Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints

Györgyi, Péter and Kis, Tamás (2017) Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints. Other. UNSPECIFIED. (Submitted)

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Abstract

In this paper we describe new complexity results, and approximation algorithms for single ma- chine scheduling problems with non-renewable resource constraints and the total weighted completion time ob- jective. This problem is hardly studied in the literature, and most of the published results establish the compu- tational complexity of various special cases with differ- ent objective functions. In this paper we discuss some polynomially solvable special cases and also show that under very strong assumptions, like the processing time, the resource consumption and the weight is the same for each job, minimizing the total weighted completion time is still NP-hard. In addition, we also propose a 2- approximation algorithm for this variant, and a PTAS for the case when the processing time equals the weight for each job, while the resource consumptions are arbi- trary.

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