Abstract
The paper considers a dynamic risk model with periods of equal length for stocking and selling products where the selling price of the stocked item is under control of the management. A preset price ( y) may appear unsatisfactory to a fraction (1- ψ( y)) of the arrived demand and this fraction of demand is lost irrespective of the stock on hand. The other fraction ( ψ( y)) of the demand is retained if there is stock on hand and in case of stockout a fixed fraction ( π) of the demand, is backlogged whereas (1 - π) of the unmet demand is lost. ψ( y) is decreasing in y. where y is at least as high as the procurement cost, and both ψ( y) and π are either known or can be estimated from past experience. Arrival of demand over a reorder interval is continuous, following some known probabilistic Jaw and is independent of price. Optimal values of stock height and selling price have been obtained through maximization of profit, given that both of them are to be set at the beginning of a reorder interval.
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