A parallel ordering problem in facilities layout

The layout positioning problem of facilities on a straight line is known as Single Row Facility Layout Problem (SRFLP). The objective of SRFLP, categorized as NP-Complete problem, is to arrange the layout such that the sum of distances between all facilities’ pairs can be minimized. Extended Artificial Chromosome Genetic Algorithm (eACGA) is a promising algorithm that has been proposed recently. eACGA extends the probabilistic model in Estimation of Distribution Algorithms (EDAs) and then hybridize it with Genetic Algorithms (GAs). eACGA is proven to produce an excellent solution for scheduling problem. In this paper, we modify the eACGA to solve SRFLP. Computational results on benchmark problems show the effectiveness of eACGA for solving SRFLP. Key Words: single row facility layout, estimation distribution algorithm, genetic algorithm.

Free AccessAboutSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack CitationsPermissionsReprints ShareShare onFacebookTwitterLinked InEmail Go to SectionFree Access HomeOperations ResearchVol. 19, No. 1 Technical Note—A Further Note on One-Dimensional Space AllocationDonald M. SimmonsDonald M. SimmonsPublished Online:1 Feb 1971https://doi.org/10.1287/opre.19.1.249"Technical Note—A Further Note on One-Dimensional Space Allocation." Operations Research, 19(1), p. 249 Previous Back to Top Next FiguresReferencesRelatedInformationCited bySingle-row equidistant facility layout as a special case of single-row facility layout15 August 2013 | International Journal of Production Research, Vol. 52, No. 5A polyhedral approach to the single row facility layout problem21 March 2012 | Mathematical Programming, Vol. 141, No. 1-2A computational study and survey of methods for the single-row facility layout problem6 September 2012 | Computational Optimization and Applications, Vol. 55, No. 1Optimal solutions for the double row layout problem30 November 2011 | Optimization Letters, Vol. 7, No. 2A Hybrid Clonal Selection for the Single Row Facility Layout Problem with Unequal DimensionsiBusiness, Vol. 04, No. 03A new lower bound for the single row facility layout problemDiscrete Applied Mathematics, Vol. 157, No. 1An Exact Approach to the One-Dimensional Facility Layout ProblemAndré R. S. Amaral, 1 August 2008 | Operations Research, Vol. 56, No. 4Death Penalty Abolition and the Ratification of the Second Optional ProtocolSSRN Electronic JournalApplications of Set Covering, Set Packing and Set Partitioning Models: A SurveyA heuristic procedure for the single-row facility layout problemEuropean Journal of Operational Research, Vol. 87, No. 1Deux problèmes d'affectation non linéaires29 March 2011 | RAIRO - Operations Research, Vol. 16, No. 3The Layout of Divisible Activities on the Line9 July 2007 | A I I E Transactions, Vol. 10, No. 1On Solving A One-Dimensional Space Allocation Problem With Integer Programming25 May 2016 | INFOR: Information Systems and Operational Research, Vol. 14, No. 2A Minimax Layout Problem on the Line Involving Distances between Classes of Objects9 July 2007 | A I I E Transactions, Vol. 6, No. 3 Volume 19, Issue 1January-February 1971Pages 1-256 Article Information Metrics Information Published Online:February 01, 1971 © 1971 INFORMSCite asDonald M. Simmons, (1971) Technical Note—A Further Note on One-Dimensional Space Allocation. Operations Research 19(1):249-249. https://doi.org/10.1287/opre.19.1.249 PDF download

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.

Differential evolution is an efficient evolutionary optimization paradigm that has shown a good ability to solve a variety of practical problems, including combinatorial optimization ones. Single row facility layout problem is an NP-hard permutation problem often found in facility design, factory construction, production optimization, and other areas. Real-world problems can be cast as large single row facility location problem instances with different high-level properties and efficient algorithms that can solve them efficiently are needed. In this work, the differential evolution is used to solve the single row facility location problem and the ability of three different variants of the algorithm to evolve solutions to various problem instances is studied.

In this paper, an artificial immune system (AIS) algorithm is proposed to solve single row facility layout problem (SRFLP) for obtaining a best layout design of machines, which simultaneously minimises the multiple objectives. The multi-product environment with multiple objectives is considered in this work and it is a non-polynomial hard problem too. Total number of machines in the layout, total flow distance of products, total length of the flow line and total material handling cost are considered as objectives. Four problems are taken from Lenin et al. (2018) and four problems are randomly generated to obtain the best layout using AIS. The reduction in objective values is good by the proposed AIS algorithm compared with Lenin et al. (2018). In addition, the computational time for all the eight problems by the proposed AIS method is less compared with Lenin et al. (2018).

The Algebraic Differential Evolution for Permutations (ADEP) has been recently proposed as an effective evolutionary algorithm for permutation-based optimization problems. ADEP is built upon a framework that exploits the rich algebraic structure of the permutations search space. In this paper we further explore the abilities of ADEP by presenting an implementation for the Single Row Facility Layout Problem (SRFLP): a permutation problem with interesting real-world applications ranging from designing the layouts of machines in certain manufacturing systems to optimally arranging rooms in hospitals. An experimental investigation was conducted on a set of commonly adopted benchmarks and different settings ADEP were compared among them and with respect to the other methods in the literature. Interestingly, the experimental results confirm the validity of ADEP by showing its competitiveness with respect to the state-of-the-art results for the SRFLP.

Single-Row Facility Layout Problem (SRFLP) is a special class of facility layout problems, consists of finding an optimal linear placement of rectangular facilities with varying dimensions on a straight line. In this research, we first present a theorem to find the optimal solution of a special case of SRFLP. The results obtained by this theorem are very useful in reducing the computational efforts when, later on, a new algorithm based on tabu search is presented for SRFLP. Computational results of the proposed algorithm on benchmark problems show the efficiency of the algorithm compared to the other heuristics. The proposed algorithm can easily find near-optimal solutions in less than one minute for instances consist of 200 departments. However, the largest instances reported to be solved by the other methods had only 80 departments and took more than 10 hours to reach the solution.

The single row facility layout is the NP-Hard problem of arranging facilities with given lengths on a line, so as to minimize the weighted sum of the distances between all pairs of facilities. Owing to its computational complexity, researchers have developed several heuristics to obtain good quality solutions. In this paper, we present a genetic algorithm called GENALGO to solve large single row facility layout problem instances. Our algorithm uses standard genetic operators and periodically improves the fitness of all individuals. Our computational experiments show that our genetic algorithm yields high quality solutions in spite of starting with an initial population that is randomly generated. Our algorithm improves the previously best known solutions for the 19 instances of 58 benchmark instances and is competitive for most of the remaining ones.

The Single-Row Facility Layout Problem (SRFLP) is a well-known combinatorial optimization problem. The objective of SRFLP is to find out the arrangement of facilities with given lengths on a line so that the weighted sum of the distances between all pairs of facilities is minimized. This problem is known to be NP-hard. Hence, a population-based improvement heuristic algorithm with local search is presented in this article to solve SRFLP. The proposed algorithm works well also for the Single-Row Equidistant Facility Layout Problem (SREFLP), where the length of each facility is equal. The computational efficiency of the proposed algorithm is checked with the instances of sizes ranging from 5 to 300 available in the literature for SRFLP and SREFLP. The obtained results are compared to those from different state-of-the-art algorithms. The proposed algorithm achieves best known solutions to date for every instance considered in this article in reasonable computational time.

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.

This paper presents a spreadsheet-based decision support system (DSS) for any parameter optimization problem, in the small- and medium-sized enterprises to help the managers to make better decisions. Microsoft Excel is used as a DSS development platform. The DSS application requires the quality characteristics and the level of parameters affecting the problem. The proposed system considers three multi-criteria decision-making methods: TOPSIS, VIKOR and GRA. These methods are integrated into the Taguchi method to convert the multi-response optimization problem to a single-response problem. The DSS suggests proper Taguchi experimental designs and provides the decision maker with an opportunity to use different metrics and to validate the experimental results. Several issues and an application are provided for illustrative purposes. The proposed DSS is tested on a case study (the performance of the mixed integer programming (MIP) formulation solver) and the results highlight that the system is capable of offering satisfactory outcomes. Using such a quick and flexible DSS might help to reduce the daily workload of the decision makers. The different metrics used for the response variables which results with the different parameter combination. Using the optimal parameter combination of TOPSIS (come to the fore in case MinBest metric used), the MIP formulation solver gives the best integer objective function value of 609 and a GAP value of 1.93%, both of which are less than the values obtained using the other methods. Using the optimal parameter combination of GRA (come to the fore in case OptBest metric used), the MIP formulation gives a best integer objective function value of 632 and a GAP value of 6.52%, both of which are less than the values obtained by using the other methods.

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