An explicit integer programming model of the minimal spanning tree problem for digraphs with asymmetric weights

As far as the minimal spanning tree problem for the digraph with asymmetric weights is concerned, an explicit integer programming model is proposed, which could be solved successfully using the integer programming packages such as LINDO, and furthermore this model is extended into the stochastic version, that is, the minimal spanning tree problem for the digraph with the weights is not constant but random variables. Several algorithms are also developed to solve the models. Finally, a numerical demonstration is given.