Unrelated Machine Scheduling with Stochastic Processing Times
研究了无关机器调度问题中加工时间随机的情况，提出一种基于时间索引线性规划松弛的调度策略，在多项式时间内给出加权完成时间之和的近似保证，该保证与加工时间变异系数平方相关且紧。
Two important characteristics encountered in many real-world scheduling problems are heterogeneous processors and a certain degree of uncertainty about the processing times 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. By means of a novel time-indexed linear programming relaxation, we show how to compute in polynomial time a scheduling policy with provable performance guarantee for the stochastic version of the unrelated parallel machine scheduling problem with the weighted sum of completion times objective. Our performance guarantee depends on the squared coefficient of variation of the processing times and we show that this dependence is tight. Currently best-known bounds for deterministic scheduling problems are contained as special cases.