خوارزمية مطورة لايجاد الحل الامثل لمسائل النقل باقل كلفة ممكنة

In this paper we introduce a developed algorithm to find the optimal solution for the transportation problems with the least possible cost. This algorithm contains an essential theorem that demonstrates the necessary and sufficient situation that includes the conditions needed in order to get the feasible solution of primal and dual transportation problems. At last, we had numerical experiments to illustrate the efficacy of the developed algorithm for many problems, and we compared this developed algorithm with other algorithm to solve the transportation problems. Results showed that the developed algorithm gives the optimal solution with the least possible cost and in a way faster than any other studied algorithm.