OPTIMIZATION OF FACILITY LAYOUT PROBLEMS USING GENETIC ALGORITHM

The facility layout problem (FLP) is one of the most important classic industrial engineering and production management problems that have attracted the attention of many researchers over the last few decades. Poor production facility layout planning can result in additional operational costs; one of them is the cost of material handling. Although crucial, FLP is a challenging issue to resolve. A unique method is needed depending on the constraint, case study, and layout type. This research was conducted in order to improve the existing layout of PT. XYZ to minimize material handling costs. The layout type in this case is the Open-field layout problem (OFLP). A genetic algorithm is proposed to optimize the layout. The result is 18.1% material handling costs can be reduced.


Introduction
The facility layout problem (FLP) is one of the most important classic industrial engineering and production management problems that has attracted the attention of many researchers over the last few decades.To operate production and service systems efficiently, companies must not only operate with optimal operational planning and policies but must also have a well-designed facility layout.The facility layout problem (FLP) is defined as an attempt to find the most efficient arrangement of elements on the factory floor subject to different constraints to fulfill one or more objectives.Effective facility layout design improves throughput, overall productivity and efficiency.Conversely, poor facility layout results in increased work-in processes and manufacturing lead times.
The most significant indicator of layout efficiency is material handling cost (MHC) (Emami & S. Nookabadi, 2013).Since 20-50% of a manufacturing company's total operating costs and 15-70% of a product's total production costs are attributed to MHC (Mohamadghasemi & Hadi-Vencheh, 2012), companies can reduce these costs by at least 10-30% (Madhusudanan Pillai et al., 2011), and increase their productivity if their facilities are managed effectively.In contrast, an ineffective layout can increase MHC by as much as 36% (Ripon et al., 2013).In addition, another research shows that more than 35% of system efficiency is likely to be lost by applying the wrong location layout and design (Izadinia & Eshghi, 2016).
Several model studies based on area and proximity of facilities have been conducted since the 1960s to 1990s, Muther (1973) which includes Systematic Layout Planning (SLP) and Heragu & Kusiak, (1990) using the Quadratic Assignment Problem (QAP) to solve equal area .Also, many improvements have been made to the models to increase their adaptability.Meanwhile, with the wide application of computer-aided technology, a large number of related software and technologies have also been developed such as CORELAP, ALDEP, graphic theory, CRAFT, MultiPLE and so on.Since the 1990s, optimization algorithms have been introduced to the field of FLP (Liu & Sun, 2012).
In the literature review (Hosseini-Nasab et al., 2018) classify facility layouts based on material handling systems as follows, Single-row layout problem (SRLP), This problem is concerned with arranging a number of adjacent rectangular facilities along a line to minimize the total arrangement cost of the total product flow and facility-tofacility distance.Several shapes of SRLP can be detected, such as straight line, semicircular, or U shape.

Figure 1. Single-row layout problem (SRLP)
Multi-row layout problem (MRLP) locates a set of rectangular facilities on a fixed number of lines in two-dimensional space, so that the weighted sum total centerto-center distance between all pairs of facilities is minimized.In this type of configuration, each resource can be assigned to any of the given rows.All of these rows are the same height, and the spacing between adjacent rows is all the same

Parallel-row ordering problem (PROP)
In PROP, the sub-facilities with several characteristics in common are arranged in one row, while the remaining facilities are left in parallel rows.DRLP and PROP differ in that PROP assumes that the settings in both lines start from the same point and no space is allowed between two adjacent facilities, whereas DRLP makes no such assumption.Also, DRLP assumes that the distance between two parallel lines is zero, while PROP does not

Loop Layout Problem (LLP)
This type of layout aims to find n facility assignments to n predefined candidate locations in a closed loop, so that the total handling cost can be minimized.LLP incorporates loading/unloading stations, i.e. locations from which a section enters and exits the loop.This station is unique, and is assumed to lie between positions n and 1.

Open-Field Layout Problem (OFLP)
Open-field layouts (OFLP) correspond to situations where facilities can be located without restrictive arrangements such as single-row, double-row, parallel-row, multi-row, or loop layouts.The most prominent limitations of Open-field layouts (OFLP) are the non-overlapping constraints that force the facility to lie on the ground without overlapping.

Multi-Floor Layout Problem (MFLP)
Insufficient space in cities and the very high cost of providing living space, especially in metropolitan cities, makes designers and engineers consider the Multifloor layout problem (MFLP) instead of a single-floor layout.Also, in rural areas where land can be provided more cheaply than in urban areas, multi-storey factories are preferred to store land for future expansion.Figure 7 shows that sections can move not only horizontally on a given floor (ie in the horizontal flow direction) but also from one floor to another which is located at a different level (ie in the vertical flow direction).

Genetic Algorithm
The genetic algorithm was first developed in the 1970s by John Holland (a professor from the University of Michigan, USA).At the time, Holland aimed to create software whose underlying principles mimicked natural evolutionary processes.To do this, he wanted to abstract the processes that occur in nature over the course of evolution.Genetic algorithms can therefore genuinely resolve issues that cannot be resolved by doing regular mathematical operations.
A genetic algorithm is a search technique and optimization technique that mimics the process of evolution and changes in the genetic structure of living things.The main principle of how the genetic algorithm works is inspired by the process of natural selection and the principles of the science of genetics.In natural selection, individuals compete to survive and reproduce.Individuals who are more fit will have the opportunity to continue to survive and reproduce (produce offspring).Conversely, individuals who are less fit will die and become extinct (this principle is also used as "survival of the fittest".Crossover) and mutation.Both of these processes occur in the chromosomes of individuals who reproduce.This process of selection and reproduction (crossover and mutation) takes place repeatedly, until the most fit individual is produced.This most suitable solution is the solution to the problem faced.
the problems that can be solved with the genetic algorithm are as follows (Al-Tabtabai & Alex, 1999): 1) The range of the ideal answer is enormous.
3) Solutions to these problems can be encoded in the form of strings or characters.4) The difference between optimal and near optimal solutions can be considered.5) Some of the advantages of using GA are as follows: 6) Simultaneous search of various cost surface samples 7) Can solve cases with wide variables 8) Is well suited for parallel computers 9) Optimizing variables with very complex surface costs 10) Can encode variables According to the explanation above, GA is considered as a very effective method to solve the temporary facility location problem.
The fitness function is used to test the optimality of the chromosomes.Chromosomes that are proven to be more optimal are allowed to multiply and produce new, better generation chromosomes.The Fitness function must be developed for each problem to be solved.

Related Works
One of the commonly used optimization algorithms to solve several FLPs is the Genetic Algorithm.Several studies using genetic algorithms have been carried out, but not many researchers have optimized the open-field layout problem (OFLP).In fact, many cases of FLP in the field are of the open-field layout type.Some of the latest research on the Facility Layout Problem including (Datta et al., 2011) optimized the Single Row Facility Layout Problem (SRFLP) case using a permutation-based genetic algorithm, then (Kothari & Ghosh, 2014;Lenin et al., 2013) also optimized the case of the Single row facility layout problem (SRFLP) using a genetic algorithm, then (Khaksar-Haghani et al., 2013;Kia et al., 2014)also used a genetic algorithm to optimize the Multi-floor layout problem (MFLP) case.Next (Aiello et al., 2013;Gonçalves & Resende, 2015;Paes et al., 2017;Palomo-Romero et al., 2017) used a genetic algorithm to solve the Unequal-Area Facility-Layout Problem (UA-FLP) case.

Problem Formulation
The problem presented in this study can be modeled as a Quadratic Assignment Problem (QAP) which is the same as the number of existing facilities and locations.If the number of locations exceeds facilities, dummy facilities can be added to the model (with zero distance or frequency to existing real facilities so as not to affect layout planning).The model incorporates the following decision parameters that contribute to the total cost to be minimized.
The proposed mathematical model for distance optimization and movement costs is as follows: Then   defined as follows: where, Z : moment of movement from station i to Station (Meters/month) Fij : frequency of movement from station i to station j(times/month) Dij : the distance between station i and station j (meter) n : the number of machines used for each product Xi,Yi : the orthogonal coordinates of the centre of facility i

Subject to
The constraints for this research is adopted from (Said & El-Rayes, 2013) as follow: Boundaries Constraint Boundary restrictions are put in place to ensure that all temporary facilities are located within the site boundaries.As shown in the fig.8. Facility 3 and Facility 4 are violating the constraints. (1) (2)    U In this study the number of products is 4 namely; Granit Poles, Granit Bakar, Granit Brush Hammer, dan Granit Honned.Each product almost all uses the same machines.Differences in the use of machines for the production of each product.The machines used on the production floor are presented in Table 2.The operations process chart in this study was made separately for each product to make it easier to understand each production operation for each product.In Fig. 12 Granit Poles products went through a process from the raw material warehouse, block cutter machine, polishing machine 1, polishing machine 2, to the storage warehouse with a total time of 57 minutes per product.

Figure 12. Operations Process Chart Granit Poles
In the figure Fig. 13 Granit Bakar products went through a process from raw materials, block cutter machines, angle cutting machines, Burning machines, to storage warehouses with a total time of 16 minutes per product.

Figure 13. Operations Process Chart Granit Bakar
In Figure 14 Granit Brush Hammer products went through a process from raw materials, block cutter machines, bush hammer machines, angle cutting machines, to warehouse storage with a total time of 29 minutes per product.

Figure 14. Operations Process Chart Granit Brush Hammer
In Figure 15 Granit Honned products went through a process from raw materials, block cutter machines, angle cutting machines, to warehouse storage with a total time of 14 minutes per product.

Figure 15. Operations Process Chart Granit Honned
Based on the Operations Process Chart, the standard time per unit for each product is; Granit Poles 57 minutes / Product, Granit Bakar 16 minutes / Product, Granit Brush Hammer 29 minutes / Product, Granit Honned 14 minutes / Product.Standard time and production capacity are presented in Table 3.After the production capacity is known, material handling costs can also be known by knowing the Distance of Movement.Movement Distance & Material Handling Cost can be seen in Table 4.The number of work stations to be arranged is n.Machines are coded according to facility layout in Fig. 16.The number of workstations allowed per column is p, and each row is q.So that the layout of the work station can be represented in a line.Then the row is changed to a positive integer number so that the chromosomes are obtained: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Testing Scenario with Code Python
The test scenario is carried out to find out the parameters in determining the best fitness value.Parameters used include iteration, mutation probability, and crossover probability.Determination of parameter values is based on previous research, including (Umam et al., 2022) using 1000 iterations and a mutation probability of 0.1 in completing flow shop scheduling using a genetic algorithm.Research by (Saputro et al., 2015) used a genetic algorithm with 400 iterations and a mutation probability of 0.5 to solve agricultural land optimization problems.Whereas (Nasution, 2015) in his research used a crossover probability of 80% and 90% to overcome the problem of traveling salesmen using a genetic algorithm.Based on previous research, the test scenario parameters in this study are as follows in Table 5.   3 and the graph in Fig. 18 it can be seen that the smallest cost value is in scenario 6 while the highest cost value is in scenario 3. The highest fitness value is obtained in scenario 3 while the lowest fitness value is obtained in scenario 6.The best solution in the genetic algorithm is generally use the highest fitness value, but for layout optimization problems the smallest cost value is needed.Therefore, scenario 6 and scenario 3 will be compared to find out the results of layout optimization as the best solution.
For scenario 3, the chromosome sequence is ( 9 8 15 13 6 12 2 4 11 5 3 14 1 17  16 7 0     Table 9 shows that the difference in material movement distance between the initial layout and the proposed layout in accordance with scenario 3 is 1105.61m or 6.7%, where the displacement distance in scenario 3 layout is larger than the displacement distance in the initial layout.Meanwhile, the difference between the displacement distance of the initial layout and the proposed layout in accordance with scenario 6 is 3002.58m or 18.3% where the displacement distance in scenario 6 layout is smaller than the displacement distance in the initial layout.This shows that the best results for optimizing the layout of production machines using genetic algorithms are in accordance with scenario 6 which can reduce the material movement distance by 3002.58 m or 18.3%.Table 10 shows that the difference in material handling costs between the initial layout and the proposed layout according to scenario 3 is Rp.42,645.49rupiah or 6.9%, where the material handling costs in scenario 3 layout are greater than the material handling costs in the initial layout.Meanwhile, the difference in material handling costs for the initial layout and the proposed layout according to scenario 6 is Rp.111,693.94or 18.1% where the material handling costs in scenario 6 layout are smaller than the material handling costs in the initial layout.This shows that the best results for optimizing the layout of production machines using genetic algorithms are in accordance with scenario 6 which can reduce material handling costs by Rp.111,693.94rupiah or 18.1%.

Conclusion
Optimization of production machine layout at PT. XYZ is carried out on 18 work stations.The optimization results using a genetic algorithm with the help of the python program produce a new layout arrangement that can reduce material movement distances and reduce material handling costs.The difference in material movement distance between the initial layout and the new layout resulting from optimization according to the best proposal is 3002.58m or 18.3%, where the displacement distance in the new layout is smaller than the displacement distance in the initial layout.The optimization results can also reduce the cost of material handling by Rp.111,693.94or 18.1% lower than the initial layout.Layout optimization using genetic algorithms is able to shorten material movement distances and reduce material handling costs.

Figure 18 .
Figure 18.The Results Of The Test Scenarios Using Code Python 10) So the sequence of work stations based on the chromosome sequence is as follows: MK MC MF MG MA MR MM ME MP MQ MS MN MB MT MH MU ML MJ Fig. 19 Shows the new Layout for Scenario 3 that repsent the New Chromosome.

Facility F2 Violating the constraint Facility F2 Violating the constraint
|  −   |≥(    +     )/2 + (    +     )/2 +   Chromosome Representation Before carrying out the chromosomal arrangement, it is necessary to have data on the facilities used on the production floor, including coordinates.Then code the facilities as shown in Table1.

The Results Of The Test Scenarios Using Code Python
Based on the results of the test scenarios using Code Python, the fitness, cost, and chromosome values for each scenario are presented in Table6: