AN EFFICIENT IMPLEMENTATION OF THE NETWORK SIMPLEX METHOD.

The adaptation of the primal simplex method for solving minimum linear cost network flow problems is well known. We present a new data structure for storing the tree associated with a basis and introduce a new adaptive heuristic method for the pivot choice. The pivot choice is modified dynamically during the application of the algorithm. The code which is based on this data structure and adaptive pivot choice has been tested on a variety of test problems. This empirical study shows that this code is among the most efficient implementations of the network simplex method. The large number of diverse problems used in this empirical study permit us to draw conclusions on the efficiency of the code on problems of varying difficulty.

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