  We consider the model of a transportation problem with the objective of
finding a minimum-cost transportation plan for shipping a given commodity from
a set of supply centers to the customers. Since the exact values of supply and
demand and the exact transportation costs are not always available for
real-world problems, we adopt the approach of interval programming to represent
such uncertainty, resulting in the model of an interval transportation problem.
The interval model assumes that lower and upper bounds on the data are given
and the values can be independently perturbed within these bounds. In this
paper, we provide an overview of conditions for checking basic properties of
the interval transportation problems commonly studied in interval programming,
such as weak and strong feasibility or optimality. We derive a condition for
testing weak optimality of a solution in polynomial time by finding a suitable
scenario of the problem. Further, we formulate a similar condition for testing
strong optimality of a solution for transportation problems with interval
supply and demand (and exact costs). Moreover, we also survey the results on
computing the best and the worst optimal value. We build on an exact method for
solving the NP-hard problem of computing the worst (finite) optimal value of
the interval transportation problem based on a decomposition of the optimal
solution set by complementary slackness. Finally, we conduct computational
experiments to show that the method can be competitive with the
state-of-the-art heuristic algorithms.
