Optimal markdown pricing for holiday basket with customer valuation

We consider a problem in which a retailer who plans to sell holiday basket during a holiday and needs to determine an optimal markdown price for remaining inventory after the holiday. The retailer also needs to determine an optimal inventory level to maximise the total expected profit during and after the holiday. We assume customers’ total intended spending on the holiday basket is a random variable that is realised during the holiday and customers purchase the holiday basket based on their valuations. We formulate the problem as a two-stage stochastic programming model with the first-stage decision determining an optimal inventory level and the second stage determining an optimal markdown price based on remaining inventory and the realisation of customers’ total intended spending. We show that we can derive a unique optimal markdown price corresponding to the realisation of customers’ total intended spending. At last, we provide numerical results to illustrate the impact of holiday price of the basket, the highest customer valuation as well as the salvage value of the basket, all of which affect the retailer’s decision on markdown price.