# An Optimal Inventory Policy for Items Having Constant Demand and Constant Deterioration Rate with Trade Credit

R. P. Tripathi, S. S. Misra
DOI: 10.4018/jisscm.2012040106
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## Abstract

In most of the classical inventory models the demand is considered as constant. In this paper the model has been framed to study the items whose demand and deterioration both are constant. The authors developed a model to determine an optimal order quantity by using calculus technique of maxima and minima. Thus, it helps a retailer to decide its optimal ordering quantity under the constraints of constant deterioration rate and constant pattern of demand.
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## Mathematical Formulation

In this model, constant demand is considered with constant deterioration rate. Depletion of the inventory occurs due to demand as well as due to deterioration which occurs only when there is inventory during the period [0, T]. The level of inventory I(t) gradually decreases mainly due to meet demands and partially due to deterioration. The variation of inventory with respect to time can be described by the following differential equation: + θ I(t) = – D, 0 ≤ t ≤ T (1) with I(0) = Q (initial inventory level)

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