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

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.