  Dual-sourcing inventory systems, in which one supplier is faster (i.e.
express) and more costly, while the other is slower (i.e. regular) and cheaper,
arise naturally in many real-world supply chains. These systems are notoriously
difficult to optimize due to the complex structure of the optimal solution and
the curse of dimensionality, having resisted solution for over 40 years.
Recently, so-called Tailored Base-Surge (TBS) policies have been proposed as a
heuristic for the dual-sourcing problem. Under such a policy, a constant order
is placed at the regular source in each period, while the order placed at the
express source follows a simple order-up-to rule. Numerical experiments by
several authors have suggested that such policies perform well as the lead time
difference between the two sources grows large, which is exactly the setting in
which the curse of dimensionality leads to the problem becoming intractable.
However, providing a theoretical foundation for this phenomenon has remained a
major open problem.
  In this paper, we provide such a theoretical foundation by proving that a
simple TBS policy is indeed asymptotically optimal as the lead time of the
regular source grows large, with the lead time of the express source held
fixed. Our main proof technique combines novel convexity and lower-bounding
arguments, an explicit implementation of the vanishing discount factor approach
to analyzing infinite-horizon Markov decision processes, and ideas from the
theory of random walks and queues, significantly extending the methodology and
applicability of a novel framework for analyzing inventory models with large
lead times recently introduced by Goldberg and co-authors in the context of
lost-sales models with positive lead times.
