Multi-objective simulation optimization for selection and determination of order quantity in supplier selection problem under uncertainty and quality criteria


Simulation optimization is providing solutions to practical stochastic problems. Supplier selection is one of the most important decisions that determine the survival of an organization. In this paper, a novel multi-objective simulation optimization method to make decisions on selecting the suppliers and determining the order quantities is proposed. Regarding the fact that a real supply chain is multi-objective with uncertain parameters and includes both quantitative and qualitative variables, the proposed method considers these points and is applicable to real-world problems. This method also considers supplier selection and order quantity allocation to each supplier, which are totally related, as an integrated model. The proposed method consists of four basic modules: Cuckoo Optimization Algorithm (COA), Discrete Event Simulation (DES), Supply Chain Model (SCM), and Generalized Data Envelopment Analysis (GDEA). Unlike many multi-objective methods, the proposed method is not limited to the number of objective functions and this is one of its main benefits. It also pays attention to the efficiency of the organization and, at the same time, finding inputs which result in best output amounts. This method, in addition to the convergence criterion, pays special attention to the dispersion of the Pareto frontier as the second criterion for choosing the good solutions. For implementation of the proposed method, the numerical results for the problem of supplier selection in multi-product, multi-customer modes, and uncertain and qualitative variables are discussed and the Pareto frontiers are presented. The proposed method in this paper is compared with a similar method, and the results show the efficiency of the proposed method.

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  1. 1.

    Abdelaziz AY, Ali ES (2015) Cuckoo Search algorithm based load frequency controller design for nonlinear interconnected power system. Int J Electr Power Energy Syst 73:632–643

    Article  Google Scholar 

  2. 2.

    Akhilesh G, Patidar R, George NV (2015) Nonlinear system identification using a cuckoo search optimized adaptive Hammerstein model. Expert Syst Appl 42(5):2538–2546

    Article  Google Scholar 

  3. 3.

    Andradóttir, S (1998) A review of simulation optimization techniques. In: Medeiros DJ, Watson EF, Carson JS, Manivannan MS (eds) Proceedings of the 1998 Winter Simulation Conference, 151–158

  4. 4.

    Andradóttir, S (2005) An overview of simulation optimization via random search. In: Henderson SG, Nelson BL, (eds) Handbooks in Operations Research and Management Science: Simulation, 21. Elsevier, 617–631

  5. 5.

    April J, Glover F, Kelly JP, Laguna M (2003) Practical introduction to simulation optimization. In: Chick S, S´anchez PJ, Ferrin D, Morrice DJ (eds) Proceedings of the 2003 Winter Simulat Conference. Piscataway, New Jersey: Institute of Electrical and Electronics Engineers, 71–78

  6. 6.

    Arakawa M, Nakayama H, Hagiwara I, Yamakawa H (1998) Multi-objective optimization using adaptive range genetic algorithms with data envelopment analysis. In: A collection of technical papers on Seventh Symposium on Multidisciplinary Analysis and Optimization (TP98-4970). Reston, USA: American Institute of Aeronautics and Astronautics, 2074–2082

  7. 7.

    Arntzen BC, Brown GG, Harrison TP, Trafton LL (1995) Global supply chain management at digital equipment corporation. Interface 25(1):69–93

    Article  Google Scholar 

  8. 8.

    Ayhan MB, Kilic HS (2015) A two stage approach for supplier selection problem in multi-item/multi-supplier environment with quantity discounts. Comput Ind Eng 85:1–12

    Article  Google Scholar 

  9. 9.

    Cohon JL, Marks DH (1975) A review and evaluation of multiobjective programming techniques. Water Resour Res 11(2):208–220

    Article  Google Scholar 

  10. 10.

    Cohen MA, Moon S (1990) Impact of production scale economics, manufacturing complexity, and transportation costs on supply chain facility networks. J Manuf Oper Manag 3:269–292

    Google Scholar 

  11. 11.

    Dellino G, Kleijnen JPC, Meloni C (2010) Robust optimization in simulation: Taguchi and response surface methodology. Int J Prod Econ 125(1):52–59

    Article  MATH  Google Scholar 

  12. 12.

    Diewert WE (1980) Capital and the theory of productivity measurement. Am Econ Rev 70(2):260–267

    Google Scholar 

  13. 13.

    Ding H, Benyoucef LS, Xie X (2005) A simulation optimization methodology for supplier selection problem. Int J Comput Integr Manuf 18(2–3):210–224

    Article  Google Scholar 

  14. 14.

    Erenguc SS, Simpson NC, Vakharia AJ (1999) Integrated production/distribution planning in supply chains: an invited review. Eur J Oper Res 115:219–236

    Article  MATH  Google Scholar 

  15. 15.

    Freeman J, Chen T (2015) Green supplier selection using an AHP-Entropy-TOPSIS framework. Supply Chain Manag: An Int J 20(3):327–340

    Article  Google Scholar 

  16. 16.

    Fu MC (2002) Optimization for simulation: theory vs. practice. J Comput 14(3):192–215

    MathSciNet  MATH  Google Scholar 

  17. 17.

    Fu MC, Glover FW, April J (2005) Simulation optimization: a review, new developments, and applications. Paper presented at Proceedings of the 2005 Winter Simulation Conference, Piscataway, New Jersey, 83–95

  18. 18.

    Glover F, Kelly JP, Laguna M (1999) New advances for wedding optimization and simulation. In: Farrington PA, Nembhard HB, Stuffock DT, Evans GW (eds) Proceedings of the 1999 Winter Simulation Conference. Institute of Electrical and Electronics Engineers, Piscataway, New Jersey 255-260

  19. 19.

    Greasley A (2004) Using DEA and simulation in guiding operating units to improved performance. J Oper Res Soc 56(6):727–731

    Article  MATH  Google Scholar 

  20. 20.

    Gurkan G, Ozge AY, Robinson TM (1994) Sample-path optimization in simulation. In: Tew JD, Manivannan S, Sadowski DA, Seila AF (eds) Proceedings of 1994 Winter Simulation Conference, 247–254

  21. 21.

    Ho W, Dey PK, Lockström M (2011) Strategic sourcing: a combined QFD and AHP approach in manufacturing. Supply Chain Manag: An Int J 16(6):446–461

    Article  Google Scholar 

  22. 22.

    Jones DF, Mirrazavi SK, Tamiz M (2002) Multi-objective meta-heuristics: an overview of the current state-of-the-art. Eur J Oper Res 137(1):1–9

    Article  MATH  Google Scholar 

  23. 23.

    Jones MH, White KP (2004) Stochastic approximation with simulated annealing as an approach to global discrete-event simulation optimization. In: Proceedings Winter Simulation Conference, 500–507

  24. 24.

    Kahramanli H (2012) A modified Cuckoo Optimization Algorithm for engineering optimization. Int J Future Comput Commun 1(2):199–201

    Article  Google Scholar 

  25. 25.

    Lee LH, Chew EP, Teng S, Chen Y (2008) Multi-objective simulation-based evolutionary algorithm for an aircrafts spare parts allocation problem. Eur J Oper Res 189(2):476–491

    Article  MATH  Google Scholar 

  26. 26.

    Lee HL, Billington C (1993) Material management in decentralized supply chain. Oper Res 41:835–847

    Article  MATH  Google Scholar 

  27. 27.

    Liao Z, Rittscher J (2007) Integration of supplier selection, procurement lot sizing and carrier selection under dynamic demand conditions. Int J Prod Econ 107:502–510

    Article  Google Scholar 

  28. 28.

    Li X, Yin M (2015) Modified cuckoo search algorithm with self adaptive parameter method. Inf Sci 298:80–97

    Article  Google Scholar 

  29. 29.

    Lin RC, Sir YS, Pasupathy KS (2013) Multi-objective simulation optimization using data envelopment analysis and genetic algorithm: specific application to determining optimal resource levels in surgical services. Omega 41:881–892

    Article  Google Scholar 

  30. 30.

    Neddermeijer HG, Van Oortmarssen GJ, Piersma N, Dekker R (2000) A framework for response surface methodology for simulation optimization. In: Joines JA, Barton RR, Kang K, Fishwick PA (eds) Proceedings of the 32 Conference on Winter Simulation. Institute of Electrical and Electronics Engineeres, Piscataway, New Jersey,129–136

  31. 31.

    Nguyena TT, Vo DN (2015) Modified cuckoo search algorithm for short-term hydrothermal scheduling. Int J Electr Power Energy Syst 65:271–281

    Article  Google Scholar 

  32. 32.

    Rajabioun R (2011) Cuckoo Optimization Algorithm. Appl Soft Comput J 11:5508–5518

    Article  Google Scholar 

  33. 33.

    Rezaei J, Davoodi M (2011) Multi-objective models for lot-sizing with supplier selection. Int J Production Econ 130:77–86

    Article  Google Scholar 

  34. 34.

    Robinson SM (1996) Analysis of sample-path optimization. Math Oper Res 21(3):513–528

    MathSciNet  Article  MATH  Google Scholar 

  35. 35.

    Sabri EH, Beamon BM (2000) A multi-objective approach to simultaneous strategic and operational planning in supply chain design. Int J Manag Sci 28:581–598

    Google Scholar 

  36. 36.

    Schaffer JD (1984) Some experiments in machine learning using vector evaluated genetic algorithms. Doctoral dissertation, Vanderbilt University, Nashville, TN

  37. 37.

    Shadkam E, Bijari M (2014) Evaluation the efficiency of cuckoo optimization algorithm. Int J Comput Sci Appl (IJCSA) 4(2):39–47

    Google Scholar 

  38. 38.

    Shadkam E, Bijari M (2015) The optimization of bank branches efficiency by means of response surface method and data envelopment analysis: a case of Iran. J Asian Finance Econ Business 2(2):13–18

    Article  Google Scholar 

  39. 39.

    Spall JC (1998) Implementation of the simultaneous perturbation algorithm for stochastic optimization. IEEE Trans Aerosp Electron Syst 34(3):817–823

    Article  Google Scholar 

  40. 40.

    Tekin E, Sabuncuoglu I (2004) Simulation optimization: a comprehensive review on theory and applications. IIE Trans 36(11):1067–1081

    Article  Google Scholar 

  41. 41.

    Teleb R, Azadivar F (1994) A methodology for solving multi-objective simulation-optimization problems. Eur J Oper Res 72(1):135–145

    Article  MATH  Google Scholar 

  42. 42.

    Vidal C, Goetschalckx M (1997) Strategic production-distribution models: a critical review with emphasis on global supply chain models. Eur J Oper Res 98:1–18

    Article  MATH  Google Scholar 

  43. 43.

    Wang X.-J, Zhang C.-Y, Gao L, Li P.-G, (2008) A Survey and future trend of study on multi-objective scheduling. In: Proc. 4th International Conference on Natural Computation (ICNC ’08), Jinan, China, 382–391

  44. 44.

    Weber C, Current JR (1993) A multi-objective approach to vendor selection. Eur J Oper Res 68:173–184

    Article  MATH  Google Scholar 

  45. 45.

    Weber C, Current JR, Benton WC (1991) Vendor selection criteria and methods. Eur J Oper Res 50:2–18

    Article  Google Scholar 

  46. 46.

    Whittaker G, ConfesorJr R, Griffith SM, Fare R, Grosskopf S, Steiner JJ et al (2009) A hybrid genetic algorithm for multiobjective problems with activity analysis based local search. Eur J Oper Res 193(1):195–203

    Article  MATH  Google Scholar 

  47. 47.

    Wilson B, Cappelleri D, Simpson TW, Frecker M (2001) Efficient pareto frontier exploration using surrogate approximations. Optim Eng 2(1):31–50

  48. 48.

    Yang XS, Deb S (2009) Cuckoo search via Lévy Flights, In: Proc. World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), India. IEEE Publications, 210–214

  49. 49.

    Yang XS, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40(6):1616–1624

    MathSciNet  Article  MATH  Google Scholar 

  50. 50.

    Yun YB, Nakayama H, Tanino T, Arakawa M (2001) Generation of efficient frontiers in multi-objective optimization problems by generalized data envelopment analysis. Eur J Oper Res 129(3):586–595

    MathSciNet  Article  MATH  Google Scholar 

  51. 51.

    Yun YB, Nakayama H, Arakawa M (2004) Multiple criteria decision making with generalized DEA and an aspiration level method. Eur J Oper Res 158(3):697–706

    MathSciNet  Article  MATH  Google Scholar 

  52. 52.

    Yun YB, Nakayama H, Tanino T (2004) A generalized model for data envelopment analysis. Eur J Oper Res 157(1):87–105

    MathSciNet  Article  MATH  Google Scholar 

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Correspondence to Elham Shadkam.

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Shadkam, E., Bijari, M. Multi-objective simulation optimization for selection and determination of order quantity in supplier selection problem under uncertainty and quality criteria. Int J Adv Manuf Technol 93, 161–173 (2017).

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  • Supplier selection problem
  • Simulation optimization
  • Multi-objective problem
  • Cuckoo Optimization Algorithm
  • Generalized Data Envelopment Analysis
  • Efficiency