Target market selection and marketing effort under uncertainty: The selective newsvendor

We consider a firm that markets, procures, and delivers a good with a single selling season in a number of different markets. The price for the good is market-dependent, and each market has an associated demand distribution, with parameters that depend on the amount of marketing effort applied. Given long procurement lead-times, the firm must decide which markets it will serve prior to procuring the good. We develop a profit maximizing model to address the firm's integrated market selection, marketing effort, and procurement decisions. The model implicitly accounts for inventory pooling across markets, which reduces safety stock costs but increases model complexity. The resulting model is a nonlinear integer optimization problem, for which we develop specialized solution methods. For the case in which budget constraints exist, we provide a novel solution approach that uses a tailored branch-and-bound algorithm. Our approach solves a broad range of 3000 test instances in an average of less than 2 seconds, significantly outperforming a leading commercial global optimization solver.