Mixed Integer Linear Programming and Constraint Programming Models for the Online Printing Shop Scheduling Problem

TL;DR

This paper models and analyzes the online printing shop scheduling problem using mixed integer linear programming and constraint programming, evaluating their effectiveness through extensive numerical experiments on various instance sizes.

Contribution

It introduces precise models for a complex, real-world printing scheduling problem and assesses their practical solvability with commercial solvers.

Findings

Constraint programming solves all small instances optimally.

Mixed integer linear programming solves fewer small instances.

Feasible solutions are obtainable for large, practical-sized instances.

Abstract

In this work, the online printing shop scheduling problem is considered. This challenging real problem, that appears in the nowadays printing industry, can be seen as a flexible job shop scheduling problem with sequence flexibility in which precedence constraints among operations of a job are given by an arbitrary directed acyclic graph. In addition, several complicating particularities such as periods of unavailability of the machines, resumable operations, sequence-dependent setup times, partial overlapping among operations with precedence constraints, release times, and fixed operations are also present in the addressed problem. In the present work, mixed integer linear programming and constraint programming models for the minimization of the makespan are presented. Modeling the problem is twofold. On the one hand, the problem is precisely defined. On the other hand, the capabilities and limitations of a commercial software for solving the models are analyzed. Extensive numerical experiments with small-, medium-, and large-sized instances are presented. Numerical experiments show that the commercial solver is able to optimally solve only a fraction of the small-sized instances when considering the mixed integer linear programming model; while all small-sized and a fraction of the medium-sized instances are optimally solved when considering the constraint programming formulation of the problem. Moreover, the commercial solver is able to deliver feasible solutions for the large-sized instances that are of the size of the instances that appear in practice.