Scheduling multi-staged jobs on parallel identical machines and a central server with sequence-dependent setup times: An application to an automated kitchen

We address the problem of scheduling multi-staged jobs in a production environment with parallel identical machines and a central server with sequence-dependent setup times motivated by a real-life application in a robotic automated kitchen. The proposed model addresses a makespan minimization offline optimization problem that arises in the context of mise-en-place preparation. We present two mathematical formulations, one with a machine index and one without, as well as lower bounds. We also propose an effective general variable neighborhood search algorithm based on heuristics which aims to improve the incumbent by eliminating idle times. Through a series of experiments on random instances, we demonstrate the effectiveness of the proposed method under various combinations of instance parameters. On instances with known optimal solutions, the metaheuristic produces solutions with an average gap of 0.31% in very short computation times. On large-size instances, the metaheuristic produces solutions with an average gap of 6.04% when measured against a known lower bound. We also present a real-life case study provided by our industrial partner and we investigate how to maximise the output of the studied automated production system.