Periodic review inventory model for Gumbel deteriorating items when demand follows Pareto distribution | ||
| Journal of the Egyptian Mathematical Society | ||
| Article 10, Volume 27, Issue 1, 2019, Pages 1-13 PDF (761.49 K) | ||
| DOI: 10.1186/s42787-019-0007-z7 | ||
| Authors | ||
| O. M. Hollah; H. A. Fergany | ||
| Department of Mathematics, Higher Institute for Computers, Information & Management, Tanta, Egypt | ||
| Abstract | ||
| 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. | ||
| Keywords | ||
| Crisp environment; Lagrange multiplier technique; Newton’s method; Triangular fuzzy number; Zero lead time | ||
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