  We propose exact solution approaches for a lateral transhipment problem
which, given a pre-specified sequence of customers, seeks an optimal inventory
redistribution plan considering travel costs and profits dependent on inventory
levels. Trip-duration and vehicle-capacity constraints are also imposed. The
same problem arises in some lot sizing applications, in the presence of setup
costs and equipment re-qualifications.
  We introduce a pure dynamic programming approach and a branch-and-bound
framework that combines dynamic programming with Lagrangian relaxation.
Computational experiments are conducted to determine the most suitable solution
approach for different instances, depending on their size, vehicle capacities
and duration constraints. The branch-and-bound approach, in particular, solves
problems with up to 50 delivery locations in less than ten seconds on a modern
computer.
