Cyclic Flow Shop Robotic Cell Scheduling Problem With Multiple Part Types

Abstract

This article considers the problem of cyclic flow shop (CFS) scheduling problems in robotic cells deploying several single and dual gripper robots. In this problem, different part types are successively processed on multiple machines with different pickup criteria including free pickup, pickup within time windows, and no-waiting times. The parts are transported between the machines by the robots. We propose a novel integer programming approach that determines the optimal sequence of parts simultaneously for the sequencing of the robots’ movements and the cyclic schedule, which also results in maximizing the throughput rate. The proposed mathematical model is validated on a number of randomly generated test instances. These problem instances are constructed by varying the number of machines, part types, robots, and gripper options. This allows a detailed analysis of the model including how it scales with increasing numbers of machines, part types, robots, and grippers. An experimental evaluation shows that our proposed model is very effective for a range of small medium-sized problems. In particular, we find that differing number of robots and gripper options directly affects the cycle time and in turn, the throughput rate. Overall, our integer programming model finds good feasible solutions for up to 20 machines and 10 part types, which is comparable to real-world industrial problems.