Abstract
The fiercely competitive business environment may require the manufacturing layouts to be modified across the entire planning horizon owing to addition or deletion of new/existing products, machines or processes. The existing layout may not be appropriate for the next time periods as product combination and part demand tend to vary under multi-time scenario. Also the increased awareness of environmental concerns and paucity of vital resources like electric energy has led organizations to rethink about their manufacturing strategies and design layouts which are both cost effective as well as environmentally sustainable. An appropriately planned layout not only helps in reduction of material handling distance but can also greatly contribute to enhancement of the energy efficiency of manufacturing systems and contribute to resource productivity and sustainable value creation. To address these issues in the facility layout design, this paper models a dynamic cellular facility layout problem incorporating the sustainability aspect by considering the minimization of net electric energy consumption along with material handling and rearrangement costs. The model presented in this work is a mixed integer non-linear program. The model aims to minimize the aggregated cost of overall material handling for both the inter and intra-cell movements simultaneously. Additionally the model also minimizes the net electrical energy consumption across the entire time horizon. Twenty five data sets corresponding to varying combinations of machines, time periods and cells have been taken from extant literature to validate the proposed model. LINGO 10 optimization software has been used to solve the proposed model. However, due to NP-Hard nature of cellular facility layout problem, the proposed model is computationally difficult to be solved in reasonable time using LINGO 10, particularly, for layouts pertaining to larger dimensions. To overcome these complexities, a meta-heuristic based on simulated annealing (SA) is also employed to solve the model. It is discerned from the experimental results that LINGO is not able to optimally solve the model whereas the SA optimally solves the model for larger dimensions as well in reasonable computational time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Alhourani, F., & Saxena, U. (2009). Factors affecting the implementation rates of energy and productivity recommendations in small and medium sized companies. Journal of Manufacturing Systems,28(1), 41–45.
Aljuneidi, T., & Bulgak, A. A. (2017). Designing a cellular manufacturing system featuring remanufacturing, recycling, and disposal options: A mathematical modeling approach. CIRP Journal of Manufacturing Science and Technology,19, 25–35.
Altuntas, S., Dereli, T., & Selim, H. (2013). Fuzzy weighted association rule based solution approaches to facility layout problem in cellular manufacturing system. International Journal of Industrial and Systems Engineering,15(3), 253–271.
Ariafar, S., & Ismail, N. (2009). An improved algorithm for layout design in cellular manufacturing systems. Journal of Manufacturing Systems,28(4), 132–139.
Balakrishnan, J., & Cheng, C. H. (2007). Multi-period planning and uncertainty issues in cellular manufacturing: A review and future directions. European Journal of Operational Research,177(1), 281–309.
Baykasoğlu, A., & Gindy, N. N. (2001). A simulated annealing algorithm for dynamic layout problem. Computers & Operations Research,28(14), 1403–1426.
Bayram, H., & Şahin, R. (2016). A comprehensive mathematical model for dynamic cellular manufacturing system design and linear programming embedded hybrid solution techniques. Computers & Industrial Engineering,91, 10–29.
Benjaafar, S. (2002). Modeling and analysis of congestion in the design of facility layouts. Management Science,48(5), 679–704.
Bougain, S., Gerhard, D., Nigischer, C., & Uĝurlu, S. (2015). Towards energy management in production planning software based on energy consumption as a planning resource. Procedia CIRP,26, 139–144.
Brown, J. R. (2015). A capacity constrained mathematical programming model for cellular manufacturing with exceptional elements. Journal of Manufacturing Systems,37, 227–232.
Dalfard, V. M. (2013). New mathematical model for problem of dynamic cell formation based on number and average length of intra and intercellular movements. Applied Mathematical Modelling,37(4), 1884–1896.
de Oliveria Gomes, V. E., de Oliveira Gomes, J., & Grote, K. H. (2013). Discrete event simulation inserted into Kaizen event to assess energy efficiency. Re-engineering manufacturing for sustainability (pp. 499–503). Singapore: Springer.
Duflou, J. R., Sutherland, J. W., Dornfeld, D., Herrmann, C., Jeswiet, J., Kara, S., et al. (2012). Towards energy and resource efficient manufacturing: A processes and systems approach. CIRP Annals-Manufacturing Technology,61(2), 587–609.
Feng, H., Da, W., Xi, L., Pan, E., & Xia, T. (2017). Solving the integrated cell formation and worker assignment problem using particle swarm optimization and linear programming. Computers & Industrial Engineering,110, 126–137.
Gupta, M., & Sharma, K. (1996). Environmental operations management: An opportunity for improvement. Production and Inventory Management Journal,37, 40–46.
Hu, S., Liu, F., He, Y., & Hu, T. (2012). An on-line approach for energy efficiency monitoring of machine tools. Journal of Cleaner Production,27, 133–140.
Iqbal, A., & Al-Ghamdi, K. A. (2018). Energy-efficient cellular manufacturing system: Eco-friendly revamping of machine shop configuration. Energy,163, 863–872.
Kao, Y., & Fu, S. C. (2006). An ant-based clustering algorithm for manufacturing cell design. The International Journal of Advanced Manufacturing Technology,28(11–12), 1182–1189.
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science,220(4598), 671–680.
Kumar, R., & Singh, S. P. (2018). Simulated annealing-based embedded meta-heuristic approach to solve bi-objective robust stochastic sustainable cellular layout. Global Journal of Flexible Systems Management,19(1), 69–93.
Kumar, R., Singh, S. P., & Lamba, K. (2018). Sustainable robust layout using big data approach: A key towards industry 4.0. Journal of Cleaner Production,204, 643–659.
Langer, T., Schlegel, A., Stoldt, J., & Putz, M. (2014). A model-based approach to energy-saving manufacturing control strategies. Procedia CIRP,15, 123–128.
Mahdavi, I., Aalaei, A., Paydar, M. M., & Solimanpur, M. (2012). A new mathematical model for integrating all incidence matrices in multi-dimensional cellular manufacturing system. Journal of Manufacturing Systems,31(2), 214–223.
May, G., Stahl, B., Taisch, M., & Kiritsis, D. (2017). Energy management in manufacturing: From literature review to a conceptual framework. Journal of Cleaner Production,167, 1464–1489.
McKendall, A. R., Jr., Shang, J., & Kuppusamy, S. (2006). Simulated annealing heuristics for the dynamic facility layout problem. Computers & Operations Research,33(8), 2431–2444.
Meller, R. D., & Bozer, Y. A. (1996). A new simulated annealing algorithm for the facility layout problem. International Journal of Production Research,34(6), 1675–1692.
Mohammadi, M., & Forghani, K. (2016). Designing cellular manufacturing systems considering S-shaped layout. Computers & Industrial Engineering,98, 221–236.
Moslemipour, G., & Lee, T. S. (2012). Intelligent design of a dynamic machine layout in uncertain environment of flexible manufacturing systems. Journal of Intelligent Manufacturing,23(5), 1849–1860.
Niakan, F., Baboli, A., Moyaux, T., & Botta-Genoulaz, V. (2016). A bi-objective model in sustainable dynamic cell formation problem with skill-based worker assignment. Journal of Manufacturing Systems,38, 46–62.
Olson, D. L., & Swenseth, S. R. (1987). A linear approximation for chance-constrained programming. Journal of the Operational Research Society,38(3), 261–267.
Rabbani, M., Farrokhi-Asl, H., Rafiei, H., & Khaleghi, R. (2017). Using metaheuristic algorithms to solve a dynamic cell formation problem with consideration of intra-cell layout design. Intelligent Decision Technologies,11(1), 109–126.
Rafiee, K., Rabbani, M., Rafiei, H., & Rahimi-Vahed, A. (2011). A new approach towards integrated cell formation and inventory lot sizing in an unreliable cellular manufacturing system. Applied Mathematical Modelling,35(4), 1810–1819.
Raoofpanah, H., Ghezavati, V., & Tavakkoli-Moghaddam, R. (2018). Solving a new robust green cellular manufacturing problem with environmental issues under uncertainty using Benders decomposition. Engineering Optimization,51, 1–22.
Safaei, N., Saidi-Mehrabad, M., & Jabal-Ameli, M. S. (2008). A hybrid simulated annealing for solving an extended model of dynamic cellular manufacturing system. European Journal of Operational Research,185(2), 563–592.
Selim, H. M., Askin, R. G., & Vakharia, A. J. (1998). Cell formation in group technology: Review, evaluation and directions for future research. Computers & Industrial Engineering,34(1), 3–20.
Shang, J. S. (1993). Multicriteria facility layout problem: An integrated approach. European Journal of Operational Research, 66(3), 291–304.
Singh, S. P., & Sharma, R. R. (2006). A review of different approaches to the facility layout problems. The International Journal of Advanced Manufacturing Technology,30(5–6), 425–433.
Singh, S. P., & Singh, V. K. (2011). Three-level AHP-based heuristic approach for a multi-objective facility layout problem. International Journal of Production Research,49(4), 1105–1125.
Solimanpur, M., & Jafari, A. (2008). Optimal solution for the two-dimensional facility layout problem using a branch-and-bound algorithm. Computers & Industrial Engineering,55(3), 606–619.
Tavakkoli-Moghaddam, R., Aryanezhad, M. B., Safaei, N., & Azaron, A. (2005). Solving a dynamic cell formation problem using metaheuristics. Applied Mathematics and Computation,170(2), 761–780.
Tavakkoli-Moghaddam, R., Javadian, N., Javadi, B., & Safaei, N. (2007). Design of a facility layout problem in cellular manufacturing systems with stochastic demands. Applied Mathematics and Computation,184(2), 721–728.
Tayal, A., Gunasekaran, A., Singh, S. P., Dubey, R., & Papadopoulos, T. (2017). Formulating and solving sustainable stochastic dynamic facility layout problem: A key to sustainable operations. Annals of Operations Research,253(1), 621–655.
Tayal, A., & Singh, S. P. (2017). Formulating multi-objective stochastic dynamic facility layout problem for disaster relief. Annals of Operations Research. https://doi.org/10.1007/s10479-017-2592-2.
Tompkins, J. A., White, J. A., Bozer, Y. A., & Tanchoco, J. M. A. (2010). Facilities planning. Hoboken: Wiley.
Urban, T. L. (1998). Solution procedures for the dynamic facility layout problem. Annals of Operations Research,76, 323–342.
Van Laarhoven, P. J., & Aarts, E. H. (1987). Simulated annealing. Simulated annealing: Theory and applications (pp. 7–15). Dordrecht: Springer.
Vikhorev, K., Greenough, R., & Brown, N. (2013). An advanced energy management framework to promote energy awareness. Journal of Cleaner Production,43, 103–112.
Wang, T. Y., Wu, K. B., & Liu, Y. W. (2001). A simulated annealing algorithm for facility layout problems under variable demand in cellular manufacturing systems. Computers in Industry,46(2), 181–188.
Wang, R., Zhao, H., Wu, Y., Wang, Y., Feng, X., & Liu, M. (2018). An industrial facility layout design method considering energy saving based on surplus rectangle fill algorithm. Energy,158, 1038–1051.
Wemmerlov, U., & Johnson, D. J. (1997). Cellular manufacturing at 46 user plants: Implementation experiences and performance improvements. International Journal of Production Research,35(1), 29–49.
Wu, X., Chu, C. H., Wang, Y., & Yan, W. (2007). A genetic algorithm for cellular manufacturing design and layout. European Journal of Operational Research,181(1), 156–167.
Yang, L., Deuse, J., & Jiang, P. (2013). Multiple-attribute decision-making approach for an energy-efficient facility layout design. The International Journal of Advanced Manufacturing Technology,66(5–8), 795–807.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendix: SA solutions for the proposed sustainable-DCFLP for datasets DS1–DS25
Appendix: SA solutions for the proposed sustainable-DCFLP for datasets DS1–DS25
T = 1 | T = 2 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
DS1 (OFV = 38,512) | ||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 1 | 3 | 5 | 2 | 4 | 1 | 3 | 5 | 2 | 4 |
Cell 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
Cell 2 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
T = 1 | T = 2 | T = 3 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS2 (OFV = 53,650) | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 5 | 4 | 1 | 3 | 2 | 5 | 4 | 1 | 3 | 2 | 5 | 4 | 1 | 3 | 2 |
Cell 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
Cell 2 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
T = 1 | T = 2 | T = 3 | T = 4 | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS3 (OFV = 71,137) | ||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 |
Cell 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 |
Cell 2 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
T = 1 | T = 2 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
DS4 (OFV = 67,789) | ||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 2 | 1 | 3 | 4 | 5 | 2 | 1 | 3 | 4 | 5 |
Cell 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 |
Cell 2 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
T = 1 | T = 2 | T = 3 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS5 (OFV = 88,222) | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 3 | 1 | 2 | 5 | 4 | 3 | 1 | 2 | 5 | 4 | 3 | 2 | 1 | 5 | 4 |
Cell 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
Cell 2 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
b | T = 1 | T = 2 | T = 3 | T = 4 | ||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS6 (OFV = 109,776) | ||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 | 4 | 1 | 3 | 5 | 2 | 5 | 1 | 3 | 4 | 2 |
Cell 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
Cell 2 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
T = 1 | T = 2 | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
DS7 (OFV = 130,395) | ||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 1 | 2 | 4 | 3 | 5 | 1 | 2 | 4 | 3 | 5 |
Cell 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 |
Cell 2 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
T = 1 | T = 2 | ||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS8 (OFV = 171,578) | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 4 | 5 | 3 | 2 | 1 | 4 | 5 | 3 | 2 | 1 | 4 | 2 | 3 | 5 | 1 |
Cell 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 |
Cell 2 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
T = 1 | T = 2 | T = 3 | T = 4 | |||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS9 (OFV = 232,990) | ||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 |
Machine | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 | 5 | 3 | 1 | 4 | 2 | 4 | 5 | 1 | 2 | 3 |
Cell 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
Cell 2 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS10 (OFV = 57,218) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 1 | 2 | 4 | 3 | 5 | 6 | 7 | 1 | 2 | 4 | 3 | 5 | 6 | 7 |
Cell 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
Cell 2 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS11 (OFV = 57,276) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 5 | 3 | 1 | 4 | 2 | 7 | 6 | 1 | 3 | 5 | 2 | 4 | 7 | 6 |
Cell 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 |
Cell 2 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
Cell 3 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS12 (OFV = 103,936) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 7 | 3 | 2 | 6 | 4 | 1 | 5 | 1 | 3 | 5 | 2 | 4 | 7 | 6 |
Cell 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
Cell 2 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS13 (OFV = 103,936) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 7 | 3 | 2 | 6 | 4 | 1 | 5 | 1 | 3 | 5 | 2 | 4 | 7 | 6 |
Cell 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
Cell 2 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
Cell 3 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS14 (OFV = 192,708) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 7 | 3 | 1 | 6 | 2 | 5 | 4 | 1 | 3 | 5 | 2 | 4 | 7 | 6 |
Cell 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 |
Cell 2 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
T = 1 | T = 2 | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS15 (OFV = 192,723) | ||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Machine | 1 | 3 | 5 | 2 | 4 | 7 | 6 | 1 | 3 | 5 | 2 | 4 | 7 | 6 |
Cell 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Cell 2 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
Cell 3 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS16 (OFV = 64,761) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 6 | 1 | 2 | 7 | 3 | 4 | 5 | 8 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS17 (OFV = 120,365) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 3 | 1 | 2 | 7 | 6 | 4 | 5 | 8 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS18 (OFV = 221,636) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 6 | 1 | 2 | 7 | 3 | 4 | 5 | 8 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
Cell 2 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS19 (OFV = 98,377) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 4 | 5 | 6 | 2 | 3 | 7 | 8 | 1 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
Cell 2 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS20 (OFV = 160,290) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 4 | 6 | 7 | 2 | 3 | 8 | 5 | 1 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
T = 1 | T = 2 | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
DS21 (OFV = 323,310) | ||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Machine | 4 | 6 | 7 | 2 | 3 | 8 | 5 | 1 | 4 | 6 | 5 | 2 | 3 | 7 | 8 | 1 |
Cell 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 |
Cell 2 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
DS22 (OFV = 293,560) | |||||||||||||||
T = 1 | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Machine | 3 | 2 | 15 | 14 | 13 | 4 | 5 | 10 | 11 | 12 | 1 | 6 | 7 | 8 | 9 |
Cell 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 |
Cell 2 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
Cell 3 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
T = 2 | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Machine | 13 | 11 | 10 | 2 | 9 | 14 | 12 | 7 | 5 | 4 | 15 | 6 | 8 | 3 | 1 |
Cell 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
Cell 3 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
T = 3 | |||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Machine | 1 | 5 | 9 | 11 | 12 | 2 | 6 | 7 | 10 | 15 | 3 | 4 | 8 | 13 | 14 |
Cell 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
Cell 3 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
DS23 (OFV = 405,414) | ||||||||||||||||||||
T = 1 | ||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Location | 1 | 9 | 19 | 8 | 16 | 5 | 20 | 12 | 2 | 18 | 13 | 4 | 10 | 6 | 11 | 7 | 17 | 14 | 15 | 3 |
Cell 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
Cell 2 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
Cell 3 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
Cell 4 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
T = 2 | ||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Location | 18 | 6 | 13 | 8 | 3 | 10 | 14 | 16 | 19 | 9 | 20 | 11 | 5 | 12 | 4 | 7 | 1 | 15 | 2 | 17 |
Cell 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
Cell 2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
Cell 3 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
Cell 4 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
T = 3 | ||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
Location | 5 | 10 | 1 | 11 | 6 | 15 | 20 | 19 | 3 | 18 | 7 | 17 | 8 | 4 | 12 | 9 | 16 | 14 | 13 | 2 |
Cell 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Cell 2 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
Cell 3 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 |
Cell 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
DS24 (OFV = 529,748) | |||||||||||||||||||||||||
T = 1 | |||||||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
Location | 13 | 14 | 20 | 21 | 22 | 12 | 15 | 19 | 23 | 24 | 11 | 16 | 18 | 17 | 25 | 10 | 7 | 5 | 3 | 2 | 9 | 8 | 6 | 4 | 1 |
Cell 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
Cell 2 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Cell 3 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
Cell 4 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
T = 2 | |||||||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
Location | 19 | 20 | 14 | 13 | 17 | 24 | 21 | 16 | 12 | 11 | 23 | 22 | 15 | 10 | 9 | 25 | 18 | 4 | 7 | 6 | 1 | 2 | 3 | 5 | 8 |
Cell 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 |
Cell 2 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 |
Cell 3 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Cell 4 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
T = 3 | |||||||||||||||||||||||||
Machine | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
Location | 10 | 12 | 25 | 23 | 21 | 9 | 8 | 24 | 22 | 20 | 7 | 13 | 14 | 16 | 19 | 3 | 11 | 6 | 15 | 17 | 2 | 1 | 4 | 5 | 18 |
Cell 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
Cell 2 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |
Cell 3 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Cell 4 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
DS25 (OFV = 627,062) | ||||||||||||||||||||||||||||||
T = 1 | ||||||||||||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Machine | 5 | 4 | 2 | 3 | 19 | 20 | 22 | 24 | 26 | 23 | 6 | 7 | 1 | 12 | 18 | 14 | 15 | 25 | 27 | 30 | 8 | 9 | 10 | 11 | 13 | 17 | 16 | 21 | 28 | 29 |
Cell 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
Cell 2 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
Cell 3 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
Cell 4 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
Cell 5 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
T = 2 | ||||||||||||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Machine | 24 | 25 | 21 | 19 | 16 | 14 | 12 | 1 | 4 | 2 | 27 | 29 | 26 | 20 | 17 | 13 | 11 | 9 | 8 | 3 | 28 | 23 | 22 | 30 | 18 | 15 | 10 | 7 | 6 | 5 |
Cell 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
Cell 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
Cell 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Cell 4 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
Cell 5 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
T = 3 | ||||||||||||||||||||||||||||||
Location | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 |
Machine | 24 | 26 | 25 | 21 | 22 | 23 | 5 | 2 | 1 | 3 | 28 | 27 | 20 | 19 | 15 | 13 | 11 | 9 | 7 | 4 | 29 | 30 | 18 | 17 | 16 | 14 | 12 | 10 | 8 | 6 |
Cell 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Cell 2 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 |
Cell 3 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
Cell 4 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
Cell 5 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
Rights and permissions
About this article
Cite this article
Lamba, K., Kumar, R., Mishra, S. et al. Sustainable dynamic cellular facility layout: a solution approach using simulated annealing-based meta-heuristic. Ann Oper Res 290, 5–26 (2020). https://doi.org/10.1007/s10479-019-03340-w
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-019-03340-w