Order acceptance and scheduling in capacitated job shops

TL;DR

The paper tackles throughput maximization in a capacitated job shop with order acceptance motivated by agricultural R&D pipelines. It develops a time-indexed mixed-integer programming model using binary acceptance variables $z_j$ and time-indexed start variables $x_{ijt}$, with machine capacities $Q_i$ and release/due dates $r_j$, $d_j$, to decide which jobs to start and when. Computational experiments on up to 2,000 jobs show the model can provide decision support and reveal how capacity tightness and time windows affect problem difficulty, with optimality gaps generally shrinking as capacities loosen. The work offers practical implications for throughput-oriented planning and points to future directions including profit-based objectives, waiting-time minimization, constraint programming, and scalable heuristics for very large-scale instances.

Abstract

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.