Single-machine scheduling problems with a batch-dependent aging effect and variable maintenance activities
研究了单机调度中批次依赖的老化效应和批次间可变维护时间问题，开发了多项式时间算法和启发式算法来最小化最大完工时间和总完工时间。
We consider single-machine scheduling problems with a batch-dependent ageing effect and variable maintenance activities between batches. The machine can process several jobs as a batch. It requires maintenance activities where the maintenance time depends on the flow time of the pre-batch, i.e. the batch processed before a batch. A job’s actual processing time is an increasing exponential function of its operation time within a batch. The objectives are to minimise the makespan and the total completion time. We develop polynomial time algorithms for the makespan minimisation problem and the total completion time minimisation problem under the condition that the ageing factor is greater than one. We also provide a mathematical programming approach and two heuristic algorithms to analyse the total completion time minimisation problem when the ageing factor is less than one for even one batch. The computational analysis indicates that the proposed heuristic algorithms are more efficient for the smaller ageing factor, whereas the Modified Shortest Processing Time algorithm is more efficient than the proposed heuristic algorithms for the larger ageing factor.