Cell Formation Problem Research Articles

Assessing the number of cells for a cell formation problem

Cellular manufacturing design is concerned with the creation and operation of manufacturing cells to take the advantage of flexibility, efficient flow and high production rate. Cell formation problem (CFP) is the assignment of part types and machines to specific cells based on their similarity. Several exact and heuristic methods are provided in literature to solve the problem and test problems in literature are commonly used for comparison. This study presents a Clonal Selection Algorithm (CSA) to solve a classical CFP that outperforms current available heuristics in the literature. The number of cells may be critical in the environments where cell formation costs are high and singletons occur in a design. It is concluded that the CFP results should be assessed not only based on efficacy values but also the number of cells.

Machine cell formation: using genetic algorithm-based heuristic considering alternative route

In this paper, genetic algorithm-based heuristic is proposed to solve the cell formation problem. The proposed algorithm selects the optimum part route with certain set of machines before clustering the machine cell. A heuristic is applied within the genetic algorithm for assignment of parts to independent cell. Further, trade-off between part inter-cell movement and machine duplication is permitted to optimise the machine cell design. The proposed model simultaneously considers relevant production data such as production volume, alternative part process route, operation sequence and process time. Conventional optimisation method for the optimal cell formation problem requires significant amount of time and large memory space. Hence, a genetic algorithm-based heuristic method has been developed for solving the proposed model. To evaluate the computational performance of the proposed approach, the algorithm is tested on four benchmark problems collected from literature. The results approve the effectiveness of the proposed method in the manufacturing cell formation.

Constraint-driven exact algorithm for the manufacturing cell formation problem

This paper deals with the manufacturing cell formation (MCF) problem, which is based on group technology (GT) principles, by using a graph-theoretic model. Due to the exponential nature of the problem, various heuristics and meta-heuristics have been proposed to solve it. However, only few studies have attempted to develop exact algorithms. In this paper, we develop two BB Revised 10 March 2014; Accepted 3 August 2014]

Fuzzy and stochastic mathematical programming for optimisation of cell formation problems in random and uncertain states

Applying mathematical programming models to solve the cellular manufacturing problems is a challenging task as decision makers find it difficult to specify goals and constraints because some of the involved parameters cannot be estimated precisely. This study presents a modelling approach for design of a dynamic cellular manufacturing system with uncertain characteristics and parameters. It provides mathematical models for solving cell formation problems (CFPs) in three different conditions: 1) crisp state in which all parameters are known and fixed; 2) fuzzy state in which setup cost, outsourcing cost and capacity of machines are considered as fuzzy parameters; 3) stochastic state in which probability distributions are used to model the assumed randomness. The general algebraic modelling system (GAMS) software is used to solve all test problems by CPLEX solver. This is the first study that presents mathematical programming models for solving CMS problems in crisp, stochastic and fuzzy states.

A dynamic programming–enhanced simulated annealing algorithm for solving bi-objective cell formation problem with duplicate machines

Article history: Received June 10, 2014 Accepted October 22, 2014 Available online October 22 2014 Cell formation process is one of the first and the most important steps in designing cellular manufacturing systems. It consists of identifying part families according to the similarities in the design, shape, and presses of parts and dedicating machines to each part family based on the operations required by the parts. In this study, a hybrid method based on a combination of simulated annealing algorithm and dynamic programming was developed to solve a biobjective cell formation problem with duplicate machines. In the proposed hybrid method, each solution was represented as a permutation of parts, which is created by simulated annealing algorithm, and dynamic programming was used to partition this permutation into part families and determine the number of machines in each cell such that the total dissimilarity between the parts and the total machine investment cost are minimized. The performance of the algorithm was evaluated by performing numerical experiments in different sizes. Our computational experiments indicated that the results were very encouraging in terms of computational time and solution quality. Growing Science Ltd. All rights reserved. 5 © 201

Comparative study of Constructive and Improvement Algorithms for Cell Formation with Alternative Routings

This paper describes a comparison of genetic algorithm and state space search algorithm for simultaneous formation of manufacturing cells and selection of process plans for parts with alternative plans. Both algorithms perform two simultaneous decisions: selection of process plan for parts between several alternatives, and assignment of parts and required machines to manufacturing cells. For genetic algorithm, a chromosome represents an assignment of machines to cells, and fitness function defined as number of inter-cell transfer is used to select the part route alternative with minimal inter-cell movements. The space search algorithm is based on classification and ordering of machines and application of space search to recursively assign the most critical machines and parts to cells. Both algorithms have been studied with several decision making criteria: intercellular traffic, size of the machine cells, ratio of state space expansion, and so on. The results presented in the paper include inter-cell transfers and the cell size. Both algorithms have been applied to the same set of cell formation problems with alternate routings from literature and representative results are shown. Performance of both algorithms is evaluated with respect to the quality of the obtained solution (as compared with different algorithms on the same problem from literature). The conclusions from this experiment are presented at the end of the paper.

Identification of Bottleneck Elements in Cellular Manufacturing Problem

The cell formation problem which arises in cellular manufacturing can be formulated in graph theoretic terms. The input for a cellular manufacturing problem consists of a set X of m machines and a set Y of p parts and an m × p matrix A = (ai j), where ai j = 1 or 0 according as the part pj is processed on the machine mi. This data can be represented as a bipartite graph G with bipartition X, Y and mi is joined to pj if ai j = 1. Let G1, G2,. . ., Gk be nontrivial connected subgraphs of G such that V(G1), V(G2),. . ., V(Gk ) forms a partition of V(G). Then π = {G1, G2,. . ., Gk} is called a k-cell partition of G. Any edge of G with one end in Gi and the other end in Gj with i * j represents an intercellular movement of a part. The set V(Gi) is called a cell. Any part in a cell which is to be processed by a machine in another cell is called a bottleneck part and any machine which processes a part in another cell is called a bottleneck machine. In this paper we use graph theoretic techniques to develop an efficient algorithm for identifying bottleneck elements with respect to a given solution of the cellular manufacturing problem. If H is the subgraph of G induced by the set of all exceptional edges with respect to the cell partition π, then any vertex of H is a bottleneck element and its degree in H is the strength of the bottleneck elements. Thus the bottleneck elements of high strength identified by our algorithm are to be either duplicated if it is a machine or to be subcontracted if it is a part, in order to ensure a smooth flow in the manufacturing process.

Hybrid Genetic Algorithm for Machine-Component Cell Formation

This paper considers machine-component cell formation problem of cellular manufacturing system. Since this problem comes under combinatorial category, development of a meta-heuristic is a must. In this paper, a hybrid genetic algorithm is presented. Normally, in genetic algorithm, the initial population is generated by random assignment of genes in each of the chromosomes. In this paper, the initial population is created using ideal seed heuristic. The proposed algorithm is compared with four other algorithms using 28 problems from literature. Through a completed factorial experiment, it is observed that the proposed algorithm outperforms the other algorithms in terms of grouping efficiency as well as grouping efficacy.

Book review “Cell formation in industrial engineering: theory, algorithms and experiments” by Boris Goldengorin, Dmitry Krushinsky, Panos M. Pardalos

When I saw the title of the book, I thought of that as another sortie at bioinformatics by the operations research community. Indeed by googling “Cell formation” one gets within a lot of stuff on the biological cell processes. What a group of combinatorial optimization experts can do to advance a murky business of life developments? Yet by looking at the intro, I see the book is on “industrial cell formation”, which is a quite different business. It appears the cell formation problem (CFP) here belongs in a growing field of research related to the issues of partitioning a set of technology units in clusters that concentrate as many operations as possible within themselves so that those remaining in-between are minimized. I cannot help but bring inmymemories related to this “discovery”. That was exactly the problem posed before me by Arkady Gelman who unexpectedly entered my office in the Summer 1967 at which I, a fresh PhD in ComputationalMathematics, was trying to penetrate the mathematics of competitive equilibrium and fixed point theorems. This was the starting point of my lifelong addiction to cluster analysis research. Back then I formalized the Gelman’s problem as of finding a partition with the maximum within cluster summary similarities or, equivalently, the minimum between-cluster summary similarities. Jointly with my only collaborator of that time, late Volodia Kupershtokh (1945–2001), we came to the conclusion that the problem as is, at nonnegative similarities, has trivial solutions only. One way to go was to restrict ourselves with pre-specified cluster cardinalities at which we came up with what later was called Kernighan-Lin algorithm, and estimates that hold “almost always” ([1], Our first results: [2]). Another way tomove onwas foundwhenwe noticed that the problem

Integrated cell formation and layout problem considering multi-row machine arrangement and continuous cell layout with aisle distance

Cellular manufacturing is an important application of group technology and the cell formation process is one of the important steps in designing cellular manufacturing system. In recent years, researchers have noticed potential benefits when the layout problem is considered within the cell formation process. Nevertheless, there are not sufficient studies about consideration of real-life features in the cell formation and layout design process. In this paper, a new approach is presented to integrate the cell formation and its layout design. The proposed approach has three important design features not found in other papers. These design features are multi-row intra-cell layout (layout of machines within the cells), continuous inter-cell layout (layout of rectangular shape cells on the planar area), and aisle distance. The objective of the proposed approach is to form machine cells, find the layout of machine cells, and obtain the arrangement of machines within the cells such that the total material handling cost is minimized. In order to have a more accurate layout design, the material handling cost is calculated in terms of the actual position of machines within the cell. Due to the computational complexity of the proposed problem, a heuristic method is proposed to solve medium- and large-scale problems in a reasonable computational time. Three lower bounds are developed for the proposed integrated problem in which the tightest of them is chosen for evaluating the solution of the heuristic method. Finally, numerical examples adopted from the literature are solved to verify the performance of the proposed heuristic method and illustrate the advantages of the proposed integrated approach. The results indicated that the heuristic method is both effective and efficient in solving real-sized problems. The results also demonstrated that the proposed layout approach gives better layout design in comparison with the existing approaches.

Development of a cell formation heuristic by considering realistic data using principal component analysis and Taguchi’s method

Over the last four decades of research, numerous cell formation algorithms have been developed and tested, still this research remains of interest to this day. Appropriate manufacturing cells formation is the first step in designing a cellular manufacturing system. In cellular manufacturing, consideration to manufacturing flexibility and production- related data is vital for cell formation. The consideration to this realistic data makes cell formation problem very complex and tedious. It leads to the invention and implementation of highly advanced and complex cell formation methods. In this paper an effort has been made to develop a simple and easy to understand/implement manufacturing cell formation heuris- tic procedure with considerations to the number of production and manufacturing flexibility-related parameters. The heu- ristic minimizes inter-cellular movement cost/time. Further, the proposed heuristic is modified for the application of principal component analysis and Taguchi's method. Numerical example is explained to illustrate the approach. A refinement in the results is observed with adoption of prin- cipal component analysis and Taguchi's method.

An effective methodology for cell formation and intra-cell machine layout design in cellular manufacturing system using parts visit data and operation sequence data

Cellular manufacturing is an efficient approach for implementing the principles of Group Technology in a manufacturing environment. Most of the previous studies in CMS have focused mainly on cell formation problem. However, only few researches have discussed on CFP and CLP, simultaneously. In this paper, we present a new heuristic approach based on modified flow matrix which simultaneously considers cell formation, intracellular machine layout, exceptional elements and voids issues in the CMS design using sequence data and number of parts visit data between the machines. Above-mentioned data provide valuable information about the various jobs in a manufacturing system. The objective of our proposed approach is to group similar parts and corresponding different machines in same cells and additionally considering the sequence of machines, exceptional elements and voids. Moreover, our proposed approach considers inter-cell movement, backward movements, number of voids and number of operations. A new performance measure modified group technology efficacy is proposed for evaluating the performance of the proposed methodology. Two well-known benchmark problems from the literature are considered and results are compared with the existing methods. The results clearly demonstrated that our proposed approach outperforms the previously proposed methods.

Approaches to solve cell formation, machine layout and cell layout problem: A Review

Cell formation, machine layout and cell layout problems in cellular manufacturing system are NP-Complete optimization problems. Good cell formation & layout design in cellular manufacturing system is achieved by finding optimum or near-optimum solutions of these problems, which substantially reduces manufacturing cost and time. Many approaches have been advocated by researchers to obtain better cell formation & layout design. An attempt has been done in this paper to review such approaches based on heuristics, meta-heuristics, hybrid methods and exact solution methods developed by past researchers to solve these problems. The main objective of this review paper is to find out the effective and efficient approaches by comparing them based on performance criteria, their benefits and drawbacks in solving cellular manufacturing system problems and find out future research scope in this area.

Proposal for a decision support software for the design of cellular manufacturing systems with multiple routes

This study presents operational decision support software to efficiently solve cell formation problems with multiple routes. The software includes two revised algorithms that assist decision makers in choosing the best cellular layout. These revised algorithms are the multiobjective genetic algorithm that uses two different scalarization methods such as conic scalarization and weighted sum scalarization and the fuzzy c-means algorithm for problems with multiple routes. From these algorithms, the multiobjective genetic algorithm with conic scalarization has important advantages over many multiobjective approaches in the literature for being able to reach all efficient solutions for linear and nonlinear multiobjective models. These revised algorithms and the decision support software were tested on some data sets collected from an engine manufacturing plant and the literature. The test results showed that, in many cases, the revised multiobjective genetic algorithm with conic scalarization results in better performance than the revised fuzzy c-means algorithm and the methods used in the test problems for problems with multiobjective and multiple routes. Practitioners and researchers can use this operational decision support software and the multiobjective genetic algorithm with conic scalarization to obtain higher-quality cellular layout solutions compared with other software applications in the literature.

Multi-objective cell formation problem considering work-in-process minimization

This paper addresses designing a dynamic cellular manufacturing system which considers optimizing batch sizes for inter-cell moves in order to pursue fundamentals of Just-In-Time production philosophy. To do so, a bi-objective mixed-integer nonlinear programming model is proposed with two conflicting objective functions: minimizing sum of machine purchasing, operating, inter-cell moves, machine relocation, and machine transferring cost, and minimizing work-in-process (WIP) with regard to inter-cell batch sizes. Also, the best time to sell unused machines is obtained by calculating their salvage values. Finally, the proposed model is validated using numerical experiments and hence, the resulted WIP inventories are assessed through the conducted numerical experiments, and sensitivity analysis is provided with respect to three major parameters (machine purchasing cost, inter-cell material handling cost, and part demand) applied in the proposed model.

A Simulated Annealing Algorithm for Machine Cell Formation Under Uncertain Production Requirements

Due to customized products, shorter product life cycles, and unpredictable patterns of demand, the manufacturing industries are faced with stochastic production requirements. The production requirements (product mix and demand) may not be known exactly at the time of designing the manufacturing cell. It is likely that a set of possible production requirements (scenarios) with certain probabilities may be given at the design stage. Though a large number of research works on manufacturing cell have been reported, very few of them have considered random product mix constraint at the design stage. This paper presents a nonlinear mixed-integer mathematical model for the cell formation problem with the uncertainty of the product mix for a single period. The model incorporates real-life parameters such as alternate routing, operation sequence, duplicate machines, uncertain product mix, uncertain product demand, batch size, processing time, machine capacity, and various cost factors. The cost factors considered are machine amortization costs, operating costs, inter-cellular material handling costs, and intra-cellular material handling costs. A consultancy work is carried out for the proposed auto-components manufacturing industry to be located in the suburb of Chennai. In this paper, a solution methodology for best possible cell formation using simulated annealing algorithm is presented and the computational procedure has been illustrated for the case study undertaken.

A multi-objective mathematical model for cellular manufacturing systems design with probabilistic demand and machine reliability analysis

This paper presents a dynamic multi-objective mixed integer mathematical model for cell formation problem with probabilistic demand and machine reliability analysis, where the total system costs, machine underutilization cost, and maximum system failure rate over the planning time periods are to be minimized simultaneously. The total system cost objective function calculates machine operating, internal part production, intercellular material handling, and subcontracting costs. Since in this type of problems, objectives are in conflict with each other, so finding an ideal solution (a solution that satisfies all objectives simultaneously) is not possible. Therefore, this study uses the augmented e-constraint method (to solve small size problems) and a nondominated sorting genetic algorithm (NSGAII) (to solve large size problems) to find the Pareto optimal frontier that decision makers can select her/his preferred solution. Numerical examples will be solved to demonstrate the efficiency of the proposed algorithm.

APPLYING SIMULATED ANNEALING TO A GENERALIZED CELL FORMATION PROBLEM CONSIDERING ALTERNATIVE ROUTINGS AND MACHINE RELIABILITY

One of the most important steps in designing a cellular manufacturing system is cell formation which includes grouping the machines in cells and the parts as part families, so that the costs are minimized. Several aspects of the problem should be taken into account in cell formation; more specifically, machines and their reliability are among the most important issues that should be modelled correctly. Another important facet of a cellular manufacturing system is material handling cost consisting of inter-cellular and intra-cellular movement costs. In addition, setup cost may play a significant role in decision-making in many real world problems of cell formation. Obviously, cell formation cannot be completed without considering the demands for parts. Considering all these aspects of the problem in this research, a generalized model for solving cell formation problem is proposed. Exact methods, e.g., B&B, are cumbersome in solving such complex models for large-size problems. Therefore, in this paper, a modified version of simulated annealing algorithm is designed and numerical examples are provided to show that the proposed method is efficient and effective.

A Comparison between Two Metaheuristics Applied to the Cell Formation Problem with Alternative Routings

This work proposes a genetic algorithm for optimization of the cell formation problem with alternative routings. A series of test problems were generated and used to evaluate the performance of the proposed Genetic Algorithm and a Simulated Annealing algorithm as well. The novelty of the proposed work lies in the representation technique and the transformations that allow treating the original multidimensional problem as a two-dimensional one. That simplified the programming tasks and the resolution method.

A hybrid GA-AUGMECON method to solve a cubic cell formation problem considering different worker skills

Part quality and consequently customer satisfaction besides cost functions are two of the most important issues for any firm. Balancing between these two goals leads to full utilization from manufacturing resources. Formerly, in cubic cell formation problem, where a part on a machine can be processed by various workers, worker assignment was done just by minimizing inter-cell movement criterion; so, the workers assigned into the processing cell are mostly selected rather than outsider workers. But, it is rational for the ties to be broken by skills of different workers in performing a special part on the dedicated machine. In this paper, a bi-objective cubic cell formation is presented with two non-homogeneous objective functions in order to minimize the inter-cell movements and maximize a part quality index. Quality index for each part is represented through a cubic matrix containing integer values of 1–5 (representing very bad, bad, medium, well and very well), which qualifies the process of part on a specific machine by a specific worker. To solve the problem, a hybrid GA-augmented ε-constraint method (GA-AUGMEON) is developed to reduce time consuming difficulty of AUGMECON method. To validate the model and the GA-AUGMECON algorithm, some randomly generated examples in small and large size are solved.