Variability in Modeling the Cyclic Scheduling of an FMC Depending on the Underlying TSP Models

TL;DR

This paper compares four TSP modeling approaches to optimize cyclic scheduling in flexible robotic cells, highlighting which models can be adapted for minimizing cycle time in production systems.

Contribution

It evaluates and contrasts four TSP models for their applicability to cyclic scheduling, identifying the limitations and advantages of each approach.

Findings

DFJ approach cannot be adapted to the scheduling problem.

Miller-Tucker-Zemlin, Vajda's n-step, and network flow approaches are successfully adapted.

Differences and similarities among models are discussed with numerical examples.

Abstract

Flexible robotic cells are utilized to produce standardized products at a high speed production rate, and to set up the production floors based on rapid operating environment changes. In FRC, there are a number of computer numerical control machines, an input buffer, an output buffer, and a robot. The input and output buffers contain unprocessed and finished products, respectively, whereas the robot performs the loading and unloading activities and transports the items among buffers and machines. The system repeats a cyclic schedule in its run and the cycle time depends on the order of robot activities. In order to maximize the efficiency of the system, the order of the robot activities yielding the minimum cycle time should be determined. The aim of this research is to find novel exact models to solve this cycling scheduling problem. These types of problems have tight relations with traveling salesman problem. In this study, four main modeling approaches of the TSP, such as Dantzig-Fulkerson-Johnson approach, Miller-Tucker-Zemlin approach, Vajda's n-step approach, and the network flow approach are studied. Only the DFJ approach cannot be adapted to the scheduling problem. The three other approaches are adapted successfully. Similarities and differences are discussed by using several numerical examples.