Hybrid of the weighted minimum slack and shortest processing time dispatching rules for the total weighted tardiness single machine scheduling problem with availability constraints

The paper addresses the total weighted tardiness single-machine scheduling problem with machine availability constraints. Each machine can handle one job at a time and has a set of maintenance periods, during which the machine must be stopped for service. Each maintenance period lasts for a fixed interval of time and starts after a fixed interval of processing non-resumable jobs. A non-resumable job must be processed and completed outside the maintenance periods. The single–machine periodic maintenance problems with a total weighted tardiness objective appear to be a new class of problems for which, in this paper, a mixed integer linear programming formulation and a new composite dispatching rule based on a combination of the weighted minimum slack and shortest processing time rules are introduced. New data set instances with different characteristics are generated using existing benchmarks from the literature. Extensive computational results are reported to testify the power of the proposed dispatching-based rule heuristic by comparing it to other heuristics inspired from the literature and developed for this new problem. Finally the paper concludes with a summary and highlights further research directions.

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