Models, constructive heuristics, and benchmark instances for the flexible job shop scheduling problem with sequencing flexibility and position-based learning effect

TL;DR

This paper introduces models and heuristics for a complex flexible job shop scheduling problem with sequencing flexibility and learning effects, relevant to modern printing industry challenges.

Contribution

It presents new mixed integer and constraint programming models, constructive heuristics, and benchmark instances for this advanced scheduling problem.

Findings

Models outperform traditional approaches in specific scenarios

Heuristics provide good initial solutions for complex instances

Benchmark instances facilitate future research in this area

Abstract

This paper addresses the flexible job shop scheduling problem with sequencing flexibility and position-based learning effect. In this variant of the flexible job shop scheduling problem, precedence constraints of the operations constituting a job are given by an arbitrary directed acyclic graph, in opposition to the classical case in which a total order is imposed. Additionally, it is assumed that the processing time of an operation in a machine is subject to a learning process such that the larger the position of the operation in the machine, the faster the operation is processed. Mixed integer programming and constraint programming models are presented and compared in the present work. In addition, constructive heuristics are introduced to provide an initial solution to the models' solvers. Sets of benchmark instances are also introduced. The problem considered corresponds to modern problems of great relevance in the printing industry. The models and instances presented are intended to support the development of new heuristic and metaheuristics methods for this problem.