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

TL;DR

Mixed integer programming and constraint programming models are presented and compared to support the development of new heuristic and metaheuristics methods for the flexible job shop scheduling problem with sequencing flexibility and position-based learning effect.

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.

Figures (6)

• Figure 1: On the left, representation of operations' precedence constraints by a directed acyclic graph $D=(\mathcal{O},\widehat{A})$, where $\mathcal{O} = \{ 1, 2, \dots, 12 \}$ represents the set of operations and $\widehat{A}$ is the set of arcs that represent the precedence constraints. On the right, standard processing times of the twelve operations on each of the three machines. In the table cells, "--" means that the machine cannot process the operation.
• Figure 2: Representation of an optimal solution to the instance in Figure \ref{['fig1']}.
• Figure 3: Gantt chart representation of the optimal solution shown in Figure \ref{['fig2']} to the instance of Figure \ref{['fig1']}.
• Figure 4: Representation of an optimal solution to the instance in Figure \ref{['fig1']} in the presence of learning effect.
• Figure 5: Gantt chart representation of the optimal solution shown in Figure \ref{['fig4']} to the instance of Figure \ref{['fig1']} in the presence of learning effect.