figure an example of the transportation network in this we have supply vertexes (with supply values and ) demand vertexes (with demand values and )and transshipment node each edge has two numberscapacity and costdivided by comma bi bj uij,cij notes - - - representing the flow on arc (ije by xijwe can obtain the optimization model for the minimum cost flow problemc ij xij minimize (xi subject to = ij : ij : <xij <uij for all vfor all (ije the first constraint states that the total outflow of node minus the total inflow of the node must be equal to mass balance (supply/demand valueof this node this is known as the mass balance constraints nextthe flow bound constraints model physical capacities or restrictions imposed on the flow' range as you can seethis optimization model describes typical relationship between warehouses and shopsfor examplein case where we have only one kind of product we need to satisfy the demand of each shop by transferring goods from the subset of warehouseswhile minimizing the expenses on transportation this problem could be solved using simplex-methodbut in this article we concentrate on some other ideas related to network flow theory before we move on to the three basic algorithms used to solve the minimum cost flow problemlet' review the necessary theoretical base finding solution when does the minimum cost flow problem have feasible (though not necessarily optimalsolutionhow do we determine whether it is possible to translate the goods or notif ddef siv bi then the problem has no solutionbecause either the supply or the demand dominates in the network and the mass balance constraints come into play lovely professional university