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The (minimizing) achievement function of the traditional Goal Programming (GP) model has five basic forms: ni, pi, (ni+pi), (ni-pi), and (pi-ni), where ni and pi are th nonnegative under and over achievement variables in the i goal-constraint. Zhang and Shang (2001) proposed the theory of Goal Programs with -ni, -pi, and -(ni+pi) goals, which has many interesting and practical applications. This paper...
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