Stochastic Scheduling on Unrelated Machines
Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the sizes of jobs. In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. Here, the processing time of job j on machine i is governed by random variable P_{ij} , and its realization becomes known only upon job completion. With w_j being the given weight of job j, we study the objective to minimize the expected total weighted completion time E[Sum w_j.C_j] , where C_j is the completion time of job j. By means of a novel time-indexed linear programming relaxation, we compute in polynomial time a scheduling policy with performance guarantee (3+D)/2+e. Here, e>0 is arbitrarily small, and D is an upper bound on the squared coefficient of variation of the processing times. When jobs also have individual release dates r_{ij}, our bound is (2+D)+e. We also show that the dependence of the performance guarantees on D is tight. Via D=0, currently best known bounds for deterministic scheduling on unrelated machines are contained as special case.
Stochastic Scheduling
Unrelated Machines
Approximation Algorithm
639-650
Regular Paper
Martin
Skutella
Martin Skutella
Maxim
Sviridenko
Maxim Sviridenko
Marc
Uetz
Marc Uetz
10.4230/LIPIcs.STACS.2014.639
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode