Abstract

AN EPQ MODEL FOR NON-INSTANTANEOUS DETERIORATING ITEMS WITH STOCK-DEPENDENT DEMAND RATE UNDER TWO-PHASE PRODUCTION RATE AND SHORTAGES

A. Ali Baba* and Y.M. Baraya

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Abstract This paper proposes a production inventory model for non-instantaneous deteriorating items in which two-phase production rates are considered. The demand during production time is constant while it is stock-dependent after production stops. Shortages are allowed and completely backlogged. In reality, not all kinds of items such as meat, bread, cassava, and so on, deteriorate as soon as they are produced, but they maintain their freshness for some period before they begin to deteriorate. Demands for such items is constant at the initial stage of the products life cycle; at the end stage of life cycle and/or after production stopping time, the demand rate is sometimes influenced by the stock level. During the shortage period, the backlogging rate is complete. The purpose is to determine the optimal cycle length and optimal inventory level in each cycle so that the total cost is minimized. The necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. Also, the decision rule of Newton-Raphson method has been used to determine the optimal solutions and maple software version 13.0 were also used in plotting graph in order to show the convexity of the propose model. Then numerical example, sensitivity analysis and graphical presentation are provided to illustrate the application of the proposed model. Keywords: EPQ, two-phase production rate, non-instantaneous, deterioration, shortages.

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