 
Summary: A note on :"A Superior Representation Method for
Piecewise Linear Functions" by Li, Lu, Huang and Hu
Juan Pablo Vielma, Shabbir Ahmed and George Nemhauser
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765
Ferst Drive, NW, Atlanta, GA 303320205, USA, {jvielma@isye.gatech.edu, sahmed@isye.gatech.edu,
george.nemhauser@isye.gatech.edu}
This paper shows that two Mixed Integer Linear Programming (MILP) formulations for
piecewise linear functions introduced by Li et al. (2008) are both theoretically and compu
tationally inferior to standard MILP formulations for piecewise linear functions.
Key words: Mathematics:Piecewise linear; Programming:Integer;
History:
1. Introduction
Two new Mixed Integer Linear Programming (MILP) formulations for modeling a univariate
piecewise linear function f were introduced in Li et al. (2008). The first formulation (given
by (1)(3) in Li et al.) uses "BigM" type constraints, so we denote it by LiBigM. The
second formulation (given by (23)(33) in Li et al.) uses a number of binary variables that is
logarithmic in the number of segments in which f is affine, so we denote it by LiLog. Based
on computational results that show that LiLog outperforms LiBigM, Li et al. declare LiLog
to be superior to other MILP formulations for piecewise linear functions. In this paper we
show that LiBigM and LiLog are both theoretically and computationally inferior to standard
