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

## DOI:

https://doi.org/10.14807/ijmp.v6i1.262## Keywords:

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

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.

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