Optimization of Inventory Level Using Fuzzy Probabilistic Exponential Two Parameters Model


  • Eka Susanti Universitas Sriwijaya, Palembang, Indonesia
  • Indrawati Universitas Sriwijaya, Palembang, Indonesia
  • Robinson Sitepu Universitas Sriwijaya, Palembang, Indonesia




Fuzzy probabilistic inventory, Exponential distribution, Pareto distribution


Inventory control is an important factor in trading activities. Inventory control aims to ensure product availability. Several factors affect the level of inventory including the level of demand factor, maximum inventory, and the level of deterioration. If the influencing factors cannot be defined with certainty and follow a certain statistic distribution then the fuzzy probabilistic approach can be applied. This research discusses the problem of optimizing the inventory of red chillies at the retail level. The level of deterioration is assumed to follow an exponential distribution and demand follows a Pareto distribution. Statistical parameters are estimated using the Maximum likelihood method and cost parameters are expressed by triangular fuzzy numbers. Based on the calculation results for several beta values, the highest total cost is 405143.6 rupiah, a maximum inventory level of 15 kg, and an order cycle time of 0.923 days.


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X. Zheng, M. Yin, and Y. Zhang, “Integrated Optimization of Location, Inventory and Routing In Supply Chain Network Design,” Transp. Res. Part B, vol. 121, pp. 1–20, 2019.

S. Sanni and B. O. Neill, “Computers & Industrial Engineering Inventory optimization in a three-parameter Weibull model under a prepayment system,” Comput. Ind. Eng., vol. 128, no. December 2018, pp. 298–304, 2019.

L. E. Cárdenas-barrón, A. A. Shaikh, S. Tiwari, and G. Treviño-garza, “An EOQ inventory model with nonlinear stock dependent holding cost, nonlinear stock dependent demand and trade credit,” Comput. Ind. Eng., 2018.

X. Luo and C. Chou, “International Journal of Production Economics Technical note : Solving inventory models by algebraic method,” Int. J. Prod. Econ., vol. 200, no. March, pp. 130–133, 2018.

S. M. Mousavi, N. Alikar, S. T. . Niaki, and A. Bahreininejad, “Optimizing a location allocation-inventory problem in a two-echelon supply chain network : A modified Fruit Fly optimization algorithm,” Comput. Ind. Eng., vol. 87, pp. 543–560, 2015.

J. Rezaeian, S. Haghayegh, and I. Mahdavi, “Designing an Integrated Production / Distribution and Inventory Planning Model of Fixed-life Perishable Products,” J. Optimization Ind. Eng., vol. 19, pp. 47–59, 2016.

Y. Perlman and I. Levner, “Perishable Inventory Management in Healthcare,” J. Serv. Manag., vol. 2014, no. February, pp. 11–17, 2014.

Z. Azadi, S. D. Eksioglu, B. Eksioglu, and G. Palak, “Stochastic Optimization Models for Joint Pricing and Inventory Replenishment of Perishable Products,” Comput. Ind. Eng., vol. 127, no. January, pp. 625–642, 2019.

S. J. Sadjadi, A. Makui, E. Dehghani, and M. Pourmohammad, “Applying queuing approach for a stochastic location-inventory problem with two different mean inventory considerations,” Appl. Math. Model., vol. 40, no. 1, 1-596, pp. 578–596, 2016.

M. Rahdar, L. Wang, and G. Hu, “A tri-level optimization model for inventory control with uncertain demand and lead time,” Int. J. Prod. Econ., vol. 195, pp. 96–105, 2018.

C. Canyakmaz, S. Özekici, and F. Karaesmen, “An inventory model where customer demand is dependent on a stochastic price process,” Int. J. Prod. Econ., vol. 212, pp. 139–152, 2019.

Y. Zhang, G. Hua, S. Wang, J. Zhang, and V. Fernandez, “Managing Demand Uncertainty: Probabilistic Selling Versus Inventory Substitution,” Int. J. Prod. Econ., vol. 196, pp. 56–67, 2018.

E. Shekarian, S. Hanim, A. Rashid, E. Bottan, and S. K. De, “Fuzzy inventory models : A comprehensive review,” Appl. Soft Comput. J., vol. 55, pp. 588–621, 2017.

B. P. Dash, T. Singh, and H. Pattnayak, “An Inventory Model for Deteriorating Items with Exponential Declining Demand and Time-Varying Holding Cost,” vol. 2014, no. January, pp. 1–7, 2014.

H. A. Fergany and O. M. Hollah, “A Probabilistic Inventory Model with Two-Parameter Exponential Deteriorating Rate and Pareto Demand Distribution,” Int. J. Res. Manag., vol. 6, no. 5, pp. 31–43, 2018.

M. Braglia, D. Castellano, L. Marrazzini, and D. Song, “A continuous review, ( Q , r ) Inventory Model for a Deteriorating Item with Random Demand and Positive Lead Time,” Comput. Oper. Res., vol. 109, pp. 102–121, 2019.

T. Vovan, “An improved fuzzy time series forecasting model using variations of data,” Fuzzy Optim. Decis. Mak., vol. 18, no. 2, pp. 151–173, 2019.

D. Martinetti, S. Montes, S. Díaz, and B. De Baets, “On a correspondence between probabilistic and fuzzy choice functions,” Fuzzy Optim. Decis. Mak., vol. 17, no. 3, pp. 247–264, 2018.

P. Kundu, S. Majumder, S. Kar, and M. Maiti, “A method to solve linear programming problem with interval type-2 fuzzy parameters,” Fuzzy Optim. Decis. Mak., vol. 18, no. 1, pp. 103–130, 2019.

H. Wu, “Applying the concept of null set to solve the fuzzy optimization problems,” Fuzzy Optim. Decis. Mak., vol. 18, no. 3, pp. 279–314, 2019.

P. T. Ngastiti, B. Surarso, and S. Sutimin, “Comparison Between Zero Point and Zero Suffix Methods in Fuzzy Transportation Problems,” J. Mat. “MANTIK,” vol. 6, no. 1, pp. 38–46, 2020, doi: 10.15642/mantik.2020.6.1.38-46.




How to Cite

Susanti, E., Indrawati, & Sitepu, R. (2021). Optimization of Inventory Level Using Fuzzy Probabilistic Exponential Two Parameters Model. Jurnal Matematika MANTIK, 7(2), 124–131. https://doi.org/10.15642/mantik.2021.7.2.124-131