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Economic Analysis of Sinusoidal Cash Flow Inventory System for Non-Instateneous Deteriorating Items: Present Worth Approach

Manjusri Basu, Samiran Senapati, Sudipta Sinha


In this paper we consider a problem of determining the optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand. Shortages are allowed and the backlogging rate is variable and dependent on the waiting time for the next replenishment. Any inventory system is periodic and repetitive in nature. We think that the periodicity of an inventory system is best taken care by a sinusoidal curve. Several inventory models have been developed so far to suit the real-time inventory systems. Sinusoidal inventory system in one such real-time model. The traditional EOQ ignores the time value of money .In this regard the present worth (PW) approach is used to justify EOQ w.r.t. the time value of money. Hence the sinusoidal inventory model is analyzed based on the present worth approach to determine the optimum period length and the economic order quantity. The necessary and sufficient conditions of the existence of the optimal solution are shown. The model is illustrated with a numerical example and sensitivity analysis has been performed.


Non instantaneous deteritation,Sinusoidal, Present worth, Partial backlogging

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