Single Row Facility Layout Problem Research Articles

A thin-provisioned and functionalized memetic algorithm for the single row facility layout problem

The objective of single row facility layout problem (SRFLP) is to assemble a full permutation of facilities along a straight line so that the weighted sum of pairwise distances is minimized. This category of layout positioning problem was proven to be NP-hard. In this work, a thin-provisioned and functionalized memetic algorithm (TPFMA) for solving this problem is developed. The three main contributions of TPFMA are as follows: (i) a fixed population of four individuals equipped with different roles helps to remove redundancy and maintain the balance between exploitation and exploration; (ii) a pairwise precedences-based crossover contributes to the rapid identification of common good genes; and (iii) a specific probabilistic model assists in repairing infeasible solutions and restarting the population in a low-cost, efficient way. In particular, evaluations over 43 small instances show that this method successfully achieves the optimum solution but employs considerably less computing time than its competitors over quite a few examples. Moreover, TPFMA improves 21 previous best results out of the 40 most challenging large instances when running for the same amount of computing time. The results on other SRFLP instances with up to 1000 facilities suggest that TPFMA matches the best known values for the 40 benchmark instances out of the total 50 instances.

Solving the Single-Row Facility Layout Problem by K-Medoids Memetic Permutation Group

The single-row facility layout problem (SRFLP) is concerned with arranging facilities along a straight line so as to minimize the sum of the products of the flow costs and distances among all facility pairs. SRFLP has rich practical applications and is however NP-hard. In this article, we first investigate a dedicated symmetry-breaking approach based on the permutation group theory for reducing the solution space of SRFLP. Relevant symmetry properties are identified through the alternating group of the original solution space or the corresponding coordinate rotation space. Then, a memetic algorithm is proposed to explore promising search regions regarding the reduced solution space. The memetic algorithm employs a problem-specific crossover operator guided by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula> -medoids clustering technique to produce meaningful offspring solutions. The algorithm additionally uses a simulated annealing procedure to intensively exploit a given search region and a distance-and-quality-based population management strategy to ensure a reasonable diversity of the population. Experimental results on commonly used benchmark instances and newly introduced large-scale instances with sizes up to 2000 facilities show that the proposed algorithm competes favorably with state-of-the-art SRFLP algorithms. It attains all but one previous best known upper bounds (BKS) and discovers new upper bounds for 33 instances out of the 93 popular benchmark instances.

A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem

The dynamic single row facility layout problem (DSRFLP) is defined as the problem of arranging facilities along a straight line during a multi-period planning horizon with the objective of minimizing the sum of the material handling and rearrangement costs. The material handling cost is the sum of the products of the flow costs and center-to-center distances between facilities. In this paper, we focus on metaheuristic algorithms for this problem. The main contributions of the paper are three-fold. First, a variable neighborhood search (VNS) algorithm for the DSRFLP is proposed. The main version of VNS uses an innovative strategy to start the search from a solution obtained by constructing an instance of the single row facility layout problem (SRFLP) from a given instance of the DSRFLP and applying a heuristic algorithm for the former problem. Second, a fast local search (LS) procedure is developed. The innovations of this procedure are two-fold: (i) the fast insertion and swap neighborhood exploration techniques are adapted for the case of the dynamic version of the SRFLP; and (ii) to reduce the computational time, the swap operation is restricted on pairs of facilities of equal lengths. Provided the number of planning periods is a constant, the neighborhood exploration procedures for n facilities have only O(n2) time complexity. The superiority of these procedures over traditional LS techniques is also shown by performing numerical tests. Third, computational experiments on DSRFLP instances with up to 200 facilities and three or five planning periods are carried out to validate the effectiveness of the VNS approach. The proposed VNS heuristic is compared with the simulated annealing (SA) method which is the state of the art algorithm for the DSRFLP. Experiments show that VNS outperforms SA by a significant margin.

A modified squirrel search algorithm for solving facility layout problems

With the huge advance in artificial intelligence and the rapid development of intelligent swarm algorithms, the exploration of facility layout problem (FLP) with its non-deterministic polynomial-time (NP-Hard) nature has gained much more attention. The squirrel search algorithm is one of the swarm algorithms that is known for its effective gliding feature that provides cheap exploration of lengthy distances. In this work, Msqrl algorithm is presented as a modification of squirrel search algorithm to be capable of handling permutation-specific FLP. The modification is done by introducing two new operators: Msqrl-Exchange and Msqrl-Winter. It is used to investigate the effectiveness in finding acceptable solutions to variable-size, single-row FLPs in a fast and efficient manner. Tests included small and large benchmark instances for comparisons. Outcomes show that Msqrl was able to improved quite a few previously found solutions by acting efficiently and converging rapidly to solutions. It outperformed both semidefinite programming and cuckoo optimization in finding optimal solutions in an acceptable number of iterations and relatively small population sizes.

Solving the constrained Single-Row Facility Layout Problem with Integer Linear Programming

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.

A Thin-Provisioned and Functionalized Memetic Algorithm for the Single Row Facility Layout Problem

A Thin-Provisioned and Functionalized Memetic Algorithm for the Single Row Facility Layout Problem

Solving Multi-Objective Paired Single Row Facility Layout Problem Using Hybrid Variable Neighborhood Search

The footwear industry is distinguished by its manual assembly line and a high proportion of shared workstation configuration. This study focuses on a subset of the single row facility layout problem known as the paired single row facility layout problem. As one of type of single-row facility layout, the paired single row facility layout problem cannot be solved quickly. Further, different objectives also need to be considered in the decision-making process. Therefore, multi-objective approaches are proposed to minimize the penalty of material handler usage while maximizing the adjacency function based on each workstation's closeness rating. A Single Row Facility Layout is an NP-hard problem; this problem also belongs to the NP-hard problem class. As a result, we propose a hybrid method combining variable neighborhood search (VNS) and genetic algorithm (GA) to solve the problem of obtaining the optimal configuration of a multi-objective paired single-row assembly line. A heuristic approach was used to create the schematic representation solution. To obtain the neighborhood solutions, a hybrid VNSGA was used. The schematic representation solution employs crossover and variable neighborhood descent. Using the concept of VNS, the neighborhood was changed in each generation.

Optimizing 2-opt-based heuristics on GPU for solving the single-row facility layout problem

The optimization of most combinatorial problems is NP-hard, which can be solved by heuristic algorithms to obtain approximately optimal solutions, especially for large-scale problems. Many heuristic algorithms can apply the 2-opt local search to find better solutions. In complete 2-opt local search, every valid neighboring solutions of swapping mechanism will be compared, which is very time consuming especially when a sequential algorithm is adopted. Nowadays, graphic processing units (GPUs) have evolved into powerful and flexible parallel computation platforms that have been widely used to accelerate the solving of NP-hard problems. Therefore, in this study, we focus on how to use GPUs to solve the single-row facility layout problem (SRFLP) with the 2-opt-based simulated annealing (SA) heuristic algorithm. As far as we know, this study is the first to solve SRFLP by using a GPU. After analyzing the fitness function and the move gains calculation between parent and child solutions, we propose a prefix-sum formula table to eliminate a large amount of replicated computation. To calculate move gains for the 2-opt local search during each iteration, many GPU threads are created and they construct and lookup the table in parallel. According to experimental results, if the prefix-sum formula table is not adopted, the GPU version outperforms the sequential CPU counterpart with the best speedup of 123. However, if the table is used in the GPU version, the best speedup can reach up to 3208. Because the proposed parallelization approach with the prefix-sum formula table is based on the features of the 2-opt local search and the SRFLP fitness function, it can be applied to any 2-opt-based heuristic algorithm for solving SRFLP even though the SA algorithm is used in this study.

Mathematical formulation and hybrid meta-heuristic solution approaches for dynamic single row facility layout problem

In this study, for the first time, the classical single row facility layout problem is extended to its dynamic type by considering several planning periods. This new problem consists of two types of costs e.g. material handling cost and rearrangement cost of the departments at the beginning of each period. The problem is formulated by a mixed integer linear programming model. Because of the high complexity of the problem, two well-known meta-heuristic algorithms e.g. the GA and the SA are proposed to solve the problem. In addition, both of the algorithms are hybridized considering the restart and acceptance probability strategies. In order to study the performance of the proposed algorithms, 20 benchmark problems are generated randomly. Considering one of the generated benchmarks, the parameters of the algorithms are tuned by a typical method and final experiments are performed accordingly. The obtained results strongly prove the superiority of the SA hybridized by the restart strategy as it shows much better performance comparing to other proposed algorithms in more than 60% of the benchmarks.

An improved fireworks algorithm for the constrained single-row facility layout problem

The single-row facility layout problem (SRFLP) decides upon the arrangement of facilities in a straight row so as to minimise the material handling cost. Generally, this problem allows the placement of the facilities in any location in any order without any restriction, but some practical SRFLP cases are required to meet various types of constraints imposed on the placement of its facilities in the engineering of the placement of factory machinery and equipment. According to this new perspective, we studied the constrained SRFLP (cSRFLP) in this paper. In this problem, a few facilities need to be placed in certain positions or specified orders with or without the requirement to be located next to each other. To address this novel layout problem, related constraints are defined and classified, and novel mixed-integer programming models for the problem are formulated. Subsequently, the CPLEX software is employed to solve this problem. Then a constrained improved fireworks algorithm is presented, which is discretised to solve the considered cSRFLP. Our computational experiments demonstrate that the proposed algorithm performs better than the existing algorithms in solving the problem.

An Algorithm for Solving Generalized Single Row Facility Layout Problem

Layout design problem is to determine a suitable arrangement for the departments so that the total costs associated with the flow among departments become least. Single Row Facility Layout Problem, SRFLP, is one of the layout problems that have many practical applications. This problem and its specific scenarios are often used to model many of the raised issues in the field of facility location. SRFLP is an arrangement of n departments with a specified length in a straight line so that the sum of the weighted distances between the pairs of departments is minimized. This problem is NP-hard. In this paper, first, a lower bound for a special case of SRFLP is presented. Then, a general case of SRFLP is presented in which some new and real assumptions are added to generate more practical model. Then a lower bound, as well as an algorithm, is proposed for solving the model. Experimental results on some instances in literature show the efficiency of our algorithm.

Application of artificial immune system algorithm for simultaneous minimisation of multiple objectives in single row facility layout problems

Application of artificial immune system algorithm for simultaneous minimisation of multiple objectives in single row facility layout problems

Population-based improvement heuristic with local search for single-row facility layout problem

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.

Layout optimization of injection process by considering integrated resilience engineering: a fuzzy-DEA approach

ABSTRACT According to the impact of the layout design on the performance of high volumes production line, a single-row facility layout problem is considered in a process diagnosed as a bottleneck. In this regard, a discrete-event-simulation method is employed for modeling all possible layouts of an injection process. The results of the fuzzy simulation are imported to the output-oriented fuzzy data envelopment analysis (F-DEA) to rank different layouts as decision-making units. Then, the optimum layout is selected by considering the average waiting time and utility of resource as traditional key performance indicators, in addition to fault-tolerant, flexibility, and teamwork as resilience engineering (RE) factors. Also, the results are validated and verified by using some statistical tests. The sensitivity analysis is performed to find the most influential factor and weight of each factor. This is the first study to model the RE factors in the injection molding process by using the F-DEA method. Herein, a unique fuzzy mathematical-simulation model is tailored. Finally, the solution quality is pointed by a real case study in a refrigerator injection process of a home appliances company.

Application of Artificial Immune System Algorithm for Simultaneous Minimization of Multiple Objectives in Single Row Facility Layout Problems

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).

Mixed Integer Programming Formulations for Single Row Facility Layout Problems with Asymmetric Material Flow and Corridor Width

In both the research and industry studies, mixed integer programming (MIP) is often the default method for solving facility layout problems. While MIP models for the single row layout problem have existed since the 1970s, comprehensive computational research has not been performed since then. In this paper, four different MIP models for the single row facility layout problem with simultaneous asymmetric material flow and corridor width (dubbed SRFLP_AC) are developed based on the decision variable paradigm. We present the computational results and discuss the model efficacy in terms of solution quality and computational budget. Moreover, the performance of two disjunctive models, MIP1 and MIP2, with indicator constraints is also analyzed. Finally, we analyze the effect of the symmetry-breaking constraint and different non-overlapping constraints on the most promising model.

A GRASP algorithm for solving large-scale single row facility layout problems

The single-row facility layout problem (SRFLP) is an NP-hard problem, which consists of arranging facilities along a straight line in order to minimize the weighted sum of distances between all pairs of facilities. In this paper, an implementation of the Greedy Randomized Adaptive Search Procedure (GRASP) meta-heuristic is presented to solve large-scale instances of the problem. The novelty of the proposed implementation is that it is endowed with a diversification phase based on frequency memory. The algorithm was tested on 93 instances with sizes up to one thousand facilities. To date, in the literature, there is only one work, which has considered instances of such magnitude. Computational experiments demonstrate the efficiency of the proposed algorithm, which improved the best-known values for 29 out of 93 instances.

A Tailored Fuzzy Simulation Integrated with a Fuzzy DEA Method for a Resilient Facility Layout Problem: A Case Study of a Refrigerator Injection Process

Abstract When a process diagnosed as a bottleneck in a manufacturing system, we can improve its performance by redesigning the layout of facilities. In this study, the facilities are considered resilient for the first time, since due to resilience engineering principles the flexible and redundant facilities are considered in the production line beside the maintenance center with teamwork between its members. To encounter the proposed single-row facility layout problem, a unique fuzzy simulation and fuzzy mathematical model is tailored. In this regard, a discrete-event-simulation method is used to model all the possible layouts of an injection process. Then the results of the fuzzy simulation are imported to the fuzzy data envelopment analysis (F-DEA) to rank different layouts and find the optimal one. The criteria for this assessment are average waiting time (WT) and utility of resource (UR) as conventional key performance indicators (KPIs), in addition to fault tolerant, and flexibility as resilience engineering factors. Finally, the weights of the effective factors are obtained by sensitivity analysis. Also, implementing an integrated model in a real case study of a refrigerator injection process for a home appliance firm in Iran presents the solution quality.

A constrained single-row facility layout problem

The single-row facility layout problem (SRFLP) seeks the arrangement of given facilities along a straight row in such a way that the total material handling cost among the facilities is minimized. The SRFLP is studied till date as an unconstrained problem allowing the placement of the facilities in any location in any order without any restriction. However, a practical SRFLP instance may need to satisfy different types of constraints imposed on the placement of its facilities, e.g., the operation sequencing with precedence constraints in a process planning can be modeled as a SRFLP with ordering constraints. Such a SRFLP model, named as the constrained SRFLP (cSRFLP), is introduced here by instructing to place some facilities in fixed positions, and/or in specified orders with or without allowing the placement of other facilities in between two ordered facilities. Since it would be computationally too expensive for any search technique to satisfy such constraints, a permutation-based genetic algorithm (pGA), named as the constrained pGA (cpGA in short), is also proposed with some specially designed operators for exploring only feasible solutions of cSRFLP. In the numerical experimentation, investigating three case studies of the operation sequencing problem of process planning as cSRFLP instances, the cpGA found new sequences of operations with the same best-known objective value for the smaller-size case study, while improved the best-known solutions of the other two case studies of larger sizes. Further, transforming some large-size benchmark instances of SRFLP into cSRFLP, the cpGA found marginally inferior solutions than their best-known SRFLP solutions, which is obvious due to the constraints imposed in the transformed cSRFLP instances.

Solution for bi-objective single row facility layout problem using artificial bee colony algorithm

The single row facility layout problem (SRFLP) is concerned with the arrangements of machineries in a single line for processing multiple products. This arrangement is termed as linear machine sequence (lms). The aim of the proposed work is to design a best lms that simultaneously minimises the objectives: the total flow distance of the products (D); and the total length of the flow line (L) needed for accommodating the machineries in the shop floor. Consideration of more than one objective in a multi-product environment in bi-objective single row facility layout problem (BOSRFLP) is an NP-hard problem. Hence, artificial bee colony (ABC) algorithm is applied to identify the best lms. The effectiveness of the proposed algorithm is verified by solving the problems discussed in the literature. Maximum of 37.54% reduction in total flow distance and 9.31% reduction in total length of the flow line are achieved by the proposed method. [Revise 21 September 2017; Received 27 November 2016; Accepted on 29 December 2017]