1.2 Assumptions and notations,

• The numbers of replenishment are finite or infinite.

• The total single of item is mentioned.

• Demand and deterioration, breakability rates may constant or non-constant.

• There is no inventory replenishment back order.

• Planning horizon is a finite.

• The lead time is zero or non zero.

• The inventory level at the end of the planning horizon will be zero or non zero.

• The cost factors are deterministic.

• The order and shortage quantity.

• Purchasing, holding, shortage interest payable & interest earned.

• The last order is only being placed to satisfy the shortage of the last period.

• The goal of the model is to determine the EOQ and optimal total cost and find out the optimal inventory level.

1.3 Research Objectives

Some of the objectives of the research study are

? To derive the optimal order quantities, shortage quantities and deterioration rate is a function of time when

• When the demand rate is constant.

• When the demand rate is non constant.

? To derive and try to develop the mathematical model to obtain the optimal order quantities when demand rate, deterioration rate are constant.

? To obtain the optimal order quantities, the shortage is not allowed function, demand rate is nonlinear.

? Try to develop the optimal costs including inventory cost, holding cost &shortage cost, purchasing cost, interest cost and interest earned cost.

? To find optimal order quantity for one price break, multi-price breaks, if they are possible.

? To analyze the sensitivity analysis by numerical example.

? Try to develop the management order economic quantity in case deterioration items.

Try to develop a model for real-life data set for Yemen situated industries quantity in case deterioration items.

1.4 Research methodology

? Differential equation technique will be used to find the general solution and special solution for our two differential equations by using the Bernoulli equation over the bounded of time when the shortage is allowed or not allowed.

? Simulation technique will be implemented for finding quantities based in special equations when shortages or without shortages allowed based on the inventory level.

? The goodness of fit for the demand rate by using the distribution theory technique based on the data which is collected by using the Chi-square test.

? Regression analysis technique to estimate the demand rate, deterioration as linear or nonlinear regression for the data which is collected.

1.5 Significance of Research

? It can be used to find minimum deterioration for goods (permissible quality) and optimal quantity to satisfy the customers based on the data which is collected.

? This research can handle the inventory model with non-zero inventory level.

? It can manage all goods have deterioration and break-ability characteristics through optimal quantity, optimal inventory cost in the Republic of Yemen by representing the best model for the demand rate, deterioration rate, and break-ability.

? It can be applicable for Yemen situated industries for their development &it will help to increase the profit of the industries.

1.6 Applications

Some of the application of the study is stated below:

? It can use it in all chemical inventory include goods have deterioration and some medicines.

? It can use it to manage the problems in the bank of blood.

? It can use it in the marketing of fruits and vegetables.

? It can control the quantities in stock.

? It can minimize the deterioration rate to get the best quality of the items.

? It will be tried to development the EOQ model based on the deterioration rate and demand rate.

? It can use to increase the profits by finding the optimal cost associated to purchase cost, holding cost and carrying a cost.

? It can handle the many situations for deteriorating items with inflation.

? It can estimate the effects of the parameters together, changes on the derived results by the proposed methods; a sensitivity analysis is performed by changing the values of some parameters and taking one parameter at a time, keeping remaining parameters at their original levels. This analysis is performed on numerical examples.

- Jon Bellion might not sound familiar by name to the general public
- Valerie Acosta Mr