We study the prize-collecting job sequencing problem with one common and multiple secondary resources. In this problem, a set of jobs is given, each with a profit, multiple time windows for its execution, and a duration during which it requires the main resource. Each job also requires a preassigned secondary resource before, during, and after its use of the main resource. The goal is to select and schedule the subset of jobs that maximize the total profit. We present a new mixed integer linear programming formulation of the problem and a branch-cut-and-price algorithm as an exact solution method. We also introduce a heuristic algorithm to tackle larger instances. Extensive numerical experiments show that our exact algorithm can solve to optimality literature instances with up to 500 jobs for a particular dataset and up to 250 jobs for another dataset with different characteristics. Our heuristic builds high-quality solutions in a small computational time. It computes new best-known solutions for most of the larger instances.

我们研究了具有一个公共和多个二级资源的奖品收集工作排序问题。在这个问题中，给出了一组作业，每个作业都有利润、执行的多个时间窗口以及需要主要资源的持续时间。每个作业在使用主要资源之前、期间和之后还需要预先分配的辅助资源。目标是选择和安排使总利润最大化的作业子集。我们提出了该问题的新混合整数线性规划公式和分支切割价格算法作为精确求解方法。我们还引入了一种启发式算法来处理更大的实例。大量的数值实验表明，我们的精确算法可以解决特定数据集最多 500 个作业和另一个具有不同特征的数据集最多 250 个作业的最优文献实例。我们的启发式算法可以在很短的计算时间内构建高质量的解决方案。它为大多数较大的实例计算新的最著名的解决方案。