We consider the following transportation problem with both random and
fuzzy factors. There exist m supply points and n demand points. For each route
between supply point and demand point, unit transportation cost is a random variable
according to a normal distribution and existence possibility denoting the preference
choosing this route is attached. The probability that the total transportation cost
is not greater than the budget F should be not less than the fixed probability level.
Under the above setting, we seek transportation pattern minimizing F and maximizing
the minimal preference among the routes used in a transportation. Since usually
there is no transportation pattern optimizing two objectives at a time, we propose a
solution algorithm to find some non-dominated transportation patterns after defining
non-domination. Finally we discuss the further research problems.