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

Document Type : Original Article

Authors

1 Mathematics Department, Faculty of Science, Al-Azhar University (Girls campus).

2 Statistic Department, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

3 Mathematics Department, Faculty of Science, Tanta University.

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.

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