An important and challenging real-life problem is considered, involving workforce assignment and job scheduling for shutdown maintenance in a large oil refinery. A limited number of maintenance employees must be divided into several teams that work in parallel on different maintenance tasks. The objective is to minimize the shutdown cost by minimizing the total shutdown period, i.e., the time to complete all the maintenance tasks. Different team sizes are possible, and the size of the given team determines the speed of finishing the assigned maintenance tasks. Constraints include job availability (arrival) times, and precedence relations between different jobs. This problem can be considered as a resource-constrained parallel-machine scheduling problem, in which the objective is to minimize the makespan, and both the number and the speeds of the machines are decision variables. An integer programming model of this problem is formulated, but optimum solution is difficult because the problem is NP-hard. Therefore, a two-stage heuristic solution algorithm is developed and shown to be quite effective for solving this problem.

考虑了一个重要且具有挑战性的现实问题，涉及大型炼油厂停机维护的劳动力分配和工作调度。必须将有限数量的维护人员分成几个团队，并行处理不同的维护任务。目标是通过最小化总停机时间（即完成所有维护任务的时间）来最小化停机成本。不同的团队规模是可能的，给定团队的规模决定了完成分配的维护任务的速度。约束包括工作可用性（到达）时间，以及不同工作之间的优先关系。这个问题可以被认为是一个资源受限的并行机调度问题，其目标是最小化制造时间，机器的数量和速度都是决策变量。制定了该问题的整数规划模型，但由于该问题是 NP-hard 问题，最优解是困难的。因此，开发了一种两阶段启发式求解算法，并证明对解决该问题非常有效。