Kevin Taaffe, Joseph Geunes, H. Edwin Romeijn
Target market selection with demand uncertainty:
the selective newsvendor problem
We consider a firm that markets and delivers a good with a single selling season
(e.g., fashion goods, holiday items). The net revenue that can be extracted for the
good varies by market, as do the market demand and required marketing effort. The
firm's choice of markets will determine both the expected value and uncertainty of
the firm's total demand during the single selling season. Given long procurement lead
times, the firm must decide prior to placing its order with its primary supplier, which
markets it will plan to serve, which will drive its order quantity decision. We develop a
profit maximizing model to address the firm's integrated market selection and ordering
decisions. Using this model, we investigate several alternatives for the relationship
between sales and advertising and the implied demand distribution in each market as
a function of advertising effort. When faced with budgetary restrictions, the resulting
problem is a specially structured knapsack problem with a nonlinear objective. Despite
this, we can obtain quality upper bounds on optimal profit by solving a relaxation of
the problem in polynomial time. The relaxation solution then serves as a starting point
for an exact solution via branch-and-bound.