This paper addresses the tactical production planning problem of engineer-to-order companies. For this, we extend the resource-constrained project scheduling problem with flexible resource profiles (FRCPSP) to the multi-project case as well as flexible resource availability. We model the problem as a deterministic discrete-time mixed-integer program using step-variables. For each activity the start time, the duration, and the allocation of a given resource requirement over time has to be determined, taking into account precedence constraints between activities and availability of resources. The capacity of resources is not fixed but can vary subject to working time accounts. Using a lexicographic ordering approach, the primary objective is to minimize the total weighted lateness of projects, while the secondary objective is to balance working time accounts. In our computational study, we solve real-world instances from a mid-size company with up to 100 projects and 1725 activities. We show that optimal solutions can be derived in reasonable computation time with off-the-shelf commercial solvers. From a managerial point of view, our results demonstrate the value of flexibility.

本文解决了按订单设计的公司的战术生产计划问题。为此，我们将具有灵活资源配置文件 (FRCPSP) 的资源受限项目调度问题扩展到多项目情况以及灵活的资源可用性。我们将问题建模为使用步进变量的确定性离散时间混合整数程序。对于每项活动，必须确定开始时间、持续时间和给定资源需求随时间的分配，同时考虑活动和资源可用性之间的优先约束。资源的容量不是固定的，但可以根据工作时间帐户而有所不同。使用字典排序方法，主要目标是最小化项目的总加权延迟，而次要目标是平衡工作时间账户。在我们的计算研究中，我们解决了来自一家拥有多达 100 个项目和 1725 个活动的中型公司的真实世界实例。我们表明，可以使用现成的商业求解器在合理的计算时间内推导出最优解。从管理的角度来看，我们的结果证明了灵活性的价值。