Convex Combination Method on Probabilistic Fuzzy Multiobjective Transportation Problem with Pareto Distribution

Eka Susanti; Oki Dwipurwani; Novi Rustiana Dewi; Indrawati Indrawati; Indri Yune Safira

doi:10.35877/454RI.jinav1538

Authors

Eka Susanti Department of Mathematics, Universitas Sriwijaya, Indralaya Ogan Ilir South Sumatera, Indonesia
Oki Dwipurwani Department of Mathematics, Universitas Sriwijaya, Indralaya Ogan Ilir South Sumatera, Indonesia https://orcid.org/0000-0003-1761-0959
Novi Rustiana Dewi Department of Mathematics, Universitas Sriwijaya, Indralaya Ogan Ilir South Sumatera, Indonesia
Indrawati Department of Mathematics, Universitas Sriwijaya, Indralaya Ogan Ilir South Sumatera, Indonesia
Indri Yune Safira Department of Mathematics, Universitas Sriwijaya, Indralaya Ogan Ilir South Sumatera, Indonesia

DOI:

https://doi.org/10.35877/454RI.jinav1538

Keywords:

Convex Combination, Multiobjective, Transportation, Pareto Distribution.

Abstract

This article introduces a transportation model with two objective functions. The first objective function is the function which minimizes the total cost and the second objective function is the function which minimizes the total time. Parameters of source, destination and maximum capacity of transportation means are assumed to follow the Pareto distribution. The multiobjective transportation model is the development of a single objective transportation model. Parameters of the objective function are expressed by triangular fuzzy numbers. Fuzzy multi objective problems are transformed into a deterministic single objective using the convex combination method. The formulated model is applied to the problem of shipping metal crates. There are 3 types of conveyances namely HDL, Engkel and Wingbox. Obtained the optimal total cost of Rp. 3,770,294 and metal crates delivery time to be for 13 hours.

References

Adhami, A. Y., & Ahmad, F. (2020). Interactive Pythagorean-Hesitant Fuzzy Computational Algorithm for Multiobjective Transportation Problem Under Uncertainty. International Journal of Management Science and Engineering Management, 15(4), 288–297.

Bagheri, M., Ebrahimnejad, A., Razavyan, S., Hosseinzadeh Lotfi, F., & Malekmohammadi, N. (2020). Fuzzy Arithmetic DEA Approach for Fuzzy Multi-Objective Transportation Problem. In Operational Research. Springer Berlin Heidelberg.

Barik, S. K. (2015). Probabilistic Fuzzy Goal Programming Problems Involving Pareto Distribution: Some Additive Approaches. Fuzzy Information and Engineering, 7(2), 227–244.

Boumediene, T. H. (2019). Multi-objective interval solid transportation problem with fuzzy equality under stochastic environment. March 2020.

Chakraborty, A., Maity, S., Jain, S., Mondal, S. P., & Alam, S. (2021). Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem. Granular Computing, 6(3), 507–521.

Chen, K., Xin, X., Niu, X., & Zeng, Q. (2020). Coastal Transportation System Joint Taxation-Subsidy Emission Reduction Policy Optimization Problem. Journal of Cleaner Production, 247, 119096.

Dalman, H. (2018). Uncertain programming model for multi-item solid transportation problem. International Journal of Machine Learning and Cybernetics, 9(4), 559–567.

Fergany, H. A., & Hollah, O. M. (2018). A Probabilistic Inventory Model with Two-Parameter Exponential Deteriorating Rate and Pareto Demand Distribution. International Journal of Scientific Research and Management, 6(5), 31–43.

Gowthami, R., & Prabakaran, K. (2019). Solution of Multi Objective Transportation Problem under Fuzzy Environment. Journal of Physics: Conference Series, 1377(1).

Hemalatha, S., & Annadurai, K. (2020). A fuzzy EOQ inventory model with advance payment and various fuzzy numbers. Materials Today: Proceedings.

Kakran, V. Y., & Dhodiya, J. M. (2020). for Solving Uncertain Multi-objective , Multi-item Solid Transportation Problem with Linear Membership Function (Vol. 949). Springer Singapore. Roy, S. K., Ebrahimnejad, A., Verdegay, J. L., & Das, S. (2018). New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana - Academy Proceedings in Engineering Sciences, 43(1).

S, B. M., & S, K. (2020). Fuzzy Inventory Model with Quadratic demand, Linear Time Dependent Holding Cost, Constant Deterioration Rate and Shortages. Malaya Journal of Matematik, S(1), 157–162.

Samanta, S., Jana, D. K., Panigrahi, G., & Maiti, M. (2020). Novel Multi-Objective, Multi-Item and Four-dimensional Transportation problem with vehicle speed in LR-type intuitionistic fuzzy environment. Neural Computing and Applications, 32(15), 11937–11955.

Singh, S., Pradhan, A., & Biswal, M. P. (2019). Multi-Objective Solid Transportation Problem under Stochastic Environment. Sadhana - Academy Proceedings in Engineering Sciences, 44(5), 1–12.

Susanti, E., Dwipurwani, O., Sitepu, R., Wulandari, & Natasia, L. (2019). Triangular fuzzy number in probabilistic fuzzy goal programming with pareto distribution. Journal of Physics: Conference Series, 1282(1).

Tang, C. H. (2020). Optimization for Transportation Outsourcing Problems. Computers and Industrial Engineering, 139, 106213.

Waliv, R. H., Mishra, U., Garg, H., & Umap, H. P. (2020). A Nonlinear Programming Approach to Solve the Stochastic Multi-objective Inventory Model Using the Uncertain Information. Arabian Journal for Science and Engineering, 45(8), 6963–6973.

Zimmermann, H. J. (2010). Fuzzy set theory. Wiley Interdisciplinary Reviews: Computational Statistics, 2(3), 317–332.