Understanding Complexity in a Practical Combinatorial Problem Using Mathematical Programming and Constraint Programming

  • Beatriz B. Oliveira
  • Maria Antónia Carravilla
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 223)


Optimization problems that are motivated by real-world settings are often complex to solve. Bridging the gap between theory and practice in this field starts by understanding the causes of complexity of each problem and measuring its impact in order to make better decisions on approaches and methods. The Job-Shop Scheduling Problem (JSSP) is a well-known complex combinatorial problem with several industrial applications. This problem is used to analyse what makes some instances difficult to solve for a commonly used solution approach – Mathematical Integer Programming (MIP) – and to compare the power of an alternative approach: Constraint Programming (CP). The causes of complexity are analysed and compared for both approaches and a measure of MIP complexity is proposed, based on the concept of load per machine. Also, the impact of problem-specific global constraints in CP modelling is analysed, making proof of the industrial practical interest of commercially available CP models for the JSSP.


Job-shop scheduling problem Mathematical programming Constraint programming Global constraints Complexity 



The first author was supported by grant SFRH/BD/103362/2014 from FCT - Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology). This work was also partially financed by the ERDF - European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme within project “POCI-01-0145-FEDER-006961”, and by National Funds through the FCT - Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) as part of project UID/EEA/50014/2013.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Beatriz B. Oliveira
    • 1
  • Maria Antónia Carravilla
    • 1
  1. 1.INESC TEC and Faculty of EngineeringUniversity of PortoPortoPortugal

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