  Transshipment, also known under the names of earth mover's distance,
uncapacitated min-cost flow, or Wasserstein's metric, is an important and
well-studied problem that asks to find a flow of minimum cost that routes a
general demand vector. Adding to its importance, recent advancements in our
understanding of algorithms for transshipment have led to breakthroughs for the
fundamental problem of computing shortest paths. Specifically, the recent
near-optimal $(1+\varepsilon)$-approximate single-source shortest path
algorithms in the parallel and distributed settings crucially solve
transshipment as a central step of their approach.
  The key property that differentiates transshipment from other similar
problems like shortest path is the so-called \emph{boosting}: one can boost a
(bad) approximate solution to a near-optimal $(1 + \varepsilon)$-approximate
solution. This conceptually reduces the problem to finding an approximate
solution. However, not all approximations can be boosted -- there have been
several proposed approaches that were shown to be susceptible to boosting, and
a few others where boosting was left as an open question.
  The main takeaway of our paper is that any black-box $\alpha$-approximate
transshipment solver that computes a \emph{dual} solution can be boosted to an
$(1 + \varepsilon)$-approximate solver. Moreover, we significantly simplify and
decouple previous approaches to transshipment (in sequential, parallel, and
distributed settings) by showing all of them (implicitly) obtain approximate
dual solutions.
  Our analysis is very simple and relies only on the well-known multiplicative
weights framework. Furthermore, to keep the paper completely self-contained, we
provide a new (and arguably much simpler) analysis of multiplicative weights
that leverages well-known optimization tools to bypass the ad-hoc calculations
used in the standard analyses.
