This paper considers a multi criteria cell formation
problem in Cellular Manufacturing System (CMS). Minimizing the
number of voids and exceptional elements in cells simultaneously are
two proposed objective functions. This problem is an Np-hard
problem according to the literature, and therefore, we can-t find the
optimal solution by an exact method. In this paper we developed two
ant algorithms, Ant Colony Optimization (ACO) and Max-Min Ant
System (MMAS), based on Data Envelopment Analysis (DEA). Both
of them try to find the efficient solutions based on efficiency concept
in DEA. Each artificial ant is considered as a Decision Making Unit
(DMU). For each DMU we considered two inputs, the values of
objective functions, and one output, the value of one for all of them.
In order to evaluate performance of proposed methods we provided
an experimental design with some empirical problem in three
different sizes, small, medium and large. We defined three different
criteria that show which algorithm has the best performance.
[1] T. Ertay, and D. Ruan, "Data envelopment analysis based decision
model for optimal operator allocation in CMS," European Journal of
Operational Research, 2005, 164, 800-810.
[2] A. J. Ruiz-Torres, and F. J. Lo'pez, "Using the FDH formulation of
DEA to evaluate a multi-criteria problem in parallel machine
scheduling," Computers & Industrial Engineering, 2004, 47, 107-121.
[3] I. Mahdavi, B. F. Javadi, K. Alipour and J. Slomp, "Designing a new
mathematical model for cellular manufacturing system based on cell
utilization," Applied Mathematics and Computation, 2007, 190, 662-
670.
[4] I. Mahdavi, M. M. Paydar, M. Solimanpur and A. Heidarzade, "Genetic
algorithm approach for solving a cell formation problem in cellular
manufacturing," Expert Systems with Applications, 2009, 36, 6598-
6604.
[5] A. Charnes, W.W. Cooper, and E. Rhodes, "Measuring the efficiency of
decision making units," European Journal of Operation Research, 1978,
429-444.
[6] R. D. Banker, A. Charnes, and W.W. Cooper, "Some models for
estimating technical and scale inefficiencies in data envelopment
analysis," Management Science, 1984, 30, 1078-1092.
[7] M. R. Alirezaee and M. Afsharian, "A complete ranking of DMUs using
restrictions in DEA models," Applied Mathematics and Computation,
2007, 189, 1550-1559.
[8] M. Dorigo, G. Di Caro and L. M. Gamberdella, "Ant Algorithms for
Discrete Optimization," Artificial Life, MIT Press, 1999.
[1] T. Ertay, and D. Ruan, "Data envelopment analysis based decision
model for optimal operator allocation in CMS," European Journal of
Operational Research, 2005, 164, 800-810.
[2] A. J. Ruiz-Torres, and F. J. Lo'pez, "Using the FDH formulation of
DEA to evaluate a multi-criteria problem in parallel machine
scheduling," Computers & Industrial Engineering, 2004, 47, 107-121.
[3] I. Mahdavi, B. F. Javadi, K. Alipour and J. Slomp, "Designing a new
mathematical model for cellular manufacturing system based on cell
utilization," Applied Mathematics and Computation, 2007, 190, 662-
670.
[4] I. Mahdavi, M. M. Paydar, M. Solimanpur and A. Heidarzade, "Genetic
algorithm approach for solving a cell formation problem in cellular
manufacturing," Expert Systems with Applications, 2009, 36, 6598-
6604.
[5] A. Charnes, W.W. Cooper, and E. Rhodes, "Measuring the efficiency of
decision making units," European Journal of Operation Research, 1978,
429-444.
[6] R. D. Banker, A. Charnes, and W.W. Cooper, "Some models for
estimating technical and scale inefficiencies in data envelopment
analysis," Management Science, 1984, 30, 1078-1092.
[7] M. R. Alirezaee and M. Afsharian, "A complete ranking of DMUs using
restrictions in DEA models," Applied Mathematics and Computation,
2007, 189, 1550-1559.
[8] M. Dorigo, G. Di Caro and L. M. Gamberdella, "Ant Algorithms for
Discrete Optimization," Artificial Life, MIT Press, 1999.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:53575", author = "Hossein Ali Akbarpour and Fatemeh Dadkhah", title = "Two DEA Based Ant Algorithms for CMS Problems", abstract = "This paper considers a multi criteria cell formation
problem in Cellular Manufacturing System (CMS). Minimizing the
number of voids and exceptional elements in cells simultaneously are
two proposed objective functions. This problem is an Np-hard
problem according to the literature, and therefore, we can-t find the
optimal solution by an exact method. In this paper we developed two
ant algorithms, Ant Colony Optimization (ACO) and Max-Min Ant
System (MMAS), based on Data Envelopment Analysis (DEA). Both
of them try to find the efficient solutions based on efficiency concept
in DEA. Each artificial ant is considered as a Decision Making Unit
(DMU). For each DMU we considered two inputs, the values of
objective functions, and one output, the value of one for all of them.
In order to evaluate performance of proposed methods we provided
an experimental design with some empirical problem in three
different sizes, small, medium and large. We defined three different
criteria that show which algorithm has the best performance.", keywords = "Ant algorithm, Cellular manufacturing system, Data
envelopment analysis, Efficiency", volume = "6", number = "1", pages = "24-5", }