  The robust multi-product pricing problem is to determine the prices of a
collection of products so as to maximize the worst-case revenue, where the
worst case is taken over an uncertainty set of demand models that the firm
expects could be realized in practice. A tacit assumption in this approach is
that the pricing decision is a deterministic decision: the prices of the
products are fixed and do not vary. In this paper, we consider a randomized
approach to robust pricing, where a decision maker specifies a distribution
over potential price vectors so as to maximize its worst-case revenue over an
uncertainty set of demand models. We formally define this problem -- the
randomized robust price optimization problem -- and analyze when a randomized
price scheme performs as well as a deterministic price vector, and identify
cases in which it can yield a benefit. We also propose two solution methods for
obtaining an optimal randomization scheme over a discrete set of candidate
price vectors based on constraint generation and double column generation,
respectively, and show how these methods are applicable for common demand
models, such as the linear, semi-log and log-log demand models. We numerically
compare the randomized approach against the deterministic approach on a variety
of synthetic and real problem instances; on synthetic instances, we show that
the improvement in worst-case revenue can be as much as 1300%, while on real
data instances derived from a grocery retail scanner dataset, the improvement
can be as high as 92%.
