A two-stage stochastic model for designing cellular manufacturing systems with simultaneous multiple processing routes and subcontracting

Document Type : Article


1 Department of Industrial Engineering & Management Systems, Amirkabir University of Technology, 424 Hafez Ave., 15916-34311 Tehran, Iran

2 Department of Industrial Engineering, Urmia University of Technology, Band Road, 57155-419 Urmia, West Azerbaijan, Iran.


In recent decades, many researchers have studied the cellular manufacturing system with consideration of various issues such as scheduling, production planning, layout, reliability, etc. However, limited research papers have investigated this problem in an uncertain environment. The present paper addresses a stochastic problem in cellular manufacturing systems considering simultaneous multiple routings and subcontracting. In the developed problem, each part can be simultaneously produced in multiple processing routes. It is also assumed that the unsatisfied part demands as a result of limited machine capacity or high manufacturing cost could be outsourced. A two-stage stochastic programming approach is employed to take the uncertainty into consideration and to formulate the problem. The objective function is to minimize the summation of production, subcontracting, material handling, and machine idleness costs. A sample average approximation method is applied as a solution method. Also, for further illustration of the problem, a numerical example is solved and sensitivity analyses are conducted. Finally, through some numerical examples extracted from related literature, the advantages of constructing a stochastic optimization model for the problem are demonstrated.


Main Subjects

1. Wemmerlov, U. and Hyer, N. \Procedures for the part
family/machine group identi cation problem in cellular
manufacture", Journal of Operations Management,
6, pp. 125-147 (1986).
2. Solimanpur, M., Vrat, P., and Shankar, R. \A multiobjective
genetic algorithm approach to the design of
cellular manufacturing systems", International Journal
of Production Research, 42, pp. 1419-1441 (2004).
3. Forghani, K., Mohammadi, M., and Ghezavati, V. \Integrated
cell formation and layout problem considering
multi-row machine arrangement and continuous cell
layout with aisle distance", The International Journal
of Advanced Manufacturing Technology, 78, pp. 687-
705 (2015).
4. Wu, T., Chung, S., and Chang, C. \Hybrid simulated
annealing algorithm with mutation operator to the cell
formation problem with alternative process routings",
Expert Systems with Applications, 36, pp. 3652-3661
5. Kao, Y. and Lin, C. \A PSO-based approach to cell
formation problems with alternative process routings",
International Journal of Production Research, 50, pp.
4075-4089 (2012).
6. Arkat, J., Abdollahzadeh, H., and Ghahve, H. \A
new branch and bound algorithm for cell formation
problem", Applied Mathematical Modelling, 36, pp.
5091-5100 (2012).
7. Boutsinas, B. \Machine-part cell formation using biclustering",
European Journal of Operational Research,
230, pp. 563-572 (2013).
8. Wu, X., Chu, Ch-H., Wang, Y., and Yue, D. \Genetic
algorithms for integrating cell formation with machine
layout and scheduling", Computers and Industrial
Engineering, 53, pp. 277-289 (2007).
9. Krishnan, K., Mirzaei, S., Venkatasamy, V., and Pillai,
V. \A comprehensive approach to facility layout design
and cell formation", International Journal of Advanced
Manufacturing Technology, 59, pp. 737-753 (2012).
10. Chang, C., Wu, T., and Wu, C. \An ecient approach
to determine cell formation, cell layout and intracellular
machine sequence in cellular manufacturing
systems", Computers and Industrial Engineering, 66,
pp. 438-450 (2013).
11. Mohammadi, M. and Forghani, K. \A novel approach
for considering layout problem in cellular manufacturing
systems with alternative processing routings
and subcontracting approach", Applied Mathematical
Modelling, 38, pp. 3624-3640 (2014).
12. Solimanpur, M., Vrat, P., and Shankar, R. \A heuristic
to minimize makespan of cell scheduling problem",
International Journal of Production Economics, 88,
pp. 231-241 (2004).
13. Elmi, A., Solimanpur, M., Topaloglu, S., and Elmi, A.
\A simulated annealing algorithm for the job shop cell
scheduling problem with intercellular moves and reentrant
parts", Computers and Industrial Engineering,
61, pp. 171-178 (2011).
14. Arkat, J., Farahani, M., and Ahmadizar, F. \Multiobjective
genetic algorithm for cell formation problem
considering cellular layout and operations scheduling",
International Journal of Computer Integrated
Manufacturing, 25, pp. 625-635 (2012).
15. Li, D., Meng, X., Li, M., and Tian, Y. \An ACObased
intercell scheduling approach for job shop cells
with multiple single processing machines and one batch
processing machine", Journal of Intelligent Manufacturing,
27, pp. 283-296 (2016).
16. Wang, T., Wu, K., and Liu, Y. \A simulated annealing
algorithm for facility layout problems under variable
demand in cellular manufacturing systems", Computers
in Industry, 46, pp. 181-188 (2001).
17. Jeon, G. and Leep, H. \Forming part families by
using genetic algorithm and designing machine cells
under demand changes", Computers and Operations
Research, 33, pp. 263-283 (2006).
M. Mahootchi et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2824{2837 2837
18. Tavakkoli-Moghaddam, R., Javadian, N., Javadi, B.,
and Safaei, N. \Design of a facility layout problem
in cellular manufacturing systems with stochastic demands",
Applied Mathematics and Computation, 184,
pp. 721-728 (2007).
19. Schaller, J. \Designing and redesigning cellular manufacturing
systems to handle demand changes", Computers
and Industrial Engineering, 53, pp. 478-490
20. Safaei, N., Saidi-Mehrabad, M., and Babakhani, M.
\Designing cellular manufacturing systems under dynamic
and uncertain conditions", Journal of Intelligent
Manufacturing, 18, pp. 383-399 (2007).
21. Arkan, F. and Gungor, Z. \Modeling of a manufacturing
cell design problem with fuzzy multi-objective
parametric programming", Mathematical and Computer
Modelling, 50, pp. 407-420 (2009).
22. Ghezavati, V. and Saidi-Mehrabad, M. \Designing integrated
cellular manufacturing systems with scheduling
considering stochastic processing time", International
Journal of Advanced Manufacturing Technology,
48, pp. 701-717 (2010).
23. Das, K. and Abdul-Kader, W. \Consideration of dynamic
changes in machine reliability and part demand:
a cellular manufacturing systems design model", International
Journal of Production Research, 49, pp. 2123-
2142 (2011).
24. Ghezavati, V. and Saidi-Mehrabad, M. \An ecient
hybrid self-learning method for stochastic cellular
manufacturing problem: A queuing-based analysis",
Expert Systems with Applications, 38, pp. 1326-1335
25. Rabbani, M., Jolai, F., Manavizadeh, N., Radmehr, F.,
and Javadi, B. \Solving a bi-objective cell formation
problem with stochastic production quantities by a
two-phase fuzzy linear programming approach", International
Journal of Advanced Manufacturing Technology,
58, pp. 709-722 (2012).
26. Forghani, K., Mohammadi, M., and Ghezavati, V.
\Designing robust layout in cellular manufacturing systems
with uncertain demands", International Journal
of Industrial Engineering Computations, 4, pp. 215-
226 (2013).
27. Heragu, S. and Chen, J. \Optimal solution of cellular
manufacturing system design: Benders' decomposition
approach", European Journal of Operational Research,
107, pp. 175-192 (1998).
28. Ruszczynski, A. and Shapiro, A. Handbooks in Operation
Research and Management Science: Stochastic
Programming, Elsevier, Amsterdam (2003).
29. Shapiro, A. and Homem-de-Mello, T. \On rate of convergence
of Monte Carlo approximations of stochastic
programs", SIAM Journal of Optimization, 11, pp. 70-
86 (2000).
30. Mak, W.K., Morton, D.P., and Wood, P.K. \Monte
Carlo bounding techniques for determining solution
quality in stochastic programs", Operations Research
Letters, 24, pp. 47-56 (1999).
31. Kazerooni, M., Luong, H., and Abhary, K. \A genetic
algorithm based cell design considering alternative
routing", International Journal of Computer Integrated
Manufacturing Systems, 10, pp. 93-107 (1997).
32. Ramabhatta, F.V. and Nagi, R. \An integrated formulation
of manufacturing cell formation with capacity
planning and multiple routings", Annals of Operations
Research, 77, pp. 79-95 (1998).
33. Yin, Y. and Yasuda, K. \Manufacturing cells' design in
consideration of various production factors", International
Journal of Production Research, 40, pp. 885-906
34. Chan, F.T.S., Lau, K.W., Chan, P.L.Y., and Choy,
K.L. \Two-stage approach for machine-part grouping
and cell layout problems", Robotics and Computer-
Integrated Manufacturing, 22, pp. 217-238 (2006).