一类最优排序具有∧型或∨型特征的随机单机调度问题

A CLASS OF STOCHASTIC SINGLE MACHINE SCHEDULING WITH ∨-OR ∧-SHAPED OPTIMAL SEQUENCES

本文讨论了一类加工时间随机、机器随机故障的单机调度问题．其目标函数为：（ｉ）完成时间的平方和，（ｉｉ）平均完成时间的平方，（ｉｉｉ）平均完成时间的线性组合的期望．文中首先给出了当与机器随机故障相关的点过程为广义泊松过程时，目标函数的确定形式，然后给出了使目标函数最小的最优排序依加工时间的期望具有∨型或∧型特征的条件．

In this paper,we discuss the problem of scheduling n jobs with stochastic processing times on a single machine which is subject to stochastic breakdowns to minimize the expectation of the linear combination of three functions of completion times:(i) the sum of the squares,(ii)the square of the mean and (iii)the mean. Firstly,a deterministic form of the objective function is obtained when the point process N(t) related to the machine uptime distribution is a generalized poisson process.And then a sufficient condition under which an optimal sequence of the stochastic scheduling is V-or shaped in terms of the means of the processing times is derived.