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A single machine scheduling problem with availability constraints and sequence-dependent setup costs

机译：具有可用性约束和与序列有关的设置成本的单机调度问题

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摘要

We study a single machine scheduling problem with availability constraints and sequence-dependent setup costs, with the aim of minimizing the makespan. To the authors' knowledge, this problem has not been treated as such in the operations research literature. We derive in this paper a mixed integer programming model to deal with such scheduling problem. Computational tests showed that commercial solvers are capable of solving only small instances of the problem. Therefore, we propose two ways for reducing the execution time, namely a valid inequality that strengthen the linear relaxation and an efficient heuristic procedure that provides a starting feasible solution to the solver. A substantial gain is achieved both in terms of the linear programming relaxation bound and in terms of the time to obtain an integer optimum when we use the enhanced model in conjunction with providing to the solver the solution obtained by the proposed heuristic.
机译：我们研究具有可用性约束和与序列有关的设置成本的单机调度问题，目的是最大程度地缩短工期。据作者所知，运筹学文献中未对此问题进行过处理。我们在本文中得出了混合整数规划模型来处理这种调度问题。计算测试表明，商业求解器只能解决很小的问题。因此，我们提出了两种减少执行时间的方法，即加强线性松弛的有效不等式和为求解器提供起始可行解决方案的有效启发式过程。当我们使用增强的模型并向求解器提供通过拟议的启发式方法获得的解时，无论是在线性规划松弛范围方面，还是在获得整数最优值的时间方面，都可以获得可观的收益。

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