A Note on “A Superior Representation Method for Piecewise Linear Functions”

Authors:
Juan Pablo Vielma;Shabbir Ahmed;George Nemhauser
Affiliations:
Business Analytics and Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598/ and Department of Industrial Engineering, University of Pittsburgh, Pit ...;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332
Venue:
INFORMS Journal on Computing
Year:
2010

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Abstract

This paper studies two mixed-integer linear programming (MILP) formulations for piecewise linear functions considered in Li et al. [Li, H.-L., H.-C. Lu, C.-H. Huang, N.-Z. Hu. 2009. A superior representation method for piecewise linear functions. INFORMS J. Comput.21(2) 314--321]. Although the ideas used to construct one of these formulations are theoretically interesting and could eventually provide a computational advantage, we show that their use in modeling piecewise linear functions yields a poor MILP formulation. We specifically show that neither of the formulations in this paper has a favorable strength property shared by all standard MILP formulations for piecewise linear functions. We also show that both formulations in Li et al. (2009) are significantly outperformed computationally by standard MILP formulations.