Improving schedule stability in single-machine rescheduling for new operation insertion

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Official URL: http://dx.doi.org/10.1016/j.cor.2015.05.015

The problem studied here is one of inserting a new operation into an existing predictive schedule (preschedule) on a (non--preemptive) single machine by rescheduling its operations so that the resultant schedule is the most stable one among the schedules that have the minimum maximum tardiness. Stability is measured by the sum of absolute deviations of post--rescheduling start--times from the pre--rescheduling start--times. In addition to several simple heuristics a hybrid branch--and--bound/local--search algorithm is developed. A large set of instances that include cases with inserted idle time are generated, which allow testing the performance of the heuristics for preschedules with varying degrees of robustness. The results show that algorithms can be developed that significantly improve stability of schedules with no degradation in $T_{max}$. In addition, new insights into the robustness characteristics of a preschedule have been developed. Specifically, number of gaps in the schedule, equal distribution of total slack among these gaps and slack introduced beyond the amount enforced by release--times have been demonstrated as factors that have an effect on schedule robustness and stability.