Reformulation of the modified goal programming for logarithmic piecewise linear function

The purpose of this paper is to present a reformulation of the model presented by Chang [A modified goal programming model for piecewise linear function, European Journal of Operational Research 139 (2002) 62-67]. The modified goal programming (MGP) model of Chang has been accepted as an efficient method published for solving polynomial/posynomial (P/P) programming problems. However, it still cannot be used to fully practical applications because the problem with negative variable is undefined in logarithmic piecewise linear function (LPLF). This paper presents some appropriate strategies to overcome this undefined problem. The reformulation MGP model can be used to solve P/P programming problems with negative/positive variables. In addition, an illustrative example is included for demonstrating the correctness of the proposed method.