Robust price-setting newsvendor model with interval market size and consumer willingness-to-pay

We consider a price-setting newsvendor problem with partial information. The newsvendor does not know the price-dependent probability distribution of demand, but is able to estimate lower and upper limits of the market size and consumer willingness-to-pay. The objective is to minimize the maximum loss in expected profit, or minimax regret. We derive closed-form expressions for optimal quantity and price and identify managerial insights.