Abstract
A very useful multi-objective technique is goal programming. There are many methodologies of goal programming such as weighted goal programming, min-max goal programming, and lexicographic goal programming. In this paper, weighted goal programming is reformulated as goal programming with logarithmic deviation variables. Here, a comparison of the proposed method and goal programming with weighted sum method is presented. A numerical example and applications on two industrial problems have also enriched this paper.
Highlights
The earliest goal programming formulation was introduced by Charnes et al (1955)
Wj0 values are the weights for objective functions and Wr values are the weights for the constraints
The geometric programming approach is the best tool to solve nonlinear programming problems as compared with the other approach (Khun-Tucker conditions) that is already discussed in this paper
Summary
Charnes and Cooper (1977), Ijiri (1965), Lee (1972), and Ignizio (1976) are the contributors of goal programming for which goal programming became a useful tool in multi-criteria decisionmaking (MCDM) problem. Methodologies of goal programming such as weighted goal programming, minmax goal programming, lexicographic goal programming have been discussed in the study of Romero (2004). Except for these three methods, another method, the logarithmic goal programming, is introduced (Wang et al 2005). In goal programming formulation with logarithmic deviational variables, we use geometric programming for solving because there are lots of real-life situations and many engineering applications where equations may be nonlinear.
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