New complexity measures for the facility layout problem: an empirical study using traditional and neural network analysis

This paper proposes a new heuristic approach for solving facility layout problem (FLP) which is traditionally formulated as quadratic assignment problem (QAP). In this paper, FLP is formulated as linear assignment problem (LAP) consisting of facility pair and location pair. Being linear in nature LAP can be solved efficiently. Solution of LAP provides lower bound on corresponding QAP formulation of FLP. Heuristic procedure is applied to solve FLP from sets of LAP solution. Proposed heuristic is tested on benchmark instances taken from literature and compared with other heuristics available in literature. Computational results show that proposed heuristic provides a good quality approximate solution. This solution can be taken as initial solution for any improvement heuristic to get optimal/near optimal solution for FLP.

The quality of facility layout is related to the operational efficiency of the entire system. Based on bibliometric methods, 859 related papers on the theme of facility layout included in the Web of Science core dataset from 2002 to 2021 were analyzed. First, through the visualization tools of Web of Science, the issue of facility layout is analyzed from the annual publication volume, journals and research directions. Next, based on the Citespace software, the cooperation and citation relationships among countries, institutions, and authors are analyzed from the macro, meso, and micro levels, and the cooccurrence analysis of keywords and nominal terms is carried out to generate a visual knowledge map, and to solve the problem of facility layout. The research status, hotspots and trends are reviewed. The results show that the problem of facility layout has been a hot research area. However, there are many and scattered situations in China's facility layout research, and it is necessary to strengthen cooperation. In addition, there are few studies in the fields of digital facility layout, smart factory, and digital twin, which need to be focused on.

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.

In this paper, an approximate algorithm is proposed to solve facility layout problem (FLP) which is formulated as quadratic assignment problem (QAP). In the proposed approach, linear assignment problem (LAP) is formulated which is solvable in polynomial time. The proposed heuristic is applied to solve FLP from the set of LAP solution. To evaluate the performance of the heuristic a comparison between optimal and heuristic solution is also provided. The approach is tested on numerous benchmark problems available in literature. An encouraging comparative performance of this procedure is thus reported.

Due to the combinatorial nature of the facility layout problem, current heuristic computer procedures do not always provide better solutions than visual methods. A new algorithm, FLAC (Facility Layout by Analysis of Clusters), is described which emulates the visual methods used by industrial engineers in solving facility layout problems. Initially side-stepping the combinatorial nature of the problem, FLAC is found to perform well in problems with high as well as low flow dominance, and in the presence and absence of line dominance. Computation time is attractive, especially on larger problems.

Businesses, including manufacturing companies, must reduce cost to survive in today’s economy. During the last several decades, to reduce cost, many companies began to focus on labor optimization and/or increasing productivity. This may require an increase in investment cost (e.g., equipment costs). Among the consequences of these policies is a significant reduction in direct labor cost. The necessity to reduce direct labor cost has made material handling cost more important than ever. Material handling cost reductions can be obtained by designing efficient layouts. Efficient layouts are obtained by solving machine and facility layout problems effectively. Commonly, facility and machine layout problems assume that product flows are either known or estimated before hand, and that the layout solution has enough capacity to satisfy all product demands. When product demands exceed capacities of planned production systems, it is important to select a feasible product mix that maximizes company profits. In addition, when identical machines are considered, determining material flows as well as the layout always lead to better solutions. Integrating these issues leads to the generalized machine layout problem (GMALP). More specifically, the GMALP is the designing of a facility layout by defining the product mix, selecting the number of machines to be used, assigning these machines to the plant floor, and assigning products to machines such that total profit is maximized. Moreover, the GMALP integrates the quadratic assignment problem (QAP) and the maximum profit multicommodity flow problem (MPMFP). Therefore, the GMALP is a computationally intractable problem. Consequently, a mixed integer nonlinear programming model was developed and used to solve small problem instances. In addition, construction algorithms and metaheuristics (i.e., tabu search and memetic algorithms) were developed for solving large GMALP instances in acceptable computation times. Also, a test dataset was used to evaluate the performances of the heuristics presented. Finally, the memetic algorithms performed better than the tabu search heuristics for the dataset.

The multifactor facilities layout problem is one of the important cases of quadratic assignment problem (QAP), which deals with the problem of optimum assignment of n facilities to n locations and optimizing multifactor cost objective. The authors present an alternate mathematical model for QAP that combines multiple qualitative and quantitative factors separately, treating them in a different manner for the facilities layout problem. The composite factor is obtained by combining the weighted combined qualitative and quantitative factors. The distances between the locations weigh the composite factor. The objective function is to minimize the total weighted workflow distance between the facilities. The results of the proposed model are compared with that of an existing model that handles multiple qualitative and quantitative factors in the same manner.

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.

Component lot-splitting considerations, in which the lot-size of a component item may cover only a fraction of its parent item's lot-size, have been ignored in the literature when determining lot-sizes of items in multi-stage manufacturing systems. In this paper, a multi-stage lot-sizing problem is formulated under a specified component lot-splitting policy for the case of noninstantaneous production of items and constant demand for the end item. Optimal and heuristic solution procedures for the formulated problem are provided, including experimental results of comparison between these procedures. It is shown that considerable cost savings can result if the component lot-splitting approach is employed under favorable conditions in multi-stage manufacturing environments. In addition, reduced inventory levels are achieved which translate into lower working capital requirements and a less cluttered shop floor. The heuristic procedure is recommended as an acceptable alternative to the optimal procedure if the number of items in the multi-stage system is large or if inventory carrying and setup/order costs cannot be accurately estimated. Further, component lot-splitting considerations may be ignored if production rates of facilities in the system are in balance. Finally, a methodology for application of the component lot-splitting policy where the end item demand is time-varying is discussed.

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.

This paper focuses on solving the Continuous Facility Layout Problem (CFLP), which aims to minimize material handling costs by strategically placing facilities in a known or unknown area. The objective is to find optimal or near-optimal facility arrangements while adhering to non-overlapping and spatial constraints, thus enhancing the efficiency of production systems. The study addresses various layout scenarios, including single-row facility layout (with and without clearance), continuous layout, and unequal-area facility layout problems. To achieve this, the authors propose a mixed-integer nonlinear programming (MINLP) model tailored for continuous layouts. Two meta-heuristic algorithms are developed to optimize this model: a hybrid Simulated Annealing-Genetic Algorithm (SA-GA), which leverages genetic crossover operations, and an Enhanced Harmony Search Algorithm (EHSA), featuring dynamic parameters and a novel improvisation technique. The proposed methods provide flexible and efficient solutions for both small and large-scale layout problems, offering decision-makers practical tools for real-world applications.

Semiconductor chips are the most basic components of smart wearable device and other AI devices. The problem of facility layout in semiconductor fabrication is considered very important, for it will affect the cost saving and performance improvement of the key chips implanted in artificial intelligence production such as intelligent wearable devices. Facility layout problem in semiconductor fabrication is to determine the optimal placement of facilities in a multi-row particular area. In this study, we propose a mathematical model to solve multi-row facility layout problem regarded as a predefined system of discrete points to place the processing modules at different locations in semiconductor fabrication plants (i.e., semiconductor fabrication). Considering the large amounts of computation required we use particle swarm optimization (PSO) algorithm to solve the multi-row facility layout problem by minimizing the total transportation distance between the modules. The results confirm that the PSO algorithm is an effective and practical approach for solving the multi-row facility layout problem within a shorter period. The effect of the number of particles on the efficiency of the PSO algorithm is also discussed in this paper.

This paper is survey of hybrid flow shop scheduling problems. An HFS scheduling problem is a classical flow-shop in which parallel machines are available to perform the same operation. Most real world scheduling problems are NP-hard in nature. The hybrid flow shop scheduling problems have received considerable research attention. The several optimization and heuristic solution procedures are available to solve a variety of hybrid flow shop scheduling problems. It discusses and reviews sustainability of several variants of the hybrid flow shop scheduling problem for economical analysis, each in turn considering different assumptions, constraints and objective functions. Sustainability is the long-term maintenance of responsibility, which analysis the economics and encompasses the concept of stewardship. The Hybrid flow shop problem has sustained for several decades with multi – objective constraints. The paper shows some fruitful directions for future research and opportunities in the area of hybrid flow shop.

The problem of scheduling n jobs on M machines in a flowshop has received considerable research attention over the last twenty-five years. As a result, several optimization and heuristic solution procedures are available to solve a variety of flowshop scheduling problems. This paper reviews the flowshop scheduling problem formulation, solution approaches, and analyzes the contributions of each approach to solve practical problems. Subsequently, directions for future research are outlined.

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.