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Fig.5. Graphical representation difference between actual total cost and optimal VS deterioration and breakability rates Fig.6. Graphical representation difference between actual total cost and optimal total cost VS optimal quantity

In this paper, the deterioration, breakability represented in the proposed model at the same time to reduce the total cost of eggs items and assumed the daily demand is constant, developed the mathematical model by the above assumptions and apply it in real life-based in the collected data. The output of the mathematical model is minimizing the total cost of eggs items and obtaining the economic order quantity for several breakable rate values which is including the calculated deterioration, breakable rates for eggs items. The proposed model is having two cases first case. The model is not fitted with less deterioration, breakability rates as percentage if and only if the percentage for deteriorating rate lies in the range 0%, 0.75 %, the percentage for breakability rate lies in the range 0%, 0.75% at same time the obtained economic order quantity is not satisfied the obtaining optimal total cost . The second case model is fitted when the risk of deterioration, breakability are high with a low net constant discount rate of inflation as 50 %, that makes it more significance in real life with high risk for the quality of inventory in the stock. The economic order quantity was decreasing when the deterioration, breakability rates increased so that the total cost of eggs is decreasing because the order economic quantity decreased. The difference between the total costs under assumptions of the mathematical model is increasing where deterioration, breakability rates were decreasing as the following figures. The output of the inventory model showed the optimal total cost, economic order quantity for the collected data, first cycle with 0.0000225 as deterioration rate, 0.0000448 as breakability rate obtained in maximum value with low risk level as percentages of deterioration, breakability rates lie between 0%, 0.75% respectively, which it is not satisfied the optimal total cost whereas it would be at minimum value when risk was increasing which is satisfied the optimal total cost, when the percentages of each deterioration, breakability are more than 0.75% respectively. The impression about the output of the proposed model for the tiles items is the committed policy of imported industry of eggs at the Republic of Yemen is useful with risk level as percentage of deterioration is more than 0.75%, percentage of breakability is more than 0.75% of the inventory of eggs in stock with 50% as representing the net discount rate of inflation. The optimal quantity was decreasing when optimal of first time run decreased

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