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

Macro-approach of cell formation problem with consideration of machining sequence

Cellular Manufacturing System (CMS) which is based on the concept of Group Technology (GT) has been recognized as an efficient and effective way to improve the productivity in the factory. In recent years, there has been much effort done for continuing to improve CMS. Most researches concentrated on distinguishing the part families and machine cells either simultaneously or individually by considering of minimizing intercellular and intracellular part movements. However, fewer researches have studied the impact of the sequencing of machine cells. In light of this, the main aim of this present work is to study the impact of the sequencing of allocating the machine cells in minimizing intercellular part movement. The problem scope, which is also called as machine-part grouping problem (MPGP) together with the background of cell layout problem (CLP), has been identified. A mathematical model is formulated and part incidence matrix with operational sequence is often used. Since MPGP has been proved as an NP complete, genetic algorithm (GA) is employed as cell formation algorithms in solving this problem. © 2004 IEEE.published_or_final_versio

Designing Stochastic Cell Formation Problem Using Queuing Theory

This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts are optimized based on the mean waiting time. For solving exactly, the proposed model is linearized. Since the cell formation problem is NP-Hard, two algorithms based on genetic and modified particle swarm optimization (MPSO) algorithms are developed to solve the problem. For generating of initial solutions in these algorithms, a new heuristic method is developed, which always creates feasible solutions. Also, full factorial and Taguchi methods are used to set the crucial parameters in the solutions procedures. Numerical experiments are used to evaluate the performance of the proposed algorithms. The results of the study show that the proposed algorithms are capable of generating better quality solutions in much less time. Finally, a statistical method is used which confirmed that the MPSO algorithm generates higher quality solutions in comparison with the genetic algorithm (GA)

Cell formation problem - A Lagrangean relaxation to mathematical programming approach and a linear performance measure

Two topics in the part-machine cell formation problem are discussed: In the first part, a Lagrangean relaxation in a mathematical programming model is proposed to simultaneously set machines into groups and parts into families in a cellular manufacturing system. The objective of this model is to find the optimal number of cells while minimizing inter-cellular part moves and increasing utilization of machines within the cells. The method uses a 0-1 integer programming model. The Lagrangean relaxation relaxes the model through an iterative search. In the second part, we introduce a new performance measure and compare it to some known performance measures. The new measure preserved some important features of previous performance measures and overcomes a number of drawbacks. Both the measure and the model are applied to benchmark problems as well as randomly generated problems. The new measure and model are comparable to the existing models and measures

The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession

The traditional machine-part cell formation problem simultaneously clusters machines and parts in different production cells from a zero–one incidence matrix that describes the existing interactions between the elements. This manuscript explores a novel alternative for the well-known machine-part cell formation problem in which the incidence matrix is composed of non-binary values. The model is presented as multiple-ratio fractional programming with binary variables in quadratic terms. A simple reformulation is also implemented in the manuscript to express the model as a mixed-integer linear programming optimization problem. The performance of the proposed model is shown through two types of empirical experiments. In the first group of experiments, the model is tested with a set of randomized matrices, and its performance is compared to the one obtained with a standard greedy algorithm. These experiments showed that the proposed model achieves higher fitness values in all matrices considered than the greedy algorithm. In the second type of experiment, the optimization model is evaluated with a real-world problem belonging to Human Resource Management. The results obtained were in line with previous findings described in the literature about the case study