Copyright © 2015 IJEIR, All right reserved 172 International Journal of Engineering Innovation & Research Volume 4, Issue 1, ISSN: 2277 – 5668 A Mixed-Integer Model With Genetic Algorithm for Multi-Objective Assembly Line Balancing Problem in Fuzzy Manufacturing Environment Ramin Behbamzadeh Faculty of Industrial Engg, Iran University of Science and Technology, Tehran, Iran email: RaminBehbamzadeh@gmail.com Mohammad Alaghebandha Department of Industrial Engineering, Kharazmi University, Karaj, Iran email: m.alaghebandha@gmail.com Amir Azizi Faculty of Manufacturing Engineering, University Malaysia Pahang, Malaysia email: amirazizi@ump.edu.my Abstract: In this paper, a multi-objective assembly line balancing problem (ALBP) is considered by assuming the fuzzy process time. The objective is minimizing a weighted sum of two contrast and classical criteria in literature as cycle time and the number of stations. A mixed-integer model is proposed for solving this problem. As the ALBP is NP- hard problem, genetic algorithm (GA) with a novel representation is proposed for large-scaled problem. A number of small-sized problems were considered to optimally solve in order to verify the performance of the proposed model. The obtained results present that the efficiency of the proposed model and the ability of developed GA to achieve optimal solution in reasonable time. Keywords: Assembly Line Balancing, Fuzzy, Genetic Algo- rithm, Mixed-Integer Programming 1. INTRODUCTION The history of assembly line is for more than 75 years. It means after the advent of the Ford system in assembly line, which is generally discussed in massive production, the necessary steps for production are assigned to work stations according to hypothesis to minimize the cycle time or work stations number. In recent years [1,2], the division has conducted several assembly line balancing problem that can be classified according to the objective function, problem structure and timing of jobs. In categorizing assembly line problems according to objective function, two basic models are mentioned, that different model can be generated by composition of these two models. These models include: Models of Type I and Type II. In Type I the cycle time of assembly line as the input of problem is defined and the steps to assemble the product should be assigned to workstations in such a way to minimize the required work stations. The assembly line balancing problem of Type II is also one of the categorizing of assembly line problems according to objective function, in that problem the number of assembly workstation as is designed the input of problem and the steps to assemble the product should be assigned to workstation in order to minimize the cycle time.The primary solving method of assembly line balancing problem is the linear programming, which is used by Salveson [3] for solving the assembly line balancing problem in simplest situation and after that Bowman [4], White [5] and Baker [6] solve the problem by formulating it in form of an integer linear programming, and also people like Patterson & Albrecht [7] used dynamic programming to solve this problem. Fonseca et al. [8] proposed a work to model and solve the stochastic assembly line balancing problem with a fuzzy representat- ion of the time variables as a viable alternative method. The assembly line balancing problem is one of the optimization problems for which is not possible to find the optimized result in an acceptable time. So most of the presented solutions are not efficient and proper for small size problems. Therefore to solve these problems creative solutions like Generic Algorithm, Tabu Search and Simulated Annealing are presented. One of the successful metaheuristic methods is Generic Algorithm, which is used in lots of complex optimization problems with acceptable results, high quality and effective time. In recent years, the Genetic Algorithm is used to solve assembly line balancing problem [9]-[14]. This paper proposes a metaheuristic model to solve a combined problem considering fuzzy job processing time in assembly line balancing to reduce the cycle time and the work station number using Genetic Algorithm. 2. FUZZY SET THEORY Since data in real-world problems are often afflicted with uncertainty, imprecision and vagueness due to both machine and human factors, they can only be estimated as within uncertainty. In an attempt to treat imprecise data, fuzzy numbers are introduced to represent the processing time of each job, where the membership function of a fuzzy data represents the grade of satisfaction of a decision maker [15]-[17]. Therefore Fuzzy Set Theory is a proper tool for modeling the uncertainly equals to Imprecision, ambiguity and loss of information and it is better tool for solving imprecise programming problems as below: (1) ~ . ) ~ ( ~ ~ X x t S x f Z Min   It seems problems with long-term prediction may include incomplete and imprecise information and also decisions are made according to the expert’s competence and are subjective, so it is very appropriate to use fuzzy number instead of definite numbers. The triangular numbers are very appropriate for this goal because they are created by defining the smallest, biggest and the more acceptable numbers. The analyses are based on fuzzy average instead of definite average. A. Triangular fuzzy numbers Triangular fuzzy number A with membership function ) ( x A  is defined as follow: