链优先约束工件单机随机排序问题

讨论单机随机排序问题，目标函数为确定工件的排列顺序使工件的加权完工时间和的数学期望最小。设工件问具有平行链优先约束，机器发生随机故障。考虑两种情况，第一种情况是链不允许中断．第二种情况是链允许中断，对两种情况分别给出最优算法。

Stochastic Single Machine Scheduling Problem with Chains Precedence Constraints Jobs

The stochastic single machine scheduling problem was considered in order to determine job permutation sequence that minimizes the mean weighted sum of completion times. It is assumed that job is subject to parallel chains precedence constraints and the machine is subject to a sequence of stochastic breakdowns. Two versions of the problem are addressed. In the first one the chains is not allowed be interrupted, whereas in the second one the chains can be interrupted. For both cases, the optimal algorithms are presented, respectively.