A Probabilistic Inventory Model with Two-Parameter Exponential Deteriorating Rate and Pareto Demand Distribution

A Probabilistic Inventory Model with Two-Parameter Exponential Deteriorating Rate

https://doi.org/10.18535/ijsrm/v6i5.m01

Authors

  • Hala Aly Fergany Assistant Prof. in Department of Mathematics, Faculty of Science, Tanta University, Egypt, Egypt
  • Osama Mahmoud Hollah Assistant Lecturer in Department of Mathematics, Higher Institute for Computers, Information & Management, Tanta, Egypt, Egypt
Vol. 6 No. 05 (2018)
Mathematics and Statistics
May 12, 2018

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Although the deterioration is one of the main problems that have been investigated in the inventory systems science the last twenty years ago but Most deteriorating inventory studies focused on deterministic models. This paper presents a Constraint Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM); a model is applicable when: (1) the demand is a random variable that follows Pareto distribution without lead-time, (2) some costs are varying, (3) shortages are permitted, and (4) the deterioration rate follows exponential distribution.
The objective function under a constraint is imposed here in crisp and fuzzy environment. A numerical analysis method (Newton's method) is used to solve the model. The main objective is to find the optimal values of four decision variables (maximum inventory level, stock-out time, the deteriorating time and review time), which minimize the expected annual total cost under the assumptions. At the end, the paper explains the model through an application.