Comparing Mixed & Integer Programming vs. Constraint Programming by solving Job-Shop Scheduling Problems


  • Renata Melo e Silva de Oliveira University of State of Para (Assistent Professor III) and University of Porto ( PhD Student at FEUP)
  • Maria S. F. O. de C. Ribeiro UNIVERSITY OF PORTO (UP)



Constraint Programming, Mixed an Integer Programming, Job-shop Scheduling Problem, Makespan minimization


Scheduling is a key factor for operations management as well as for business success. From industrial Job-shop Scheduling problems (JSSP), many optimization challenges have emerged since de 1960s when improvements have been continuously required such as bottlenecks allocation, lead-time reductions and reducing response time to requests.  With this in perspective, this work aims to discuss 3 different optimization models for minimizing Makespan. Those 3 models were applied on 17 classical problems of examples JSSP and produced different outputs.  The first model resorts on Mixed and Integer Programming (MIP) and it resulted on optimizing 60% of the studied problems. The other models were based on Constraint Programming (CP) and approached the problem in two different ways: a) model CP1 is a standard IBM algorithm whereof restrictions have an interval structure that fail to solve 53% of the proposed instances, b) Model CP-2 approaches the problem with disjunctive constraints and optimized 88% of the instances. In this work, each model is individually analyzed and then compared considering: i) Optimization success performance, ii) Computational processing time, iii) Greatest Resource Utilization and, iv) Minimum Work-in-process Inventory. Results demonstrated that CP-2 presented best results on criteria i and ii, but MIP was superior on criteria iii and iv and those findings are discussed at the final section of this work.

Author Biographies

Renata Melo e Silva de Oliveira, University of State of Para (Assistent Professor III) and University of Porto ( PhD Student at FEUP)

University of Porto

Faculty of Engineering of University of Porto

Student at Doctoral Program in Industrial Engineering and Management

Maria S. F. O. de C. Ribeiro, UNIVERSITY OF PORTO (UP)

Faculty of Engineering of University of Porto

Student at Master Program in Electrical and Computers Engineering


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