Maximum Multicommodity Flow with Intermediate Storage

Algorithm 1

Maximum static multicommodity flow algorithm with intermediate storage (MSMCFAIS).

	Input: given static network .
	Output: maximum static multicommodity flow with intermediate storage in .
(1)	Reconfigure the multicommodity flow problem into independent single commodity flow problems by reallocating the capacity of bundle arcs using the resource directive decomposition.
(2)	For each with , compute commodity-wise shortest distance by using Dijkstra’s algorithm.
(3)	Fix the priority order as with respect to commodity with first priority to the sink and priority for intermediate elements as , for .
(4)	For each , construct the modified network with single source and multiple sinks with dummy ports .
(5)	For :
	Compute the lexicographic maximum static flow in with priority order of Step 3 according to [10].
(6)	Transform the solution to the original network by removing the dummy ports and the dummy arcs.