User menu

Coefficient strengthening: a tool for reformulating mixed-integer programs

Bibliographic reference Andersen, Kent ; Pochet, Yves. Coefficient strengthening: a tool for reformulating mixed-integer programs. In: Mathematical Programming A, Vol. 122, no. 1, p. 121-154 (Mars 2010)
Permanent URL
  1. Andersen E.D., Andersen K.D.: Presolving in linear programming. Math. Program. 71(2), 221–245 (1995)
  2. Bixby, R.E., Ceria, S., McZeal, C.M., Savelsbergh, M.W.P.: An updated mixed integer programming library: MIPLIB 3.0, Technical report TR98-03, Department of Computational and Applied Mathematics, Rice University (1998)
  3. Bradley G.H., Hammer P.L., Wolsey L.: Coefficient reduction for inequalities in 0–1 variables. Math. Program. 7(3), 263–282 (1974)
  4. Brearley A.L., Mitra G., Williams H.P.: Analysis of mathematical programming problems prior to applying the simplex algorithm. Math. Program. 8(1), 54–83 (1975)
  5. CPLEX optimizer version 9.1, ILOG
  6. Crowder H., Johnson E.L., Padberg M.: Solving large-scale zero-one linear programming problems. Oper. Res. 31(5), 803–834 (1993)
  7. Dietrich B.L., Escudero L.F., Chance F.: Efficient reformulation for 0–1 programs: methods and computational results. Discrete Appl. Math. 42(2-3), 147–175 (1993)
  8. Escudero L.F., Martello S., Toth P.: On tightening 0–1 programs based on extensions of pure 0-1 knapsacks and subset-sum problems. Annals Oper. Res. 81, 379–404 (1998)
  9. Gomory, R.E.: An algorithm for the mixed integer problem, The Rand Corporation, Santa Monica, Technical Report RM-2597 (1960)
  10. Hoffman Karla L., Padberg Manfred, Improving LP-Representations of Zero-One Linear Programs for Branch-and-Cut, 10.1287/ijoc.3.2.121
  11. Kianfar F.: Stronger inequalities for 0,1 integer programming using knapsack functions. Operations Research 19, 1374–1392 (1971)
  12. Laundy, R., Perregaard, M., Tavares, G., Tipi, H., Vazacopoulos, A.: Solving hard integer programming problems with Xpress-MP: a MIPLIB 2003 case study, Rutcor Research Report (2007)
  13. Lougee-Heimer R., Adams W.: A conditional logic approach for strengthening mixed 0–1 linear programs. Annals Oper. Res. 139, 289–320 (2005)
  14. Martin A.: General mixed integer programming: computational issues for branch-and-cut algorithms. Lecture Notes Comput. Sci. 2241, 1–25 (2001)
  15. McDonnell, F.J.: Inequalities with small coefficients and the reformulation of integer programmes. Ph.D. thesis, The Business School, Loughborough University (1999)
  16. Nemhauser George, Wolsey Laurence, Integer and Combinatorial Optimization : Nemhauser/Integer and Combinatorial Optimization, ISBN:9781118627372, 10.1002/9781118627372
  17. Pochet, Y., Warichet, F.: A tighter continuous time formulation for the cyclic scheduling of a mixed plant. CORE Discussion Paper, DP 2007/26, UCL, Belgium (2007)
  18. Savelsbergh M. W. P., Preprocessing and Probing Techniques for Mixed Integer Programming Problems, 10.1287/ijoc.6.4.445
  19. Schilling G., Pantelides C.C.: Optimal periodic scheduling of multipurpose plants. Comput. Chem. Eng. 23(4–5), 635–655 (1999)
  20. Tomlin J.A., Welsh J.S.: Finding duplicate rows in a linear programming model. Oper. Res. Lett. 5, 7–11 (1986)
  21. Warichet, F.: Scheduling of mixed batch-continuous production lines. Ph.D. Thesis, UCL, Belgium (2007)
  22. Wu D., Ierapetritou M.: Cyclic short-term scheduling of multiproduct batch plants using continuous-time representation. Comput. Chem. Eng. 28(11), 2271–2286 (2004)