Locally ideal formulations for piecewise linear functions with indicator variables

Operations Research Letters

Volumn 41, Issue 6, 2013, Pages 627-632

  Sridhar, Srikrishna ^a   Linderoth, Jeff ^a   Luedtke, James ^a  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

Author keywords

Indicator variables; Mixed integer programming; Piecewise linear function

Indexed keywords

COMPUTATIONAL PERFORMANCE; INDICATOR VARIABLES; MIXED INTEGER LINEAR PROGRAMMING (MIP); MIXED-INTEGER PROGRAMMING; PIECE-WISE LINEAR FUNCTIONS;

INTEGER PROGRAMMING; LINEAR PROGRAMMING;

PIECEWISE LINEAR TECHNIQUES;

EID: 84884265006     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.orl.2013.08.010     Document Type: Article

References (25)

1. N. Alguacil, A.L. Motto, and A.J. Conejo Transmission expansion planning: a mixed-integer LP approach IEEE Trans. Power Syst. 18 2003 1070 1077
2. A. Balakrishnan, and S.C. Graves A composite algorithm for a concave-cost network flow problem Networks 19 1989 175 202
3. E. Balas Disjunctive programming Ann. Discrete Math. 5: Discrete Optim. 1979 North Holland 3 51
4. E.W.L. Beale, J.A. Tomlin, Special facilities in a general mathematical programming system for non-convex problems using ordered sets of variables, in: J. Lawrence (Ed.), Proc. 5th Int. Conf. Oper. Res., 1970, pp. 447-454.
5. A. Borghetti, S. Member, C.D. Ambrosio, A. Lodi, and S. Martello An MILP approach for short-term hydro scheduling and unit commitment with head-dependent reservoir IEEE Trans. Power Syst. 23 2008 1115 1124
6. M. Carrion, and J.M. Arroyo A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem IEEE Trans. Power Syst. 21 2006 1371 1378 (Pubitemid 44263531)
7. K.L. Croxton, B. Gendron, and T.L. Magnanti Comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems Manage. Sci. 49 2003 1268 1273
8. G. Dantzig On the significance of solving linear programming problems with some integer variables Econometrica 28 1960 30 44
9. B. Geißler, A. Martin, A. Morsi, and L. Schewe Using piecewise linear functions for solving MINLPs J. Lee, S. Leyffer, Mixed Integer Nonlinear Programming The IMA Vol. in Math. and its Appl. volume 154 2012 Springer 287 314
10. O. Günlük, and J. Linderoth Perspective relaxation of mixed integer nonlinear programs with indicator variables Math. Program. 104 2010 186 203
11. O. Günlük, and J. Linderoth Perspective reformulation and applications J. Lee, S. Leyffer, Mixed Integer Nonlinear Programming The IMA Vol. in Math. and its Appl. vol. 154 2012 Springer 61 92
12. V. Gupta, and I.E. Grossmann An efficient multiperiod MINLP model for optimal planning of offshore oil and gas field infrastructure Ind. Eng. Chem. Res. 51 2012 6823 6840
13. R.G. Jeroslow, and J.K. Lowe Modelling with integer variables Math. Program. at Oberwolfach II Math. Program. Stud. vol. 22 1984 Springer Berlin Heidelberg 167 184 10.1007/BFb0121015
14. A.B. Keha, I.R. de Farias, and G.L. Nemhauser Models for representing piecewise linear cost functions Oper. Res. Lett. 32 2004 44 48
15. J. Lee, and D. Wilson Polyhedral methods for piecewise-linear functions I: the lambda method Discrete Appl. Math. 108 2001 269 285 (Pubitemid 33676799)
16. L. Lodish CALLPLAN: an interactive salesman's call planning system Manage. Sci. 18 1971
17. H.M. Markowitz, and A.S. Manne On the Solution of Discrete Programming Problems Econometrica 25 1957 84 110
18. A. Martin, M. Möller, and S. Moritz Mixed integer models for the stationary case of gas network optimization Math. Program. 105 2006 563 582 (Pubitemid 41788333)
19. R.R. Meyer Integer and mixed-integer programming models: general properties J. Optim. Theory Appl. 16 1976 191 206
20. M. Padberg Approximating separable nonlinear functions via mixed zero-one programs Oper. Res. Lett. 27 2000 1 5
21. M.W. Padberg, and M.P. Rijal Location, Scheduling, Design and Integer Programming International Series in Operations Research & Management Science vol. 3 1996 Springer Boston
22. J. Vielma, Mixed integer linear programming formulation techniques, 2013 (submitted for publication).
23. J.P. Vielma, S. Ahmed, and G. Nemhauser Mixed-integer models for nonseparable piecewise-linear optimization: unifying framework and extensions Oper. Res. 58 2009 303 315
24. J.P. Vielma, and G.L. Nemhauser Modeling disjunctive constraints with a logarithmic number of binary variables and constraints Math. Program. 128 2009 49 72
25. A. Zoltners, and P. Sinha Integer programming models for sales resource allocation Manage. Sci. 26 1980 242 260 (Pubitemid 11430501)