Cell Formation Problem Research Articles

Agent-based dynamic part family formation for cellular manufacturing applications

One of the main critique on cellular manufacturing and its algorithms is their inability to handle dynamics events, especially dynamic changes in part spectrum. Unfortunately, there are not many efforts in the literature to overcome this problem. Agent oriented computing provides a marvellous opportunity to handle dynamic problems and to provide effective solutions, if carefully and intelligently implemented. In this paper, we have proposed a novel agent-based clustering algorithm for part family formation in cellular manufacturing by considering dynamic demand changes. However, it is not easy to directly compare the performance of the proposed algorithm with the literature results as there is no benchmark for dynamic cell formation problems. We attempt to compare the performance of the present algorithm on static test problems by dynamically introducing parts in these data-sets to our algorithm. Many results have been presented on these static data-sets by utilising several heuristics, meta-heuristics and optimisation-based algorithms. Although the proposed algorithm is not an optimisation-based algorithm and its operation is directed to handle dynamic changes in the problem domain through negotiation, we have shown that it has ability to provide very good results which are comparable to the best known solutions.

A novel discrete particle swarm optimization algorithm for the manufacturing cell formation problem

The manufacturing cell formation problem, with the aim of grouping parts into families and machines into cells, is considered with the objective of maximizing grouping efficacy. A new solution approach based on the particle swarm optimization (PSO) algorithm is presented for the problem. Unlike the original PSO algorithm which works with arithmetic operators and scalars, the new algorithm uses group-based operators, in place of arithmetic operators, in the body of the updating equations analogous to those of the classical PSO equations (given the fact that the cell formation problem is essentially a grouping problem, all operators in the new algorithm work with constructed cells (groups) rather than parts/machines (objects), isolatedly). We benchmark a set of 40 test problem instances from previous researches and do comparisons between the new algorithm and existing algorithms. We also compare the performance of our algorithm when it is hybridized with a local search module. Our computations reveal that the proposed algorithm performs well on all test problems, exceeding or matching the best solution’s quality presented in the literature.

Comparison of visualization of optimal clustering using self-organizing map and growing hierarchical self-organizing map in cellular manufacturing system

The present research deals with the cell formation problem (CFP) of cellular manufacturing system which is a NP-hard problem thus, the development of optimum machine-part cell formation algorithms has always been the primary attraction in the design of cellular manufacturing system. In this proposed work, the self-organizing map (SOM) approach has been used which is able to project data from a high-dimensional space to a low-dimensional space so it is considered a visualized approach for explaining a complicated CFP data set. However, for a large data set with a high dimensionality, a traditional flat SOM seems difficult to further explain the concepts inside the clusters. We propose one such possible solution for a large CFP data set by using the SOM in a hierarchical manner known as growing hierarchical self-organizing map (GHSOM). In the present work, the two novel contributions using GHSOM are: the choice of optimum architecture through the minimum pattern units extracted at layer 1 for the respective threshold values and selection. Furthermore, the experimental results clearly indicated that the machine-part visual clustering using GHSOM can be successfully applied in identifying a cohesive set of part family that is processed by a machine group. Computational experience specifically with the proposed GHSOM algorithm, on a set of 15 CFP problems from the literature, has shown that it performs remarkably well. The GHSOM algorithm obtained solutions that are at least as good as the ones found the literature. For 75% of the cell formation problems, the GHSOM algorithm improved the goodness of cell formation through GTE performance measure using SOM as well as best one from the literature, in some cases by as much as more than 12.81% (GTE). Thus, comparing the results of the experiment in this paper with the SOM and GHSOM using the paired t-test it has been revealed that the GHSOM approach performed better than the SOM approach so far the group technology efficiency (GTE) measures of performance of the goodness of cell formation is concerned.

Some clarifications on the use of Mahalanobis distance for the machine-part cell formation problem

In this paper, the clarifications regarding the usage of Mahalanobis distance (MD) for the machine-part cell formation (MPCF) are demonstrated. Perhaps, for the first time, part families are created using the correlation matrix derived from the covariance matrix of the given incidence matrix. The proposed MD-based method is compared with the existing popular methods for MPCF using the benchmark data sets from the literature. Also, in the present work, the procedure for calculation of MD for the purpose of machine-part cell formation in the event of high correlations is explained. The comparative performance analysis reveals that the grouping efficacy of the proposed MD-based method is at par or better when compared with the other popular algorithms available in the literature.

Manufacturing and Fractional Cell Formation Using a New Binary Digit Grouping Algorithm with a Pwavroid Solution Explorer Toolkit

A new algorithm is presented in order to search for the optimal solution of the manufacturing and fractional cell formation problem. In addition, this paper introduces a new toolkit, which is used to search for the various candidate solutions in a periodic and a waving (diversified) manner. The toolkit consists of 15 tools that play a major role in speeding up the obtainment of the final solution as well as in increasing its efficiency. The application of the binary digit grouping algorithm leads to the creation of manufacturing cells according to the concept of group technology. The nonzero entries, which remain outside the manufacturing cells, are called exceptional elements. When a lot of such elements is obtained, an additional cell called fractional (or remainder) cell may be formed; the aim of which is to reduce their number. This algorithm was tested by using illustrative examples taken from the literature and succeeded to give better or at least similar results when compared to those of other well-known algorithms.

A dynamic programming approach to GA-based heuristic for multi-period CF problems

In this paper we have introduced a multi-period cell formation (CF) model which is more computationally challenging than the most comprehensive CF models in the literature. A dynamic programming (DP) based approach coupled with GA-based heuristic is proposed to solve the multi-period problem. Since, the introduced dynamic programming is general and can be applied to any GA-based heuristic with full rejuvenation cycles to solve the multi-period part of the model, we focused only on the DP approach in this paper but have explained the interface with the GA-based heuristic. Illustrative example has been provided that clarifies the application of DP-heuristic. The performance of the DP-heuristic has been evaluated against LINGO and multi period GA-based heuristic.

A MULTI STAGE HEURISTIC FOR MANUFACTURING CELL FORMATION

Cellular manufacturing (CM) is a modern manufacturi ng concept based on the Group technology (GT) philo sophy. CM enables a manufacturing unit to enhance its productivity subs tantially through improved utilization of resources . In Cellular manufacturing system design process the task of solving cell form ation problem (machine ‐component grouping) is the central issue. Cell formation problem is considered as complex one due to its combinatorial nature. Research interest is g rowing towards development of novel solution methodologies for the purpose of cell formation. Even though numerous ap proaches have been implemented by researchers for the task of machine- component grouping, the effectiveness of multi stag e solution procedures based on the integration of traditional and non-tra ditional optimization techniques needs to be invest igated adequately. This paper demonstrates the development and implementati on of a multi stage heuristic based on the integrat ion of traditional cluster analysis technique and non- traditional simulated a nnealing technique for standard cell formation. The proposed heuristic is tested using a number of binary and non-binary data sets and computational results are presented. Resul ts indicate that proposed heuristic is capable of generating promising qualit y solutions when compared with a few alternate cell forming approaches.

Pareto-optimal front of cell formation problem in group technology

The earliest approaches to the cell formation problem in group technology, dealing with a binary machine-part incidence matrix, were aimed only at minimizing the number of intercell moves (exceptional elements in the block-diagonalized matrix). Later on this goal was extended to simultaneous minimization of the numbers of exceptions and voids, and minimization of intercell moves and within-cell load variation, respectively. In this paper we design the first exact branch-and-bound algorithm to create a Pareto-optimal front for the bi-criterion cell formation problem.

Exact model for the cell formation problem

The cell formation problem (CFP) consists in an optimal grouping of the given machines and parts into cells, so that machines in every cell process as much as possible parts from this cell (intra-cell operations) and as less as possible parts from other cells (inter-cell operations). The grouping efficacy is the objective function for the CFP which simultaneously maximizes the number of intra-cell operations and minimizes the number of inter-cell operations. Currently there are no exact approaches (known to the authors) suggested for solving the CFP with the grouping efficacy objective. The only exact model which solves the CFP in a restricted formulation is due to Elbenani and Ferland (Cell formation problem solved exactly with the dinkelbach algorithm. Montreal. Quebec. CIRRELT-2012-07, 1–14, 2012). The restriction consists in fixing the number of production cells. The main difficulty of the CFP is the fractional objective function—the grouping efficacy. In this paper we address this issue for the CFP in its common formulation with a variable number of cells. Our computational experiments are made for the most popular set of 35 benchmark instances. For the 14 of these instances using CPLEX software we prove that the best known solutions are exact global optimums.

New bi-objective robust design-based utilisation towards dynamic cell formation problem with fuzzy random demands

Generally, one of the most important issues which cause a production system not to be an efficient one is unemployed capacities of both machines and workers. On the other hand, adaptive design’s most exploiting facilities are not practical for any cases (huge machines). Hence, sometimes manufacturing firms are in need of robust design. In this paper, a robust design is considered to configure cells in a dynamic cellular manufacturing system to overcome the onerous machine relocation costs. Most of researches on robust design are trying to reduce the number of facilities while, here, this idea is adopted accompanying with practical concepts of facility utilisation with new mathematical formulae. Then, a multi-objective mathematical model containing the minimisation of the inter-cell movements besides maximising the machine and worker utilisation is developed. Some other supplements are the following: (1) considering a cubic space representation for calculation of inter-cell movements and (2) fuzzy random nature of part demands. Above all, a new goal programming method named ‘percentage multi-choice goal programming’ (PMCGP) is innovated to solve the proposed multi-objective model. Finally, a comprehensive numerical example is generated randomly to verify the proposed model.

Sensitivity Analysis of Dynamic Cell Formation Problem through Meta-heuristic

In spite of many researches in literature investigating dynamic of cell formation (CF) problem, further research needs to be elaborated to assay hidden aspects of cellular manufacturing system (CMS), due to inherent complexity and uncertainty on optimizing this problem. In this paper, sensitivity analysis of modified self-adaptive differential evolution (MSDE) algorithm is proposed for basic parameters of CF problem, considering to the graphical representation supported by statistical analysis. Hence, a dynamic integer model of CF problem is first presented as the NP-hard problem. Then, the two basic test CF problems are introduced thereby the performance of MSDE algorithm assessed by diverse problems sizes through 140 runs from aspects of the average runtime of algorithm and the best local optimum objective function. Finally, statistical analysis is implemented on behavior of objective function values in order to validate our computational results graphically as well as statistically, giving some insights related to importance of CF parameters on designing CMS.

Generation of Block Diagonal forms Using Hierarchical Clustering for Cell Formation Problems

While cell formation (CF) problems have been studied for few decades, the purpose of this paper is to advance the solution technique using one classical approach, hierarchical cluster analysis (HCA). In the application of HCA, one technical challenge is to cluster both machines and parts simultaneously. In this paper, this challenge is addressed by quantifying the coupling between machines and parts in the clustering process. One feature of the proposed method is to generate block diagonal forms that show some intermediate sorting of machines and parts without specifying the structural criteria (e.g., the number of cells). Consequently, engineers can specify the structural criteria after inspecting the block diagonal forms instead of specifying them at the beginning. Some numerical examples from literature are used to examine and verify the proposed method.

A new mathematical approach to supporting group technology

This paper presents a mathematical approach which can be successfully applied in different group technology problems. The method is originated from formal concept analysis (FCA). We produce some particular extent partitions of a formal context which encodes the relationship between given technical objects and their attributes. We show how to define the part type notions and also how to solve the cell formation problem by means of these extent partitions. The main focus of the paper is a solution method for the determination of master parts. The method is based on notions defined by modal operators analogously to formal concepts and uses the extent partitions of the complementary context. It follows from the nature of the problem that several solutions can exist; a consistency measure is introduced in order to rank them.

Heuristics for predictive hoist scheduling problems

This paper presents a mathematical approach which can be successfully applied in different group technology problems. The method is originated from formal concept analysis (FCA). We produce some particular extent partitions of a formal context which encodes the relationship between given technical objects and their attributes. We show how to define the part type notions and also how to solve the cell formation problem by means of these extent partitions. The main focus of the paper is a solution method for the determination of master parts. The method is based on notions defined by modal operators analogously to formal concepts and uses the extent partitions of the complementary context. It follows from the nature of the problem that several solutions can exist; a consistency measure is introduced in order to rank them.

A Multi-period Cell Formation Model for Reconfigurable Manufacturing Systems

The effective design of a reconfigurable manufacturing system (RMS) exerts the need for a design approach to group the parts into families and determine the corresponding system configurations. A mixed integer programming model was developed to form simultaneously the part families and corresponding cell configurations in RMS in a dynamic production environment. A novel reconfiguration planning heuristic, responsible for determining the econfiguration plan on both machines and system levels between successive time periods, is introduced. The model was tested by solving a dynamic cell formation problem and it was able to find the optimal solution found in the literature. Also a numerical example is included to illustrate the proposed model and the reconfiguration planning heuristic.

Reconfigurable Dynamic Cellular Manufacturing System: A New Bi-Objective Mathematical Model

Dynamic Cell Formation Problem (DCFP) seeks to cope with variation in part mix and demands using machine relocation, replication, and removing; whilst from practical point of view it is too hard to move machines between cells or invest on machine replication. To cope with this deficiency, this paper addresses Reconfigurable Dynamic Cell Formation Problem (RDCFP) in which machine modification is conducted instead of their relocation or replication in order to enhance machine capabilities to process wider range of production tasks. In this regard, a mixed integer nonlinear mathematical model is proposed, which is NP-hard. To cope with the proposed model’s intractability, an Imperialist Competitive Algorithm (ICA) is developed, whose obtained results are compared with those of Genetic Algorithm’s (GA’s), showing superiority and outperformance of the developed ICA.

A VNS algorithm for a disassembly cell formation problem with demand variability

A disassembly cell formation problem with demand variability is addressed in this paper under a reconfigurable approach. The reconfigurable approach allows the cells to be rearranged periodically to deal with demand variability in a multi-period planning horizon. We present a first mathematical programming model for this new problem as well as a solution method based on the variable neighbourhood search (VNS) methodology. Computational results on a set of random instances show the convenience of the proposed algorithm to reach near optimal solutions in short computing times. When compared with the solutions found by CPLEX after 5 hrs of CPU time, on average our proposed algorithm obtained solutions improved by 7.96%. When our VNS solution is provided to CPLEX as the starting solution, these are improved by 2.75% on average. The comparison shows that our heuristic algorithms reach high quality solutions in very short computing times.

A discrete particle swarm optimisation approach for manufacturing cell formation

Manufacturers need to improve the efficiency and productivity of their production activities to meet fluctuating demand for customised products with shorter life-cycles. Cellular manufacturing is one of the important manufacturing philosophies to achieve manufacturing flexibility. In the past, many methods have been developed for cell formation problem using zero-one machine part incidence matrix but such an approach can hardly incorporate real life production factors resulting in inefficient cell design. In the proposed approach, similarity coefficient is determined using various real life production factors. A discrete particle swarm optimisation approach is adopted to form the cluster of machines through maximising similarity coefficient within the cell and minimising similarity coefficient between the different cells. The proposed approach is tested on benchmark problems of different size from open literature for its performance using group technology efficiency and system utilisation.

A Comparison of a Standard Genetic Algorithm with a Hybrid Genetic Algorithm Applied to Cell Formation Problem

Though there are a number of benefits associated with cellular manufacturing systems, its implementation (identification of part families and corresponding machine groups) for real life problems is still a challenging task. To handle the complexity of optimizing multiple objectives and larger size of the problem, most of the researchers in the past two decades or so have focused on developing genetic algorithm (GA) based techniques. Recently this trend has shifted from standard GA to hybrid GA (HGA) based approaches in the quest for greater effectiveness as far as convergence on to the optimum solution is concerned. In order to prove the point, that HGAs possess better convergence abilities than standard GAs, a methodology, initially based on standard GA and later on hybridized with a local search heuristic (LSH), has been developed during this research. Computational experience shows that HGA maintains its accuracy level with increase in problem size, whereas standard GA looses its effectiveness as the problem size grows.

Automatic clustering for generalised cell formation using a hybrid particle swarm optimisation

This paper considers the cell formation (CF) problem in which parts have alternative process routings and the number of machine cells is not known a priori. Very few studies address these two practical issues at the same time. This paper proposes an automatic clustering approach based on a hybrid particle swarm optimisation (PSO) algorithm that can automatically evolve the number and cluster centres of machine cells for a generalised CF problem. In the proposed approach, a solution representation, comprising an integer number and a set of real numbers, is adopted to encode the number of cells and machine cluster centres, respectively. Besides, a discrete PSO algorithm is utilised to search for the number of machine cells, and a continuous PSO algorithm is employed to perform machine clustering. Effectiveness of the proposed approach has been demonstrated for test problems selected from the literature and those generated in this study. The experimental results indicate that the proposed approach is capable of solving the generalised machine CF problem without predetermination of the number of cells.