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This paper establishes performance guarantees for online algorithms thatschedule stochastic, nonpreemptive jobs on unrelated machines to minimize theexpected total weighted completion time. Prior work on unrelated machinescheduling with stochastic jobs was restricted to the offline case, andrequired linear or convex programming relaxations for the assignment of jobs tomachines. The algorithms introduced in this paper are purely combinatorial. Theperformance bounds are of the same order of magnitude as those of earlier work,and depend linearly on an upper bound on the squared coefficient of variationof the jobs' processing times. Specifically for deterministic processing times,without and with release times, the competitive ratios are 4 and 7.216,respectively. As to the technical contribution, the paper shows how dualfitting techniques can be used for stochastic and nonpreemptive schedulingproblems.

Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling