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Joint pricing and inventory control under reference price effects

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In many firms the pricing and inventory control functions are separated. However, a number of theoretical models suggest a joint determination of inventory levels and prices, as prices also affect stocking risks. In this work, we address the problem of simultaneously determining a pricing and inventory replenishment strategy under reference price effects. This reference price effect models the empirically well established fact that consumers not only react sensitively to the current price, but also to deviations from a reference price formed on the basis of past purchases. The current price is then perceived as a discount or surcharge relative to this reference price. Thus, immediate effects of price reductions on profits have to be weighted against the resulting losses in future periods. We study how the additional dynamics of the consumers' willingness to pay affect an optimal pricing and inventory control model and whether a simple policy such as a base-stock-list-price policy holds in such a setting. For a one-period planning horizon we analytically prove the optimality of a base-stock-list-price policy with respect to the reference price under general conditions. We then extend this result to the two-period time horizon for the linear and loss-neutral demand function and to the multi-period case under even more restrictive assumptions. However, numerical simulations suggest that a base-stock-list-price policy is also optimal for the multi-period setting under more general conditions. We furthermore show by numerical investigations that the presence of reference price effects decreases the incentive for price discounts to deal with overstocked situations. Moreover, we find that the potential benefits from simultaneously determining optimal prices and stocking quantities compared to a sequential procedure can increase considerably, when reference price effects are included in the model. This makes an integration of pricing and inventory control with reference price effects by all means worth the effort. (author's abstract)

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Lisa Gimpl-Heersink

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