We consider a capacitated job shop problem with order acceptance. This research is motivated by the management of a research and development project pipeline for a company in the agricultural industry whose success depends on regularly releasing new and innovative products. The setting requires the consideration of multiple problem characteristics not commonly considered in scheduling research. Each job has a given release and due date and requires the execution of an individual sequence of operations on different machines (job shop). There is a set of machines of fixed capacity, each of which can process multiple operations simultaneously. Given that typically only a small percentage of jobs yield a commercially viable product, the number of potential jobs to schedule is in the order of several thousands. Due to limited capacity, not all jobs can be started. Instead, the objective is to maximize the throughput. Namely, to start as many jobs as possible. We present a Mixed Integer Programming (MIP) formulation of this problem and study how resource capacity and the option to delay jobs can impact research and development throughput. We show that the MIP formulation can prove optimality even for very large instances with less restrictive capacity constraints, while instances with a tight capacity are more challenging to solve.

翻译：本文研究考虑订单接受的产能受限作业车间调度问题。该研究源于一家农业企业的研发项目管道管理实践，该企业的成功依赖于定期推出创新产品。这一场景需要考虑调度研究中通常未涉及的多个问题特征：每个作业具有给定的释放时间和截止时间，需要在不同机器上按特定顺序执行多个工序（作业车间）；存在一组固定产能的机器，每台机器可同时处理多个工序。鉴于通常只有少量作业能产生商业化产品，待调度的潜在作业数量可达数千个。由于产能限制，无法启动所有作业，因此目标在于最大化吞吐量，即尽可能启动更多作业。本文建立了该问题的混合整数规划模型，并研究了资源产能与作业延迟选项对研发吞吐量的影响。研究表明，对于产能约束较宽松的大规模算例，该混合整数规划模型仍能证明最优性；而产能约束严格的算例则更具求解挑战性。