Dynamic analysis of the Newsboy model with early purchase commitments

We consider a product with normally distributed random demand and a short life-cycle. In order to reduce demand uncertainty, the retailer offers a price-incentive to the customers who commit themselves to purchasing the product before the regular sale season starts. After observing the number of customers who commit, the retailer determines the optimal order quantity to maximise the total expected profit. Two different dynamic programming models are considered to solve this sequential decision problem. For both models, the optimal decisions are computed by solving the functional equations. The numerical results show that when it is optimal to offer price incentives one can reduce demand uncertainty and increase the total expected profit.