Abstract
This paper deals with scheduling n jobs on a single machine in order to minimize the weighted sum of squared waiting times of the jobs. We present a powerful decomposition mechanism, based on a precedence relation concept, that easily handles problems of the size n = 50 and 100 where the processing times and penalties are independently drawn from a uniform distribution. This mechanism is incorporated along with new branching rules in a branch-and-bound scheme that efficiently handles tough problems of the size 20 and 50.
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Szwarc, W., Mukhopadhyay, S. Minimizing a Quadratic Cost Function of Waiting Times in Single-Machine Scheduling. J Oper Res Soc 46, 753–761 (1995). https://doi.org/10.1057/jors.1995.105
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DOI: https://doi.org/10.1057/jors.1995.105