American Institute of Mathematical Sciences

Advanced
July  2016, 12(3): 907-930. doi: 10.3934/jimo.2016.12.907

Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management

Amin Aalaei 1, and  Hamid Davoudpour 1,

1. 

Department of Industrial Engineering & Management Systems , Amirkabir University of Technology, 424 Hafez Ave., P.O. Box 15875-4413, Tehran, Iran, Iran

Received  January 2015 Revised  April 2015 Published  September 2015

This paper presents a new mathematical model for integrating the virtual dynamic cellular manufacturing system into supply chain management with an extensive coverage of important manufacturing features. The considered model regards multi-plants and facility locations, multi-market allocation, multi-period planning horizons with demand and part-mix variation, machine and labor time-capacity, labor assignment, training and purchasing or selling of new machines for an increased level of plant capacity. The main constraints are market demand satisfaction in each period, machine and labor availability, production volume for each plant and the amounts allocated to each market. To validate and verify the proposed model is explained in terms of an industrial case from a typical equipment manufacturer. Some of the hard constraints of the proposed model are relaxed in order to obtain a lower bound on the objective function value. In fact, the number of machines and workers allocated to each cell are restricted to yield feasible solutions and tight upper bounds on the objective values for medium size instances in a shorter time. The relaxed model yields tight lower bounds for medium instances in a reasonable computational time. Furthermore, a Benders decomposition is developed for solving the upper bounding model.
Keywords: virtual dynamic cellular manufacturing system, supply chain management, Benders decomposition., Lower bound and upper bounding model.
Mathematics Subject Classification: Primary: 35C20, 35P20; Secondary: 93D1.
Citation: Amin Aalaei, Hamid Davoudpour. Two bounds for integrating the virtual dynamic cellular manufacturing problem into supply chain management. Journal of Industrial & Management Optimization, 2016, 12 (3) : 907-930. doi: 10.3934/jimo.2016.12.907
References:
[1]

A. Aalaei and H. Davoudpour, Designing a mathematical model for integrating dynamic cellular manufacturing into supply chain system, AIP Conf. Proc., 1499 (2012), 239-246. doi: 10.1063/1.4768994.  Google Scholar

[2]

A. Aalaei and H. Davoudpour, Revised multi-choice goal programming for incorporated dynamic virtual cellular manufacturing into supply chain management: A case study, Engineering Applications of Artificial Intelligence, in press, (2015). doi: 10.1016/j.engappai.2015.04.005.  Google Scholar

[3]

S. Ahkioon, A. A. Bulgak T. Bektas, Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration, European Journal of Operational Research, 192 (2009), 414-428. doi: 10.1016/j.ejor.2007.09.023.  Google Scholar

[4]

J. Balakrishnan and C. H. Cheng, Dynamic cellular manufacturing under multi-period planning horizons, Journal of Manufacturing Technology Management, 16 (2005), 516-530. Google Scholar

[5]

J. F. Benders, Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik, 4 (1962), 238-252. doi: 10.1007/BF01386316.  Google Scholar

[6]

H. M. Bidhandi, R. M. Yusuff, M. M. H. M. Ahmad and M. R. A. Bakar, Development of a new approach for deterministic supply chain network design, European Journal of Operational Research, 198 (2009), 121-128. Google Scholar

[7]

O. Çakιr, Benders decomposition applied to multi-commodity, multi-mode distribution planning, Expert Systems with Applications, 36 (2009), 8212-8217. Google Scholar

[8]

J. Chen and S. S. Heragu, Stepwise decomposition approaches for large scale cell formation problems, European Journal of Operational Research, 113 (1999), 64-79. doi: 10.1016/S0377-2217(97)00419-0.  Google Scholar

[9]

A. J. Conejo, E. Castillo, R. Minguez and R. Garcia-Bertrand, Decomposition Techniques in Mathematical Programming, Engineering and Science Applications, Springer, Berlin, 2006.  Google Scholar

[10]

F. Defersha and M. Chen, A comprehensive mathematical model for the design of cellular manufacturing systems, International Journal of Production Economics, 103 (2006), 767-783. doi: 10.1016/j.ijpe.2005.10.008.  Google Scholar

[11]

K. Dogan and M. Goetschalckx, A primal decomposition method for the integrated design of multi-period production-distribution systems, IIE Transactions, 31 (1999), 1027-1036. doi: 10.1080/07408179908969904.  Google Scholar

[12]

S. S. Heragu, Group technology and cellular manufacturing, IEEE Transactions of Systems, Man, and Cybernetics, 24 (1994), 203-215. doi: 10.1109/21.281420.  Google Scholar

[13]

S. S. Heragu and J. Chen, Optimal solution of cellular manufacturing system design: Benders' decomposition approach, European Journal of Operational Research, 107 (1998), 175-192. doi: 10.1016/S0377-2217(97)00256-7.  Google Scholar

[14]

S. E. Kesen, M. D. Toksari, Z. Güngr and E. Güner, Analyzing the behaviors of virtual cells (VCs) and traditional manufacturing systems: Ant colony optimization (ACO)-based metamodels, Computers and Operations Research, 36 (2009), 2275-2285. doi: 10.1016/j.cor.2008.09.002.  Google Scholar

[15]

H. Li and K. Womer, Optimizing the supply chain configuration for make-to-order manufacturing, European Journal of Operational Research, 221 (2012), 118-128. doi: 10.1016/j.ejor.2012.03.025.  Google Scholar

[16]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment, Computers and Mathematics with Applications, 60 (2010), 1014-1025. doi: 10.1016/j.camwa.2010.03.044.  Google Scholar

[17]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems, International Journal of Production Research, 49 (2011), 6517-6537. doi: 10.1080/00207543.2010.524902.  Google Scholar

[18]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system, Journal of Manufacturing Systems, 31 (2012), 214-223. doi: 10.1016/j.jmsy.2011.07.007.  Google Scholar

[19]

S. M. Mansouri, S. M. Moattar Husseini and S. T. Newman, A review of the modern approaches to multi-criteria cell design, International Journal of Production Research, 38 (2000), 1201-1218. doi: 10.1080/002075400189095.  Google Scholar

[20]

M. T. Melo, S. Nickel and F. Saldanha-da-Gama, Facility location and supply chain management, A review, European Journal of Operational Research, 196 (2009), 401-412. doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[21]

G. Nomden, J. Slomp and N. C. Suresh, Virtual manufacturing cells: A taxonomy of past research and identification of future research issues, International Journal of Flexible Manufacturing Systems, 17 (2005), 71-92. doi: 10.1007/s10696-006-8122-1.  Google Scholar

[22]

H. Osman and K. Demirli, A bilinear goal programming model and a modified Benders decomposition algorithm for supply chain reconfiguration and supplier selection, International Journal of Production Economics, 124 (2010), 97-105. doi: 10.1016/j.ijpe.2009.10.012.  Google Scholar

[23]

P. P. Rao and R. P. Mohanty, Impact of cellular manufacturing on supply chain management: Exploration of interrelationships between design issues, International Journal of Manufacturing Technology and Management, 5 (2003), 507-520. doi: 10.1504/IJMTM.2003.003706.  Google Scholar

[24]

M. Rheault, J. Drolet and G. Abdulnour, Physically reconfigurable virtual cells: A dynamic model for a highly dynamic environment, Computers & Industrial Engineering, 29 (1995), 221-225. doi: 10.1016/0360-8352(95)00075-C.  Google Scholar

[25]

L. K. Saxena and P. K. Jain, An integrated model of dynamic cellular manufacturing and supply chain system design, International Journal of Advance Manufacturing Technology, 62 (2012), 385-404. doi: 10.1007/s00170-011-3806-4.  Google Scholar

[26]

J. Schaller, Incorporating cellular manufacturing into supply chain design, International Journal of Production Research, 46 (2008), 4925-4945. doi: 10.1080/00207540701348761.  Google Scholar

[27]

D. Simchi-Levi, P. Kaminsky and R. Shankar, Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies, Irwin McGraw- Hill, 2007. Google Scholar

[28]

J. Slomp, B. V. Chowdary and N. C. Suresh, Design of virtual manufacturing cells: A mathematical programming approach, Robotics and Computer Integrated Manufacturing, 21 (2005), 273-288. doi: 10.1016/j.rcim.2004.11.001.  Google Scholar

[29]

S. Talluri and R. C. Baker, A multi-phase mathematical programming approach for effective supply chain design, European Journal of Operational Research, 141 (2002), 544-558. doi: 10.1016/S0377-2217(01)00277-6.  Google Scholar

[30]

H. Uster and H. Agrahari, A Benders decomposition approach for a distribution network design problem with consolidation and capacity considerations, Operational Research Letters, 39 (2011), 138-143. doi: 10.1016/j.orl.2011.02.003.  Google Scholar

[31]

U. Wemmerlov and N. L. Hyer, Cellular manufacturing in the U. S. industry: A survey of users, International Journal of Production Research, 27 (1989), 1511-1530. doi: 10.1080/00207548908942637.  Google Scholar

show all references

References:
[1]

A. Aalaei and H. Davoudpour, Designing a mathematical model for integrating dynamic cellular manufacturing into supply chain system, AIP Conf. Proc., 1499 (2012), 239-246. doi: 10.1063/1.4768994.  Google Scholar

[2]

A. Aalaei and H. Davoudpour, Revised multi-choice goal programming for incorporated dynamic virtual cellular manufacturing into supply chain management: A case study, Engineering Applications of Artificial Intelligence, in press, (2015). doi: 10.1016/j.engappai.2015.04.005.  Google Scholar

[3]

S. Ahkioon, A. A. Bulgak T. Bektas, Integrated cellular manufacturing systems design with production planning and dynamic system reconfiguration, European Journal of Operational Research, 192 (2009), 414-428. doi: 10.1016/j.ejor.2007.09.023.  Google Scholar

[4]

J. Balakrishnan and C. H. Cheng, Dynamic cellular manufacturing under multi-period planning horizons, Journal of Manufacturing Technology Management, 16 (2005), 516-530. Google Scholar

[5]

J. F. Benders, Partitioning procedures for solving mixed-variables programming problems, Numerische Mathematik, 4 (1962), 238-252. doi: 10.1007/BF01386316.  Google Scholar

[6]

H. M. Bidhandi, R. M. Yusuff, M. M. H. M. Ahmad and M. R. A. Bakar, Development of a new approach for deterministic supply chain network design, European Journal of Operational Research, 198 (2009), 121-128. Google Scholar

[7]

O. Çakιr, Benders decomposition applied to multi-commodity, multi-mode distribution planning, Expert Systems with Applications, 36 (2009), 8212-8217. Google Scholar

[8]

J. Chen and S. S. Heragu, Stepwise decomposition approaches for large scale cell formation problems, European Journal of Operational Research, 113 (1999), 64-79. doi: 10.1016/S0377-2217(97)00419-0.  Google Scholar

[9]

A. J. Conejo, E. Castillo, R. Minguez and R. Garcia-Bertrand, Decomposition Techniques in Mathematical Programming, Engineering and Science Applications, Springer, Berlin, 2006.  Google Scholar

[10]

F. Defersha and M. Chen, A comprehensive mathematical model for the design of cellular manufacturing systems, International Journal of Production Economics, 103 (2006), 767-783. doi: 10.1016/j.ijpe.2005.10.008.  Google Scholar

[11]

K. Dogan and M. Goetschalckx, A primal decomposition method for the integrated design of multi-period production-distribution systems, IIE Transactions, 31 (1999), 1027-1036. doi: 10.1080/07408179908969904.  Google Scholar

[12]

S. S. Heragu, Group technology and cellular manufacturing, IEEE Transactions of Systems, Man, and Cybernetics, 24 (1994), 203-215. doi: 10.1109/21.281420.  Google Scholar

[13]

S. S. Heragu and J. Chen, Optimal solution of cellular manufacturing system design: Benders' decomposition approach, European Journal of Operational Research, 107 (1998), 175-192. doi: 10.1016/S0377-2217(97)00256-7.  Google Scholar

[14]

S. E. Kesen, M. D. Toksari, Z. Güngr and E. Güner, Analyzing the behaviors of virtual cells (VCs) and traditional manufacturing systems: Ant colony optimization (ACO)-based metamodels, Computers and Operations Research, 36 (2009), 2275-2285. doi: 10.1016/j.cor.2008.09.002.  Google Scholar

[15]

H. Li and K. Womer, Optimizing the supply chain configuration for make-to-order manufacturing, European Journal of Operational Research, 221 (2012), 118-128. doi: 10.1016/j.ejor.2012.03.025.  Google Scholar

[16]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, Designing a mathematical model for dynamic cellular manufacturing systems considering production planning and worker assignment, Computers and Mathematics with Applications, 60 (2010), 1014-1025. doi: 10.1016/j.camwa.2010.03.044.  Google Scholar

[17]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, Multi-objective cell formation and production planning in dynamic virtual cellular manufacturing systems, International Journal of Production Research, 49 (2011), 6517-6537. doi: 10.1080/00207543.2010.524902.  Google Scholar

[18]

I. Mahdavi, A. Aalaei, M. M. Paydar and M. Solimanpur, A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system, Journal of Manufacturing Systems, 31 (2012), 214-223. doi: 10.1016/j.jmsy.2011.07.007.  Google Scholar

[19]

S. M. Mansouri, S. M. Moattar Husseini and S. T. Newman, A review of the modern approaches to multi-criteria cell design, International Journal of Production Research, 38 (2000), 1201-1218. doi: 10.1080/002075400189095.  Google Scholar

[20]

M. T. Melo, S. Nickel and F. Saldanha-da-Gama, Facility location and supply chain management, A review, European Journal of Operational Research, 196 (2009), 401-412. doi: 10.1016/j.ejor.2008.05.007.  Google Scholar

[21]

G. Nomden, J. Slomp and N. C. Suresh, Virtual manufacturing cells: A taxonomy of past research and identification of future research issues, International Journal of Flexible Manufacturing Systems, 17 (2005), 71-92. doi: 10.1007/s10696-006-8122-1.  Google Scholar

[22]

H. Osman and K. Demirli, A bilinear goal programming model and a modified Benders decomposition algorithm for supply chain reconfiguration and supplier selection, International Journal of Production Economics, 124 (2010), 97-105. doi: 10.1016/j.ijpe.2009.10.012.  Google Scholar

[23]

P. P. Rao and R. P. Mohanty, Impact of cellular manufacturing on supply chain management: Exploration of interrelationships between design issues, International Journal of Manufacturing Technology and Management, 5 (2003), 507-520. doi: 10.1504/IJMTM.2003.003706.  Google Scholar

[24]

M. Rheault, J. Drolet and G. Abdulnour, Physically reconfigurable virtual cells: A dynamic model for a highly dynamic environment, Computers & Industrial Engineering, 29 (1995), 221-225. doi: 10.1016/0360-8352(95)00075-C.  Google Scholar

[25]

L. K. Saxena and P. K. Jain, An integrated model of dynamic cellular manufacturing and supply chain system design, International Journal of Advance Manufacturing Technology, 62 (2012), 385-404. doi: 10.1007/s00170-011-3806-4.  Google Scholar

[26]

J. Schaller, Incorporating cellular manufacturing into supply chain design, International Journal of Production Research, 46 (2008), 4925-4945. doi: 10.1080/00207540701348761.  Google Scholar

[27]

D. Simchi-Levi, P. Kaminsky and R. Shankar, Designing and Managing the Supply Chain: Concepts, Strategies and Case Studies, Irwin McGraw- Hill, 2007. Google Scholar

[28]

J. Slomp, B. V. Chowdary and N. C. Suresh, Design of virtual manufacturing cells: A mathematical programming approach, Robotics and Computer Integrated Manufacturing, 21 (2005), 273-288. doi: 10.1016/j.rcim.2004.11.001.  Google Scholar

[29]

S. Talluri and R. C. Baker, A multi-phase mathematical programming approach for effective supply chain design, European Journal of Operational Research, 141 (2002), 544-558. doi: 10.1016/S0377-2217(01)00277-6.  Google Scholar

[30]

H. Uster and H. Agrahari, A Benders decomposition approach for a distribution network design problem with consolidation and capacity considerations, Operational Research Letters, 39 (2011), 138-143. doi: 10.1016/j.orl.2011.02.003.  Google Scholar

[31]

U. Wemmerlov and N. L. Hyer, Cellular manufacturing in the U. S. industry: A survey of users, International Journal of Production Research, 27 (1989), 1511-1530. doi: 10.1080/00207548908942637.  Google Scholar

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