A MILP and Genetic Algorithm Approach for a Furniture Manufacturing Flow Shop Scheduling Problem

A MILP and Genetic Algorithm Approach for a Furniture Manufacturing Flow Shop Scheduling Problem

Marcell S. Kalman (Universidad Panamericana, Mexico), Omar G. Rojas (Universidad Panamericana, Mexico), Elias Olivares-Benitez (Universidad Panamericana, Mexico) and Samuel Moisés Nucamendi-Guillén (Universidad Panamericana, Mexico)
DOI: 10.4018/978-1-5225-8223-6.ch011

Abstract

A MILP and genetic algorithm optimization model for the sequencing of jobs in a medium-sized factory, dedicated to the manufacturing of home furniture, where different categories and types of articles are produced and whose routes and manufacturing processing times vary widely, are proposed. Different scenarios are considered for the objective function based on minimizing makespan and tardiness. The results of the optimization for an instance of 24 jobs on five machines, chosen as a representative instance of the order sizes that are handled by the company, show important reductions in the productive system's usage times, oscillating between 10% and 20% with respect to a random initial sequence in the production plan. Improvements were similar in both techniques, the main difference being the solution time of each one.
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Background

One of the techniques used in this study is MILP, which is one of the most important techniques in operations research and mathematical optimization, where mathematical models are used to describe various types of problems where optimal decisions are to be made. Some of these decision include how to allocate resources of a given system in the most efficient manner (Kondili, Pantelides, & Sargent, 1993; M. L. Pinedo, 2008) To be able to use such a technique, the following conditions are required (Hillier & Lieberman, 2014; Rao, 2009).

  • The resources of the system are limited or have constraints.

  • There is an objective or goal to achieve (objective function).

  • There is a linear relationship between the objectives and the constraints.

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