Probabilistic Inventory Model with Lead Time Equals Single Scheduling Period and Varying Deteriorating Cost under Constraint

Authors

Hoda Abdeldaim, Mathematics Department, Faculty of Science, Al-Azhar University (Girls campus).Follow
Hala Fergany, Statistic Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia | Mathematics Department, Faculty of Science, Tanta University.Follow
Azza Omar, Mathematics Department, Faculty of Science, Al-Azhar University (Girls campus).Follow
Yasmien Morsy, Mathematics Department, Faculty of Science, Al-Azhar University (Girls campus).Follow

Corresponding Author

Morsy, Yasmien

Document Type

Original Article

Subject Areas

Mathematics, Statistics, Computer Science, Physics and Astronomy

Keywords

deterioration; Probabilistic demand rate; Scheduling period; Varying cost; Weibull distribution

Abstract

In this paper inventory model of declining goods with ambiguous and imprecise details about available storage has been established. Here, our targets are: 1- the optimal scheduling period, 2- the optimal order-level, 3- minimize the wastage cost due to the deterioration, 4- minimize the expected average total cost under a restriction on the expected average varying deteriorating cost by using the Lagrange method. This model, is developed for continuously deterioration rate is constant or follows a two-parameter Weibull distribution with varying and constrained expected deteriorating cost, Where the lead time is only one period of time, without shortage and when demand is a random variable during any scheduling time. These probabilistic models are studied in two cases: crisp numbers and trapezoidal fuzzy numbers. Some special cases are deduced. There is a numerical illustration to illustrate the proposed model in the crisp case and the fuzzy case and the sensitivity analysis is performed.

How to Cite This Article

Abdeldaim, Hoda; Fergany, Hala; Omar, Azza; and Morsy, Yasmien (2020) "Probabilistic Inventory Model with Lead Time Equals Single Scheduling Period and Varying Deteriorating Cost under Constraint," Al-Azhar Bulletin of Science: Vol. 31: Iss. 2, Article 1.
DOI: https://doi.org/10.21608/absb.2020.41932.1083