  In this work we investigate the problem of order batching and picker routing
in storage areas. These are labour and capital intensive problems, often
responsible for a substantial share of warehouse operating costs. In
particular, we consider the case of online grocery shopping in which orders may
be composed of dozens of items.
  We present a formulation for the problem based on an exponential number of
connectivity constraints and we introduce a significant number of valid
inequalities based on the standard layout of warehouses, composed of parallel
aisles and two or more cross-aisles. The proposed inequalities are highly
effective and greatly improve computational results.
  Instances involving up to 20 orders are solved to proven optimality when we
jointly consider order batching and picker routing. Instances involving up to
5000 orders are considered where order batching is done heuristically, but
picker routing is done optimally.
