman D., Jans R., Peeters M., Wagelmans A. P. M., Desaulniers G., Desrosiers J., Solomon M. Combining column generation and Lagrangian relexation. Column Generation (2005) (Springer, New York) 247–270CrossrefGoogle Scholar
  • Jans R., Degraeve Z. Improved lower bounds for the capacitated lot sizing problem with setup times. Oper. Res. Lett. (2004) 32:185–195CrossrefGoogle Scholar
  • Jans R., Degraeve Z. Meta-heuristics for dynamic lot-sizing: A review and comparison of solution approaches. Eur. J. Oper. Res. (2007) 177(3):1855–1875CrossrefGoogle Scholar
  • Kleindorfer P. R., Newson E. F. P. A lower bounding structure for lot-size scheduling problems. Oper. Res. (1975) 23(2):299–311LinkGoogle Scholar
  • Lambrecht M., Vanderveken H. Heuristic procedures for the single operation, multi-item loading problem. AIIE Trans. (1979) 11(4):319–326CrossrefGoogle Scholar
  • Lasdon L.Optimization Theory for Large Systems (1970) (Macmillan Company, New York) Google Scholar
  • Leung J. M. Y., Magnanti T. L., Vachani R. Facets and algorithms for capacitated lot sizing. Math. Programming (1989) 45:331–359CrossrefGoogle Scholar
  • Manne A. S. Programming of economic lot sizes. Management Sci. (1958) 4(2):115–135LinkGoogle Scholar
  • Martin K. Generating alternative mixed-integer programming models using variable redefinition. Oper. Res. (1987) 35(6):820–831LinkGoogle Scholar
  • Miller A. J., Nemhauser G. L., Savelsbergh M. W. P. On the capacitated lot-sizing and continuous 0-1 knapsack polyhedra. Eur. J. Oper. Res. (2000) 125:298–315CrossrefGoogle Scholar
  • Nemhauser G. L., Wolsey L. A.Integer and Combinatorial Optimization (1988) (John Wiley & Sons, New York) CrossrefGoogle Scholar
  • Pochet Y. Valid inequalities and separation for capacitated economic lot sizing. Oper. Res. Lett. (1988) 7(3):109–115CrossrefGoogle Scholar
  • Schrage L.LINDO: Optimization Software for Linear Programming (1995) (Lindo Systems Inc., Chicago, IL) Google Scholar
  • Thizy J. M., Van Wassenhove L. N. Lagrangean relaxation for the multi-item capacitated lot-sizing problem: A heuristic implementation. IIE Trans. (1985) 17(4):308–313CrossrefGoogle Scholar
  • Trigeiro W., Thomas L. J., McClain J. O. Capacitated lot sizing with set-up times. Management Sci. (1989) 35(3):353–366LinkGoogle Scholar
  • Vanderbeck F. Lot-sizing with start-up times. Management Sci. (1998) 44(10):1409–1425LinkGoogle Scholar
  • Vanderbeck F. On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. (2000) 48(1):111–128LinkGoogle Scholar
  • Vanderbeck F., Savelsbergh M. W. P. A generic view of Dantzig-Wolfe decomposition in mixed integer programming. Oper. Res. Lett. (2006) 34:296–306CrossrefGoogle Scholar
  • Wagner H. M., Whitin T. M. Dynamic version of the economic lot size model. Management Sci. (1958) 5(1):89–96LinkGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.