An algorithm for the decomposition of arc flows into path flows for the General Spatial Price Equilibrium Problem

The General Spatial Price Equilibrium Problem (GSPEP) may be formulated either in terms of path flow variables or in terms of arc flow variables. When the variables are the path flows, the solution contains the important information regarding the origin-destination demand matrix and the paths used to transport goods. When the problem is solved in terms of the arc flows, the solution gives only the flows on the arcs of the network. On the other hand, the algorithms that have been proposed in the literature to solve the GSPEP in terms of arc flows are more efficient than those for the path flow formulation due to the enormous number of possible paths. In this paper, an algorithm called CAFPF is proposed, that decomposes the arc flow equilibrium into a path flow equilibrium (by a sequence of minimal path cost computations). CAFPF is then used after the GSPEP has been solved in terms of arc flows, giving the information on the O/D demand matrix and on the path flows. Numerical results show the efficiency of CAFPF. Finally, we note that CAFPF can be used for the linear or nonlinear, symmetric or asymmetric cases of GSPEP, and that it can easily be generalized to other problems such as the Network Equilibrium Problem.