SIMULATION STUDIES FOR CREDIBILITY-BASED MULTI-OBJECTIVE LINEAR PROGRAMMING PROBLEMS WITH FUZZY PARAMETERS

Abstract

In this paper, hybrid credibility-based multi-objective linear programming models are provided to optimize expected values of objective functions subject to fuzzy chance-constraints. Triangular or non-linear fuzzy numbers are considered in problem parameters like demands and costs. To handle the uncertainty, the constraints are substituted with credibilistic fuzzy chance-constraints and the objective functions with their expected values. The credibilistic approach offers computational ease by the use of techniques which are similar to the stochastic simulation and applicable to all types of fuzzy numbers. The approach uses expected values and chance-constraints respectively to handle uncertain objective functions and to control the confidence level of fulfilling imprecise constraints. Numerical simulations are presented to compare the expected objective function values.

Keywords

• Multiple objective programming,fuzzy parameters,credibility measure,chanceconstraints,simulation

References

1. Ahmadizar, F., Zeynivand, M., (2014). Bi-objective supply chain planning in a fuzzy environment, Journal of Intelligent Fuzzy Systems, 26(1) pp. 153–164.
2. Ammar, E. E., Youness, E. A., (2005). Study on multiobjective transportation problem with fuzzy numbers, Applied Mathematics and Computation, 166(2) pp. 241–253.
3. Arenas-Parra, M., Bilbao-Terol, A., P´erez-Gladish, B., Rodr´ıguez-Ur´ıa, M. V., (2010). A new ap- proach of Romero’s extended lexicographic goal programming: fuzzy extended lexicographic goal programming, Soft Computing, 14(11) pp. 1217–1226.
4. Cheng, Y., Peng, J., Zhou, Z., Gu, X., Liu, W., (2017). A hybrid DEA-adaboost model in supplier selection for fuzzy variable and multiple objectives, IFAC-PapersOnLine, 50(1) pp. 12255–12260.
5. Jalota, H., Thakur, M., Mittal, G., (2017). Modelling and constructing membership function for uncertain portfolio parameters: A credibilistic framework, Expert Systems with Applications, 71 pp. 40–56.
6. Kacker, R. N., Lawrence, J. F., (2007). Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty, Metrologia, 44(2) pp. 117–127.
7. Kundu, P., Kar, S., Maiti, M., (2014). Multi-objective solid transportation problems with budget constraint in uncertain environment, International Journal of Systems Science, 45, (8) pp. 1668–1682. [8] Li, M., Guo, P., Singh, V.P., (2016). Biobjective optimization for efficient irrigation under fuzzy uncertainty, Journal of Irrigation and Drainage Engineering, 142, (8) pp. 05016003–1–10.
8. Liu, B., (2002). Toward fuzzy optimization without mathematical ambiguity, Fuzzy Optimization and Decision Making, 1(1) pp. 43–63.

9. Maity, K., A supply-chain production inventory model with warehouse facilities under fuzzy environ- ment, In Supply Chain Management Under Fuzziness (pp. 517–551), Springer, Berlin, Heidelberg, 2014.
10. Mehlawat, M. K., Gupta, P., (2015). COTS products selection using fuzzy chance-constrained multi- objective programming, Applied Intelligence, 43(4) pp. 732–751.
11. Mohamadi, A., Yaghoubi, S., Derikvand, H., (2015). A credibility-based chance-constrained transfer point location model for the relief logistics design (Case Study: earthquake disaster on region 1 of Tehran city), International Journal of Supply and Operations Management, 1(4) pp. 466–488.
12. Mousazadeh, M., Torabi, S. A., Pishvaee, M. S., Abolhassani, F., (2018). Health service network design: a robust possibilistic approach, International Transactions in Operational Research, 25, (1) pp. 337–373.
13. Mousazadeh, M., Torabi, S. A., Zahiri, B., (2015). A robust possibilistic programming approach for pharmaceutical supply chain network design, Computers Chemical Engineering, 82 pp. 115–128.
14. Patra, K., Mondal, S. K., (2015). Multi-item supplier selection model with fuzzy risk analysis studied by possibility and necessity constraints, Fuzzy Information and Engineering, 7, (4) pp. 451–474.
15. Pishvaee, M. S., Torabi, S. A., Razmi, J., (2012). Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty, Computers Industrial Engineering, 62, (2) pp. 624–632.
16. Salehi, M., Maleki, H. R., Niroomand, S., (2018). A multi-objective assembly line balancing problem with worker’s skill and qualification considerations in fuzzy environment, Applied Intelligence, 48, (8), pp. 2137–2156.
17. Soltani, R., Sadjadi, S. J., (2014). Reliability optimization through robust redundancy allocation models with choice of component type under fuzziness, Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 228, (5) pp. 449–459.
18. Tofighi, S., Torabi, S. A., Mansouri, S. A., (2016). Humanitarian logistics network design under mixed uncertainty, European Journal of Operational Research, 250, (1) pp. 239–250.
19. Xu, J., Zhou, X., (2013). Approximation based fuzzy multi-objective models with expected objectives and chance constraints: Application to earth-rock work allocation, Information Sciences, 238, pp. 75–95.
20. Yaghin, R. G., Fatemi Ghomi, S. M. T., Torabi, S. A., (2015). A hybrid credibility-based fuzzy mul- tiple objective optimisation to differential pricing and inventory policies with arbitrage consideration, International Journal of Systems Science, 46, (14) pp. 2628–2639.
21. Yaghin, R. G., Fatemi Ghomi, S. M. T., Torabi, S. A., (2017). Incorporating return on inventory investment into joint lot-sizing and price discriminating decisions: a fuzzy chance constraint program- ming model, Iranian Journal of Management Studies, 10, (4) pp. 929–959.
22. Yang, K., Yang, L., Gao, Z., (2017). Hub-and-spoke network design problem under uncertainty con- sidering financial and service issues: a two-phase approach, Information Sciences, 402, pp. 15–34.
23. Zhou, X., Tu, Y., Han, J., Xu, J., Ye, X., (2017). A class of level-2 fuzzy decision-making model with expected objectives and chance constraints: application to supply chain network design, International Journal of Information Technology Decision Making, 16, (04) pp. 907–938.
24. Zhou, X., Yu, N., Tu, Y., Pedrycz, W., Lev, B., (2017). Bi-level plant selection and production allocation model under type-2 fuzzy demand, Expert Systems with Applications, 86, pp. 87–98.