Machine Scheduling with Resource Dependent Processing Times

A. Grigoriev, M. Sviridenko, M.J. Uetz*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review


We consider machine scheduling on unrelated parallel machines with the objective to minimize the schedule makespan. We assume that, in addition to its machine dependence, the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. Workers. A given amount of that resource can be distributed over the jobs in process at any time, and the more of that resource is allocated to a job, the smaller is its processing time. This model generalizes the classical unrelated parallel machine scheduling problem by adding a time-resource tradeoff. It is also a natural variant of a generalized assignment problem studied previously by shmoys and tardos. On the basis of an integer linear programming formulation for a relaxation of the problem, we use lp rounding techniques to allocate resources to jobs, and to assign jobs to machines. Combined with graham’s list scheduling, we show how to derive a 4-approximation algorithm. We also show how to tune our approach to yield a 3.75-approximation algorithm. This is achieved by applying the same rounding technique to a slightly modified linear programming relaxation, and by using a more sophisticated scheduling algorithm that is inspired by the harmonic algorithm for bin packing. We finally derive inapproximability results for two special cases, and discuss tightness of the integer linear programming relaxations.
Original languageEnglish
Pages (from-to)209-228
Number of pages20
JournalMathematical Programming
Issue number1
Publication statusPublished - 1 Jan 2007

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