Competitive transportation problems

This paper extends the classical transportation model to the competitive one that demand nodes are divided into some groups. In a classical transportation problem all demand nodes cooperate and reduce the total cost of all transportation costs, and so transportation cost of goods into some demands becomes high comparing the other demand nodes. In our model each of them endeavours to minimize its own total transportation cost from supply nodes. So in place of the total cost of all demand nodes, we are requested to balance satisfaction degree with respect to the transportation cost among all groups. First in Section 2, we formulate the case of two groups. For this case, we propose an efficient procedure based on the efficient frontier approach to bi-objective programming, we propose an efficient procedure to the problem. Next general case is considered in Section 3. This problem can be formulated into the special linear programming problem and utilizing the efficient frontier of corresponding multi-objective programming problem, we propose an efficient algorithm. Finally in Section 4 we discuss further research problems.