  Given facilities with capacities and clients with penalties and demands, the
transportation problem with market choice consists in finding the minimum-cost
way to partition the clients into unserved clients, paying the penalties, and
into served clients, paying the transportation cost to serve them. We give
polynomial-time reductions from this problem and variants to the
(un)capacitated facility location problem, directly yielding approximation
algorithms, two with constant factors in the metric case, one with a
logarithmic factor in the general case.
