Mathematical Modeling and Hybrid Heuristic for Unequal Size Facility Layout Problem

This paper focuses on facility layout design problem in microfluidic device manufacturing. Microfluidics device manufacturing requires exquisite work of operators and relatively much higher material cost than other types of manufacturing. Facility layout problem can directly affect the overall cost of manufacturing, particularly in handling and transport cost. Therefore, the objective of this study is to minimize the total handling and transport cost for facility layout design problem. A genetic algorithm (GA) is employed to find a good alternative facility layout design which is based on the performance metrics. Experimental results show that this approach is more feasible in dealing with the facility layout in microfluidics device fabrication.

ABSTRACTIn manufacturing industries, the facility layout design is a very important task, as it is concerned with the overall manufacturing cost and profit of the industry. The facility layout problem (FLP) is solved by arranging the departments or facilities of known dimensions on the available floor space. The objective of this article is to implement the firefly algorithm (FA) for solving unequal-area, fixed-shape FLPs and optimizing the costs of total material handling and transportation between the facilities. The FA is a nature-inspired algorithm and can be used for combinatorial optimization problems. Benchmark problems from the previous literature are solved using the FA. To check its effectiveness, it is implemented to solve large-sized FLPs. Computational results obtained using the FA show that the algorithm is less time consuming and the total layout costs for FLPs are better than the best results achieved so far.

The most desirable characteristic of a facility layout is its ability to maintain its efficiency over time while coping with the uncertainty in product demand. In the traditional facility layout design method, the facility layout is governed by the flow intensity between departments, which is the product flow quantity between departments. Hence, an error in the product demand assessment can render the layout inefficient with respect to material handling costs. Most of the research integrates uncertainty in the form of probability of occurrence of different from-to charts. In an environment where the variability of each product demand is independent, the derivation of ‘probabilistic from-to chart’ based scenario cannot be used to address uncertainty of individual demands. This paper presents an FLP (facility layout problem) approach to deal with the uncertainty of each product demand in the design of a facility layout. Two procedures are presented: the first procedure is utilised to assess the risk associated with the layout, while the second procedure is used to develop the layout that minimises the risk. Results from case studies have shown that the procedure produces a reduction of risk as high as 68%.

The Facility Layout Problem (FLP) is a renowned and extensively researched problem that has attracted significant focus from various areas, including industry and manufacturing. One of the recent studies includes the examination of FLP issues in a large room. Analysing the layout of amenities and temperature controls in spacious areas like libraries is crucial for understanding how they affect people’s thermal comfort and energy consumption. The arrangement of facilities typically impacts the air distribution within a large room. Improper facility layout design might create indoor temperature disparities, with specific zones feeling excessively warm or chilly. Consequently, users are unevenly distributed due to each individual’s differing thermal comfort needs. Previous researchers have discussed this issue. However, after a detailed examination of previous studies, a few drawbacks have been identified in building mathematical models. These drawbacks include poorly organised mathematical modelling, ambiguous or disorganised data collection and analysis techniques, and the absence or ambiguity of variables and constraints. Therefore, this study proposed a structured mathematical approach to build a more efficient, inclusive, and reliable model. This study used a university library in Malaysia as a case study. A well-established and widely practised method for assessing mathematical modelling competency based on previous research has been adopted. Subsequently, the list of sub-competencies associated with the modelling process is utilised as a reference point for constructing a mathematical model in this research endeavour. As a result, the entire process of constructing a mathematical model is detailed, and recommendations for future enhancements are provided. This project is considered a significant advancement in the pursuit of conducting further FLP investigations in large rooms for the greater good in the future, which is part of the PhD research carried out at UUM.

A well-planned arrangement of manufacturing departments on a two-dimensional planar region considerably increases the efficiency of its production systems, which is termed facility layout problem (FLP). Conventional layout design approach often designs intercell layout (determining exact location of each department on shop floor area) and flow path layout design of material handling system (MHS) step by step in a sequential manner. This results in suboptimal solutions for FLP. In this paper, an integrated approach is adopted to design the intercell layout and the flow path layout of MHS simultaneously. The quality of the final layout is evaluated by minimizing total material handling cost. Sequence pair (SP) representation is used for layout encoding. The translation from SP to layout is efficiently made by longest common subsequence (LCS) methodology. An elitist strategy genetic algorithm using simulated annealing (E-GASAA) as a local search mechanism is developed and tested with four test problem instances available in the literature. Elitist strategy is incorporated to enhance convergence characteristic of the proposed algorithm. It is found that the proposed E-GASAA is able to produce best solutions consistently for the test problem instance of different sizes within acceptable computational effort. In addition to that, we tried to reduce the computational load with the help of adopted LCS computation methodology and achieved a good improvement.

Facility Layout Problem (FLP) can be considered as a classical problem in quantitative studies. However, the literature in FLP are largely neglected the thermal comfort as part of the objective function. Today, energy savings for buildings are a major concern in the world as they cover a big portion of energy use. The public room consumes high energy use because of its ability to occupy many people at one time. Issues arise when each person has a dissimilar thermal satisfaction rate, while each area in a room provides a different temperature. There are many factors that influence the people dispersion in the room including the facility layout. However, it is really testing to handle an air-conditioning control () system by considering the mention factors to ensure the thermal satisfaction is increased and energy is reduced. Since lack of report on thermal factors in Facility Layout Problem (FLP) area, this work aims to optimize the temperature setting of an system at the best point and achieving the finest plan for the facility layout in a room. Further, our ultimate goals to maximize the thermal comfort level and reduce energy consumption are able to accomplish. A non-linear mathematical model is utilized to optimize the thermal satisfaction rate () and room layout. At the end of the article, we proposed an Evolutionary Algorithm (EA) to find a quality solution or near optimal since it is hard to solve this problem in a reasonable time.

Since Facility Layout Problem (FLP) affects the total manufacturing cost significantly, it can be considered as a critical issue in the early stages of designing Flexible Manufacturing Systems (FMSs), particularly in volatile environments where uncertainty in product demands is inevitable. This paper proposes a new mathematical model by using the Quadratic Assignment Problem formulation for designing an optimal machine layout for each period of a dynamic machine layout problem in FMSs. The product demands are considered as independent normally distributed random variables with known Probability Density Function (PDF), which changes from period to period at random. In this model, the decision maker's defined confidence level is also considered. The confidence level represents the decision maker's attitude about uncertainty in product demands in such a way that it affects the results of the problem significantly. To validate the proposed model, two different size test problems are generated at random. Since the FLP, especially in multi-period case is a hard Combinatorial Optimization Problem (COP), Simulated Annealing (SA) meta-heuristic resolution approach programmed in Matlab is used to solve the mathematical model in a reasonable computational time. Finally, the computational results are evaluated statistically.

Facility layout design problem considers the departments’ physcial layout design with area requirements in some restrictions such as material handling costs, remoteness and distance requests. Briefly, facility layout problem related to optimization of the layout costs and working conditions. This paper proposes a new multi objective simulated annealing algorithm for solving of the unequal area in layout design. Using of the different objective weights are generated with entropy approach and used in the alternative layout design. Multi objective function takes into the objective function and constraints. The suggested heuristic algorithm used the multi-objective parameters for initialization. Then prefered the entropy approach determines the weight of the objective functions. After the suggested improved simulated annealing approach applied to whole developed model. A multi-objective simulated annealing algorithm is implemented to increase the diversity and reduce the chance of getting layout conditions in local optima.

An evolutionary optimal green layout design for a production facility by simulated annealing algorithm

Facility layout problems deal with layout of facilities or departments in a shop floor. This article studies unequal-area static facility layout problems in order to minimize the sum of the material handling costs and unequal-area dynamic facility layout problems so as to minimize the sum of the material handling costs and rearrangement costs. Unequal-area static and dynamic facility layout problems are NP-hard. Therefore, a modified particle swarm optimization was suggested to solve them where the departments have fixed shapes and areas throughout the time horizon. The modified particle swarm optimization was tested using the available problem instances chosen from the literature. The proposed algorithm applied two local search methods and the department swapping method to improve the quality of solutions and to prevent local optima for dynamic and static problems. It also utilized the period swapping method to improve the solutions for dynamic problems. The results showed that the proposed algorithm has created encouraging layouts in comparison with other approaches.

The Single-Row Facility Layout Problem (SRFLP) is one of the most studied facility layout problems in the literature. It asks for an optimal arrangement of departments with given lengths on a row such that the weighted sum of all centre-to-centre distances between department pairs is minimised. Real-world facility layouts may require taking different restrictions on the placement of departments into account, such as arrangement on a fixed position, pairwise placement, or precedence considerations. Therefore, we consider the constrained Single-Row Facility Layout Problem (cSRFLP) that additionally considers positioning, ordering, and relation constraints on single-row facility layouts. In this work, we suggest a new Integer Linear Programming (ILP) formulation for the cSRFLP, which outperforms the best available exact approach in literature. In an extensive computational study, we apply our ILP approach as well as an LP-based cutting plane algorithm on SRFLP and cSRFLP instances from the literature. We provide optimal cSRFLP layouts as well as strong lower bounds for instances with up to 42 departments. Further, we present new results for SRFLP instances from the literature. Additionally, we demonstrate the individual impact of the constraint sets on the run times of cSRFLP instances to emphasise further research on this rarely studied practice-oriented Facility Layout Problem.

Genetic search for solving construction site-level unequal-area facility layout problems

Optimization metaheuristics have become necessary due to the growing demand for better and more realistic designs. This paper proposes a metaheuristic-based approach for solving design problems in a reasonable time while browsing large spaces of solutions. The objective of this article is to compare the performance of two methods Genetic Algorithm GA and Particle swarm optimization PSO, combined with A* algorithm, in solving a constrained facility layout problem. The two chosen metaheuristics have been successfully applied in many search problems. We consider their speed and performance. The performance of the obtained solutions is measured in terms of the total distance traveled by products in the workshop. In order to determine the shortest path in a realistic way between workstations in a given irregular area (with aisle structure, or material storage areas, lunchrooms and offices), the A* algorithm was integrated with them. The comparison therefore concerns <GA, A*> and <PSO, A*>. GA and PSO algorithms generate configurations for which the shortest path for any couple of machines is identified through the A* search algorithm taking into account of obstacles. The mathematical model used and the parameters of the genetic algorithm are those developed in (Besbes et al. 2019). The numerical results show the feasibility and effectiveness of both approaches. Our results demonstrate that GA yields a better solution than Particle Swarm Optimization in total distance travelled while PSO is faster.

Construction site-level facilities layout is an important activity in site planning. The objective of this activity is to allocate appropriate locations and areas for temporary site-level facilities such as warehouses, job offices, various workshops and batch plants. Depending on the size, location, and nature of the project, the required temporary facilities may vary. The layout of facilities has an important impact on the production time and cost savings, especially for large projects. In this paper, a construction site-level facility layout problem is described as allocating a set of predetermined facilities into a set of predetermined places, while satisfying layout constraints and requirements. A genetic algorithm system, which is a computational model of Darwinian evolution theory, is employed to solve the facilities layout problem. A case study is presented to demonstrate the efficiency of the genetic algorithm system in solving the construction site-level facility layout problems.

A solution to the facility layout problem using simulated annealing