  We consider two orientation problems in a graph, namely the minimization of
the sum of all the shortest path lengths and the minimization of the diameter.
  We show that it is NP-complete to decide whether a graph has an orientation
such that the sum of all the shortest paths lengths is at most an integer
specified in the input. The proof is a short reduction from a result of
Chv\'atal and Thomassen showing that it is NP-complete to decide whether a
graph can be oriented so that its diameter is at most 2. In contrast, for each
positive integer k, we describe a linear-time algorithm that decides for a
planar graph G whether there is an orientation for which the diameter is at
most k. We also extend this result from planar graphs to any minor-closed
family not containing all apex graphs.
