This paper tackles the complex challenge of team formations, assignments, and job schedules within the static Unspecified Parallel Machine Flexible Resource Scheduling problem, specifically incorporating shift considerations. In existing literature, teams are often simplified as machines that operate continuously throughout the day without any interruptions. However, in reality, teams require breaks between shifts and cannot work continuously within a day. Therefore, we introduce shift considerations to ensure that teams do not work in consecutive shifts. We consider flexible workers, capable of performing any job, who are distributed among different teams in different shifts to undertake various jobs. The number of teams in each shift is a decision variable. The duration of each job is determined by the number of workers in a team assigned to it. The objective function is to minimize the makespan, representing the overall schedule completion time, while adhering to precedence constraints. We formulate an integer linear programming model for the proposed problem and develop a novel bilinear branch and check algorithm that introduces valid bilinear inequalities to accelerate convergence. The numerical results confirm that our algorithm’s performance optimally solves problems up to 35 jobs within a reasonable timeframe, surpassing the efficiency of the branch and cut method of IBM CPLEX and the classical branch and check algorithm.

中文翻译：

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考虑班次的未指定并行机调度的双线性分支和检查


本文解决了静态未指定并行机灵活资源调度问题中团队组建、任务分配和工作安排的复杂挑战，特别是考虑了轮班问题。在现有文献中，团队通常被简化为全天不间断运行的机器。但在现实中，团队需要轮班休息，无法在一天内连续工作。因此，我们引入了轮班注意事项，以确保团队不会连续轮班工作。我们认为灵活的员工能够胜任任何工作，他们分布在不同的团队中，轮班不同，承担不同的工作。每个班次的团队数量是一个决策变量。每项工作的持续时间取决于分配给该工作的团队中的工人人数。目标函数是最小化完工时间（代表总体计划完成时间），同时遵守优先级约束。我们针对所提出的问题制定了整数线性规划模型，并开发了一种新颖的双线性分支和检查算法，该算法引入有效的双线性不等式来加速收敛。数值结果证实，我们的算法的性能在合理的时间范围内最优地解决了多达 35 个作业的问题，超越了 IBM CPLEX 的分支和剪切方法以及经典的分支和检查算法的效率。