In the transportation problem, there may be multiple objectives such as minimization of consumption of certain scarce resources, minimization of total deterioration of goods cooured during transportation and minimization of bottleneck time, etc.
Perhaps the most effective technique that can handle these multicriteria decision making problems is goal programming. Even though it is theretically possible to use the goal programming technique for the problem, efficiency becomes a major consideration, especially for large scale problem.
In this thesis, studies are made on the following three areas. First, the Dantzing-wolfedecomposition process is applied to goal programming for the problem with multiobjective transportation in order to improve the efficiency.
Second, when the bottleneck time minimization is included as an objective, it is no longer possible to use goal programming technique for the multiobjective transportation. And so an algorithm is given for determining all efficient (Pareto up optimal or nondominated) solution pairs assuming that the time function for each route is an increasing piecewise constant function.
Finally, a stochastic transportation problem is considered with demand as a random variable. In this case we assume that it is distributed symmetrically with known mean and variance but its distribution function are unspecified.
For this model, it is transformed to an approximate equivalent convex programming problem and then minimax solution is obtained using Frank-Wolfe method.
