A Data-driven Newsvendor Model In The Presence Of A Price Promotion

Price promotion is a marketing tool frequently used by a retailer.Customer demand faced the retailer is likely to increase during a price promotion.Instead of assuming that the demand distribution after a price cut is fully known,we consider dataesdriven approaches to the problem of inventory control.We assume that the reestailer has some knowledge about the demand and forms a prior distribution.Based on demand data,the retailer updates her belief and places an order for the coming selling period.In addition to the inventory decision,we also consider the retailer's promotion decision.In particular,we find the condition under which price promoestion results in a lower profit.In this case,the retailer may consider stopping the promotion.Based on the above theoretical model,we show the numerical calculation method of the model in cases of simple distribution and complex distribution.In the case of a relatively simple distribution,it can be determined by the nature of the second derivaestive of the expected revenue function that there is one and only one order quantity that can maximize the expected revenue,and the analytical solution of optimal order quantity can be directly obtained by making the first derivative zero.In more geneseral situations,the posterior distributions of parameters is updated by discretizing the continuous domains of demand and the unknown parameter.Then the expected revenue of different order quantities is approximately calculated to obtain a numeriescal solution of the optimal order quantity.It is found from experiments that accurate priors can make the model reach the optimal solution faster.In addition,we discuss an extension of the model.In the extended model,for every additional unit of price,a new distribution is accumulated to the total demand.In this way,the price is no longer an exogenous variable.In addition to determining the optimal order quantity,the decision maker also needs to determine the price of the current period.The process of solving the expanded model involves updating the posterior distributions of multiple parameters,which is difficult to solve through both analytical and numerical methods.So,we demonstrate how to solve the model by the Markov Monte Carlo method(MCMC).Through comparative experiments,it is found that adding certain random factors to the early pricing strategy can more accurately estimate the parameters of the model.