Proposing a Bi-level Programming Model for Multi-echelon Supply Chain with an Emphasis on Reliability in Uncertainty

Document Type : Research Paper

Authors

1 Ph.D. Candidate, Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran

2 Associate Prof., Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran.

3 Prof., Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran

4 Assistant Prof., Department of Industrial Management, Management and Accounting Faculty, Shahid Beheshti University, G.C., Tehran, Iran

Abstract

Objective: Providing a bi-level programming model to solve the simultaneous problem of supplier selection and order allocation in multi-echelon supply chain is sought. The model will be proposed so that at the leader level, the supplier selection problem with the objective of increasing system reliability and at the follower level, the order allocation problem with the objective of reducing cost of system are formulated and customers’ demand at the last echelon of the supply chain is considered as an uncertain parameter.
Methods: Modeling the supplier selection and order allocation problem is based on the bi-level programming model, so the robust optimization technique was used to deal with the problem of uncertainty and a bi-level genetic algorithm was used to obtain the optimal solutions.
Results: The results obtained from solving a real problem in the steel industry under various scenarios indicated that there is an opposing relationship between reliability and cost objectives, and increasing the number of chain members can lead to an increase in system reliability and cost. On the other hand, as increased reliability can lead to higher system costs, reliability reduction, which is mainly due to lack of quality and deficiency issues, can also lead to an increase in customers' dissatisfaction and, ultimately, an increase in aggregate system costs. Moreover, the results obtained in uncertain conditions, in comparison with definite conditions, indicated an unfavorable situation.
Conclusion: In order to improve the reliability of supply chain, the average reliability of the echelons in supply chain, which are at the lowest (highest) level in comparison to other echelons, should increase (decrease) in order to avoid additional costs. Besides, the interactive approach in proposed methodology provides a suitable solution for maximizing the interests of leader and follower levels.

Keywords

References

References
Abouzari, S. & Nahavandi, N. (2016). Supplier selection and order allocation in the electrical industry. 4th National Conference on Applied Research in Management and Accounting Sciences. Tehran: Shahid Beheshti University, September. (in Persian)
Amiri, M. (2014). Reliability. Tehran: Ann Publishing. (in Persian)
Arabzad, S.M., Ghorbani, M., Razmi, J. & Shirouyehzad, H. (2015). Employing fuzzy TOPSIS and SWOT for supplier selection and order allocation problem. The International Journal of Advanced Manufacturing Technology, 76(5-8), 803–818.
Ashrafi, M. & Chaharsughi, K. (2014). Sustainable supplier selection and order allocation with modified benders decomposition. Journal of Advanced Mathematical Modeling, 3(2), 81-102. (in Persian)
Bard, J.F. (1991). Some properties of the bi-level linear programming. Journal of Optimization Theory and Applications, 68(2), 371–378.
Chen, Y.J. (2011).Structured methodology for supplier selection and evaluation in a supply chain. Information Sciences, 181(9), 1651-1670.
Colson, B., Marcotte, P. & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 153(1), 235–56.
Dhillon, B.S. (1992). Reliability and Quality Control: Bibliography on General and Specified Area. Ontario: Beta Publisher.
Ertogral, K. & Wu, S.D. (2000).Auction-theoretic coordination of production planning in the supply chain. IIE Transactions, 32(10), 1154–1168.
Esfandiari, N. & Seifbarghy, M. (2013). Modeling a stochastic multi-objective supplier quota allocation problem with price-dependent ordering. Applied Mathematical Modelling, 37(8), 5790-5800.
Faez, F., Ghodsi Pour, S.H., Fatemi Ghomi, S.M.T. (2006). Designing an integrated model for selecting supplier and allocation of orders using the method of argumentative reasoning and multi-objective mathematical programming. Journal of Faculty of Engineering, 40(4), 553-568. (in Persian)
Haleh, H. & Hamidi, A. (2011).A fuzzy MCDM model for allocating orders to suppliers in a supply chain under uncertainty over a multi-period time horizon. Expert Systems with Applications, 38(8), 9076-9083.
Hamdan, S. & Cheaitou, A. (2017). Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach. Computers & Operations Research, 81, 282-304.
Hassani Goudarzi, A. & Rabbani, R. (2012). Supplier selection in supply chain with an order-based production approach considering Value at Risk. Iranian Journal of Supply Chain Management, 36, 20-29. (in Persian)
Hassanzadeh Amin, S., Razmi, J. & Zhang, G. (2011). Supplier selection and order allocation based on fuzzy SWOT analysis and fuzzy linear programming. Expert Systems with Applications, 38(1), 334-342.
He, M., Xie, J., Wu, X., Hu, Q. & Dai, Y. (2016). Capability coordination in automobile logistics service supply chain based on reliability. Procedia Engineering, 137, 325-333.
Holland, J. H. (1975). Adaptation in natural and artificial systems. Michigan: University of Michigan Press.
Hosseini, E. & Nakhai Kamalabadi, I. (2015). Two approaches for solving non-linear bi-level programming problem. Advances in Research, 3(5), 512-525.
Kuo, R.J. & Han, Y.S. (2011). A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem-A case study on supply chain model. Applied Mathematical Modelling, 35(8), 3905–3917.
Kӧksoy, O., &Yalcinoz, T. (2008). Robust design using pareto type optimization: A genetic algorithm with arithmetic crossover. Computers & Industrial Engineering, 55(1), 208-2018.
Leng, M. & Parlar, M. (2005). Game-theoretic applications in supply chain management: a review. INFOR Information Systems and Operational Research, 43(3), 187–220.
Nasiri, M.M. & Pourmohammad Zia, N. (2015). A hybrid model for supplier selection and order allocation in supply chain. Journal of Industrial Engineering, 49(1), 117-128. (in Persian)
Ng, T.S., Sun, Y. & Fowler, J. (2010).Semiconductor lot allocation using robust optimization. European Journal of Operational Research, 205(3), 557-570.
Nour Mohammadi Shalkeh, P., Paydar, M.M. & Haji Aghaei Keshtli, M. (2016). Selecting a stable supplier and assigning order quantities with allowance for discounts. 2nd International Conference on Industrial and Systems Engineering, Mashhad: Ferdousi University. (in Persian)
Pishvaee, M.S. & Fazli Khalaf, M. (2016).Novel robust fuzzy mathematical programming methods. Applied Mathematical Modelling, 40(1), 407–418.
Pishvaee, M.S., Jolai, F. & Razmi, J. (2009).A stochastic optimization model for integrated forward/reverse logistics network design. Journal of Manufacturing Systems, 28(4), 107-114.
Porter, M. E. (1985). The Competitive Advantage: Creating and Sustaining Superior Performance. New York: Free Press.
Punniyamoorthy, M., Mathiyalagan, P. & Parthiban, P. (2011). A strategic model using structural equation modeling and fuzzy logic in supplier selection. Expert Systems with Applications, 38(1), 458–474.
Rabieh, M., Modarres, M. & Azar, A. (2011). Robust-fuzzy model for supplier selection under uncertainty: An application to the automobile industry. Scientia Iranica, In press: DOI: 10.24200/sci.2017.4456.
Ramezanzadeh Baraki, R. & Kianfar, F. (2015). Providing a model for selecting suppliers and assigning orders to them by considering green routing under uncertainty. International Conference on Recent Researches in Management and Industrial Engineering, Tehran. (in Persian)
Razmi, J. & Rafiei, H. (2010). An integrated analytic network process with mixed-integer non-linear programming to supplier selection and order allocation. The International Journal of Advanced Manufacturing Technology, 49(9-12), 1195–1208.
RoozbehNia, A., Hemmati Far, M. & Akhavan Niaki, S.T. (2015). A hybrid genetic and imperialist competitive algorithm for green vendor managed inventory of multi-item multi-constraint EOQ model under shortage. Applied Soft Computing, 30, 353-364.
Shabanpour, H., Yousefi, S. & Farzipoor Saen, R. (2017). Future planning for benchmarking and ranking sustainable suppliers using goal programming and robust double frontiers DEA. Transportation Research Part D: Transport and Environment, 50, 129–143.
Shah, N.H. & Soni, H. (2011). A multi-objective production inventory model with backorder for fuzzy random demand under flexibility and reliability. Journal of Mathematical Modelling and Algorithms, 10(4), 341–356.
Singh, A. (2014). Supplier evaluation and demand allocation among suppliers in a supply chain. Journal of Purchasing and Supply Management, 20(3), 167–176.
Sivanandam, S. N. & Deepa, S. N. (2008). Introduction to Genetic Algorithms. Berlin: Springer Berlin Heidelberg.
Stephan, J. & Badr, Y. (2007). A quantitative and qualitative approach to manage risks in the supply chain operations reference. 2nd International Conference on Digital Information Management, 1, 410–417.
Venkatesan, S.P. & Goh, M. (2016). Multi-objective supplier selection and order allocation under disruption risk. Transportation Research Part E: Logistics and Transportation Review, 95, 124-142.
Yang, S., Hong, K. & Lee, C. (2014).Supply chain coordination with stock-dependent demand rate and credit incentives. International Journal of Production Economics, 157, 105-111.
Zhang, H., Deng, Y., Chan, F.T.S. & Zhang, X. (2013). A modified multi-criterion optimization genetic algorithm for order distribution in collaborative supply chain. Applied Mathematical Modelling, 37(14-15), 7855-7864.
Industrial Management Journal
Volume 11, Issue 2
2019
Pages 177-206

Files

Share

How to cite

Statistics