Periodic review inventory model for Gumbel deteriorating items when demand follows Pareto distribution

Journal of the Egyptian Mathematical Society

H. A. Fergany¹  O. M. Hollah² 

[1] 0000 0000 9477 7793, grid.412258.8, Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt;Department of Mathematics, Higher Institute for Computers, Information & Management, Tanta, Egypt;

关键词: Crisp environment;    Lagrange multiplier technique;    Newton’s method;    Triangular fuzzy number;    Zero lead time;    90B05- 90C70 - 93A30;   

DOI  :  10.1186/s42787-019-0007-z

来源: publisher

【 摘 要 】

For the importance of deteriorating in units, this paper presents a Constraint Deteriorating Probabilistic Periodic Review Inventory Model (CDPPRIM), a model which is applicable under some assumptions: (1) the demand is a random variable that follows Pareto distribution without lead time, (2) some costs are varying and shortage is permitted, (3) the deterioration rate follows Gumbel distribution, and (4) there is a constraint on varying deteriorating cost.Here, the objective function under a constraint is imposed in crisp and fuzzy environment. A Newton’s method is used to solve the system of nonlinear equations. The 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. Finally, the model is followed by an application.

【 授权许可】

CC BY