Developed a Mathematical Model for Solving the Two-Objective Dynamic Facility Layout Problem with Budget Constraints and Optimal Allocation of Buffer Size

Author Name(s): Mohsen Manoochehri, *Marjan Mohammadjafari
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Optimal facility layout is of the factors that can affect the efficiency of any organization and annually millions of dollars costs are created for it or profits are saved. Studies done in the field of facility layout can be classified into two general categories: Facility layout issues in static position and facility layout issues in dynamic position. Because that facilities dynamic layout problem is realistic this paper investigates it and tries to consider all necessary aspects of this issue to become it more practical. In this regard, this research has developed three objectives model and tries to simultaneously minimize total operating costs and also production time. Since the calculation of production time using analytical relations is impossible, this research using simulation and regression analysis of a statistical correlation tries to measure production time. So the developed model is a combination of analytical and statistical relationships. The proposed model is of NP-HARD issues, so that even finding an optimal solution for its small scale is very difficult and time consuming. Multi-objective meta-heuristic NSGA-II and NRGA algorithms are used to solve the problem. Since the outputs of meta-heuristic algorithms are highly dependent on the algorithms input parameters, Taguchi experimental design method is also used to set parameters. Alsoin order to assess the efficiency of provided procedures, the proposed method has been analyzed on generated pilot issues with various aspects. The results of the comparing algorithms on several criteria, consistently show the superiority of the NSGA-II than NRGA in problem solving.


Dynamic Facility Layout, Simulation, Meta-Heuristic Algorithm, Taguchi Experimental Design


The placement of the facilities in the plant area, is known as ”facility layout problem”, have a significant impact upon manufacturing costs, work in process, lead times and manufacturing systems productivity (Drira et al. 2007). A good placement of facilities in manufacturing or even non-manufacturing organization and in general any organization that is faced with the layout problem contributes to the overall efficiency of operations and can reduce until 50% the total operating expenses (Tompkins et al. 1996). So the organization productivity and profitability increases.It can be said that the layout design includes planning, design, promotion, and implementation of systems consisting of the establishment of projects and transport system to maximize space efficiency and utility. Today, since the demand for products from customers is constantly changing, that system will be more successful system that better than others be able to answer the market demand, the success will be doubled when we be able to match supply and demand and thereby maximize the profitability and efficiency of production and service provision. Facility layout is one of the requirements that by taking advantage of it we can optimize the supply conditions (production or provision of services by the system. Of course, from the above description we can be found that such layout gives us the highest efficiency that according to circumstances can be flexible and makes our goals possible.Thus dynamic facility layout is desired and by understanding the requirement that each system (in particular, factories and industrial workshops) according to their layout design must fulfill the principle of profitability we decided using a practical method try to investigate and solve a problem from dynamic facility layout series.


In this study, we tried for the first time to develop a mathematical model that is able simultaneously minimize layout costs and production time. A new multi-objective meta-heuristic algorithmis also designed and its performance is compared with the existing algorithms in the literature. In other words, in this research a meta-heuristic algorithm based approach combined with statistical analysis is upon which our desired model is optimized. In this regard, using the simulation, regression equation is obtained that is actually a formula related to production. The parameter setting using Taguchi method is used to determine the input associated with NSGA-II and NRGA met heuristic algorithms. This method determines the initial population values (n_Pop), cross over

(Cross over rate), mutations (Mutation rate) and the number of repetitions (n_It) for each of the algorithms. Results of implementation of algorithms make it possible to compare two algorithms. These logical results show that the algorithm selected to solve the problem, is far better than existing algorithms in literature review and we can claim that with the help of these algorithms, finally we have values which if we used them in model will results in its optimization and enables the achievement of the objectives.  By comparing the criteria and implementation of ANOVA test it became clear that non-dominated sorting genetic algorithm (NSGA-II) is better than non-dominated rating genetic algorithm (NRGA) and in fact is an algorithm that if be used to solve the problem or problem model will become certainly optimal.

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