A transportation model with multiple criteria and multiplle constraint levels

In this paper, a transportation model with multiple criteria and multiple constraint levels (MC²) is formulated by using the framework of MC² linear programming. An algorithm is developed to solve such MC² transportation problems. In this algorithm, the traditional northwest corner rule is adopted to find an initial basic feasible solution for a given MC² transportation problem. Then the MC²-simplex method is applied to locate the set of all potential solutions over possible changes of the objective coefficient parameter and the supply and demand parameter for the MC² transportation problem. A numerical example is illustrated to demonstrate the applicability of the algorithm in solving the MC² transportation problems.