Efficient Algorithms on Multicommodity Flow over Time Problems with Partial Lane Reversals

Algorithm 5

EAMCT algorithm with partial lane reversals.

Input: given a multicommodity flow network

Output: the EAMCT with partial lane reversals

 (1) The given network is transformed to auxiliary network by adding two-way capacities in as ,

 (2) Compute the EAMCT on the transformed network by using algorithm by Kappmeier [11].

 (3) Decompose the flow along the paths and cycles and remove flows in cycles .

 (4) Reverse up to the capacity iff , replaced by whenever where and .

 (5) For each , if is reversed, and . If neither nor is reversed, , where is the saved capacity of .

 (6) Transform the solution to the original network.