On the approximate tradeoff for bicriteria batching and parallel machine scheduling problems

We consider multiobjective scheduling problems, i.e. scheduling problems that are evaluated with respect to many cost criteria, and we are interested in determining a trade-off (Pareto curve) among these criteria. We study two types of bicriteria scheduling problems: single-machine batching problems and parallel machine scheduling problems. Instead of proceeding in a problem-by-problem basis, we identify a class of multiobjective optimization problems possessing a fully polynomial time approximation scheme (FPTAS) for computing an epsilon-approximate Pareto curve. This class contains a set of problems whose Pareto curve can be computed via a simple pseudo-polynomial dynamic program for which the objective and transition functions satisfy some, easy to verify, arithmetical conditions. Our study is based on a recent work of Woeginger (Electronic Colloquium on Computational Complexity, Report 84 (short version appeared in SODA'99, pp. 820-829)) for the single criteria optimization ex-benevolent problems. We show how our general result can be applied to the considered scheduling problems. (C) 2003 Elsevier B.V. All rights reserved.