Robust-fuzzy model for supplier selection under uncertainty: An application to the automobile industry

Document Type : Article


1 Department of Industrial Management, Shahid Beheshti University, Tehran, Iran

2 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

3 Department of Industrial Management, Tarbiat Modares University, Tehran, Iran


This paper proposes an innovative robust-fuzzy method for multi-objective, multi-period supplier selection problem under multiple uncertainties. This approach integrates robust optimization and fuzzy programming. Uncertain parameters are modeled as random variables that take value within a symmetrical interval. However, due to the complexity or ambiguity of some real world problems and specially the nature of some of the available input data, the length of interval is also highly uncertain. This ambiguity motivated us to present a new approach, which can be applicable to multiple uncertainties conditions. Thus, in our approach the half-length of these intervals is also represented by fuzzy membership function. We develop a model and a solution approach to select suppliers by considering risk. The proposed method is applied to a real case of supplier selection in automobile industry under uncertainty and ambiguity conditions. To verify the proposed model, we evaluated the results by simulation technique and compared values of objective function under different scenarios.


Main Subjects

1. Li, L. and Zabinsky, Z.B. \Incorporating uncertainty
in to a supplier selection problem", Int. J. Prod. Econ.,
134(2), pp. 344-356 (2011).
2. Nam, S.-H., Vitton, J., and Kurata, H. \Robust supply
base management: Determining the optimal number of
suppliers utilized by contractors", Int. J. Prod. Econ.,
134(2), pp. 333-343 (2011).
3. Hasani, A., Zegordi, S.H., and Nikbakhsh, E. \Robust
closed-loop supply chain network design for perishable
goods in agile manufacturing under uncertainty", Int.
J. Prod. Res., 50(16), pp. 1-21 (2011).
4. Liu, Y. and Peng, B. \Achieving robustness objectives
within a supply chain by means of reliability allocation",
In Proceedings of the 2009 International Symposium
on Web Information Systems and Applications
(WISA'09) Nanchang, P.R. China, pp. 210-213 (2009).
5. Amid, A., Ghodsypour, S.H., and O'Brien, C. \Fuzzy
multiobjective linear model for supplier selection in a
supply chain", Int. J. Prod. Econ., 104(2), pp. 394-407
6. Benton, W.C. \Quantity discount decision under conditions
of multiple items, multiple suppliers and resource
limitation", Int. J. Prod. Econ., 27(1991), pp.
1953-1961 (2006).
7. Ghodsypour, S.H. and O'Brien, C. \A decision support
system for reducing the number of suppliers and
managing the supplier partnership in A JIT/TQM
environment", The Proceeding of 3rd International
Symposium on Logistics, University of Padua, Italy
8. Ghodsypour, S.H. and O'Brien, C. \A decision support
system for supplier selection using an integrated
analytic hierarchy process and linear programming",
Int. J. Prod. Econ., 56-57(1-3), pp. 199-212 (1998).
9. Ghodsypour, S.H. and O'Brien, C. \The total cost
of logistics in supplier selection, under conditions
of multiple sourcing, multiple criteria and capacity
constraint", Int. J. Prod. Econ., 73(1), pp. 15-27
10. Basnet, C. and Leung, J.M.Y. \Inventory lot-sizing
with supplier selection", Comput. Oper. Res., 32(1),
pp. 1-14 (2005).
11. Ustun, O. and AktarDemirtas, E. \An integrated
multi-objective decision-making process for multiperiod
lot-sizing with supplier selection", Omega, 36,
pp. 509-521 (2008).
12. Mendoza, A. and Ventura, J.A. \Analytical models for
supplier selection and order quantity allocation", Appl.
Math. Model., 36, pp. 3826-3835 (2012).
13. Kumar, M., Vrat, P., and Shankar, R. \A fuzzy goal
programming approach for vendor selection problem in
a supply chain", Comput. Ind. Eng., 46(1), pp. 69-85
14. Chen, C.-T., Lin, C.-T., and Huang, S.-F. \A fuzzy
approach for supplier evaluation and selection in supply
chain management", Int. J. Prod. Econ., 102(2),
pp. 289-301 (2006).
15. Kilic, H.S. \An integrated approach for supplier selection
in multi-item/multi-supplier environment", Appl.
Math. Model., 37, pp. 7752-7763 (2013).
16. Nazari-Shirkohi, S., Shakouri, H., Javadi, B., and
Keramati, A. \Supplier selection and order allocation
problem using a two-phase fuzzy multi-objective linear
programming", Appl. Math. Model., 37, pp. 9308-9323
17. Roshandel, J., Miri-Nargesi, S.S., and Hatami-
Shirkouhi, L. \Evaluating and selecting the supplier in
detergent production industry using hierarchical fuzzy
TOPSIS", Appl. Math. Model., 37, pp. 10170-10181
18. Sou Neyestani, M., Jolai, F., and Golmakani, H.R.
\An evolutionary algorithm for supplier order allocation
with fuzzy parameters considering linear and
volume discount", Scientia Iranica E, 22(3), pp. 1130-
1141 (2015).
M. Rabieh et al./Scientia Iranica, Transactions E: Industrial Engineering 25 (2018) 2297{2311 2311
19. Mahmoudi, A., Sadi-Nezhad, and Makui, A. \An
extended fuzzy VIKOR for group decision-making
based on fuzzy distance to supplier selection", Scientia
Iranica E, 23(4), pp. 1879-1892 (2016).
20. Kasilingam, R.G. and Lee, C.P. \Selection of vendors{
a mixed-integer programming approach", Comput.
Ind. Eng., 31, pp. 347-50 (1996).
21. Feng, C.-X., Wang, J., and Wang, J.S. \An optimization
model for concurrent selection of tolerances
and suppliers", Comput. Ind. Eng., 40(1-2), pp. 15-33
22. Bonser, J.S. and Wu, S.D. \Procurement planning to
maintain both short-term adaptiveness and long-term
perspective", Manage. Sci., 47, pp. 769-786 (2001).
23. Seshadri, S., Chatterjee, K., and Lilien, G.L. \Multiple
source procurement competitions", Market. Sci., 10,
pp. 246-53 (1991).
24. Ranjbar Tezenji, F., Mohammadi, M., Pasandideh,
S.H.R., and Nouri Koupaei, M. \An integrated model
for supplier location-selection and order allocation under
capacity constraints in an uncertain environment",
Scientia Iranica E, 23(6), pp. 3009-3025 (2016).
25. Van Landeghem, H. and Vanmaele, H. \Robust planning:
a new paradigm for demand chain planning", J.
Oper. Manage., 20, pp. 769-783 (2002).
26. Bertsimas, D. and Sim, M. \Robust discrete optimization
and network
ows", Math. Programming Ser. B.,
98, pp. 48-71 (2003).
27. Soyster, A.L. \Convex programming with set-inclusive
constraints and applications to inexact linear programming",
Oper. Res., 21, pp. 1154-1157 (1973).
28. Ben-Tal, A. and Nemirovski, A. \Robust convex optimization",
Math. Oper. Res., 23, pp. 769-805 (1998).
29. Ben-Tal, A. and Nemirovski, A. \Robust solutions of
uncertain linear programs", Oper. Res. Lett., 25, pp.
1-13 (1999).
30. Ben-Tal, A. and Nemirovski, A. \Robust solutions
of linear programming problems contaminated with
uncertain data", Math. Programming, Ser. A., 88, pp.
411-424 (2000).
31. El-Ghaoui, L., Oustry, F., and Lebret, H. \Robust
solutions to uncertain semide nite programs", SIAM.
J. Optim., 9, pp. 33-52 (1998).
32. El-Ghaoui, L. and Lebret, H. \Robust solutions to
least-square problems to uncertain data matrices",
SIAM. J. Matrix Anal. Appl., 18(4), pp. 1035-1064
33. Bertsimas, D. and Sim, M., The Price of Robustness.
Oper Rese, 52(1), pp. 35-53 (2004).
34. Werners, B. \Interactive multiple objective programming
subject to
exible constraints", Euro. J. Oper
Rese., 31, pp. 324-349 (1987).
35. Werners, B. \An interactive Fuzzy programming system",
Fuzzy Sets and Systems., 23, pp. 131-147 (1987).