Kevin Taaffe, H. Edwin Romeijn, Deepak Tirumalasetty
A selective newsvendor approach to order management
Consider a supplier offering a product to several potential demand sources (or orders), each with
a unique revenue, size, and probability that it will materialize. Given a long procurement lead
time, the supplier must choose, prior to the selling season, which orders to pursue as well as the
total quantity to procure. In our core single-period model, the supplier enjoys revenues from the
pursued and materialized orders, as well as either a per-unit salvage value or penalty cost at the
end of the period. We model this as a selective newsvendor problem of maximizing profits where
the (random) demand faced by the supplier is given by the set of pursued orders. To overcome the
fact that the dimensionality of a mixed-integer linear programming formulation of the problem
increases rapidly with the number of potential orders, we develop a tailored algorithm based on
the L-shaped method for two-stage stochastic programming. We then extend our model and
solution approach to account for piecewise-linear convex underage costs and piecewise-linear
concave salvage revenues as well as to a multi-period setting. We perform extensive numerical
experiments that show that our algorithm can quickly solve much larger problems to optimality
than a state-of-the-art commercial solver.