TR-2018-06

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

Péter Györgyi, Tamás Kis



Abstract

In this paper we describe new complexity results, and approximation algorithms for single machine scheduling problems with non-renewable resource constraints and the total weighted completion time objective. This problem is hardly studied in the literature, and most of the published results establish the computational complexity of various special cases with different 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 arbitrary.


Bibtex entry:

@techreport{egres-18-06,
AUTHOR = {Györgyi, P{\'e}ter and Kis, Tam{\'a}s},
TITLE = {Minimizing total weighted completion time on a single machine subject to non-renewable resource constraints},
NOTE= {{\tt www.cs.elte.hu/egres}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2018},
NUMBER = {TR-2018-06}
}


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