Tradeoff solutions in single machine production scheduling for minimizing flow time and maximum penalty

The single machine production scheduling problem addressed here involves minimization of two objectives, namely: (1) the total flow time and (2) the maximum penalty, where the penalty function defined for each job is nondecreasing in its conpletion time. A pseudopolynomial algorithm of order (n²X) is developed in this paper to generate the efficient frontier where X is the cardinality of the efficient frontier for an n job problem. The computational effort to solve this problem has been reduced significantly by proving that a small perturbation of one efficient solution generates its adjacent efficient solution. Computational performance of this method on small and medium sized problems is also investigated here.