On scheduling a single machine with resource dependent release times

Authors:
M. C. Janssen;R. J. D. Verbeek;A. Volgenant
Affiliations:
Operations Research Group, Faculty of Economics and Econometrics, University of Amsterdam, The Netherlands;NLR (National Aerospace Laboratory), Amsterdam, The Netherlands;Operations Research Group, Faculty of Economics and Econometrics, University of Amsterdam, The Netherlands
Venue:
Computers and Operations Research
Year:
2011

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Abstract

We consider a single machine scheduling problem with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. The objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. It is known that the problem is polynomially solvable in O(n^4) with n the number of jobs. We describe an improved algorithm of complexity O(nlogn). We show further how to perform sensitivity analysis on the processing time of a job without increasing the complexity.