## Bicriterion Single Machine Scheduling with Resource Dependent Processing Times

- T. C. Edwin Cheng, Adam Janiak, Mikhail Y. Kovalyov
- SIAM Journal on Optimization
- 1998

- 2000

We study problems in multiobjective optimization, in which solutions to a combinatorial optimization problem are evaluated with respect to several cost criteria, and we are interested in the trade-off between these objectives (the so-called Pareto curve). We point out that, under very general conditions, there is a polynomially succinct curve that-approximates the Pareto curve, for any > 0. We give a necessary and sufficient condition under which this approximate Pareto curve can be constructed in time polynomial in the size of the instance and 1==. In the case of multiple linear objectives, we distinguish between two cases: When the underlying feasible region is convex, then we show that approximating the multi-objective problem is equivalent to approximating the single-objective problem. If, however, the feasible region is discrete, then we point out that the question reduces to an old and recurrent one: How does the complexity of a combinatorial optimization problem change when its feasible region is intresected with a hyperplane with small coefficients; we report some interesting new findings in this domain. Finally, we apply these concepts and techniques to formulate and solve approximately a cost-time-quality trade-off for optimizing access to the worldwide web, in a model first studied by Etzioni et al [EHJ+] (which was actually the original motivation for this work).

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