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

• Main Author: Oliveira, Renata Melo e Silva de
• Publication Date: 2015
• Other Authors: Ribeiro, Maria S. F. O. de C.
• Format: Article
• Language: eng
• Source: Independent Journal of Management & Production
• Download full: http://www.ijmp.jor.br/index.php/ijmp/article/view/262
• topic: 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.