Flow Improvement in Evacuation Planning with Budget Constrained Switching Costs

Algorithm 2

Maximum dynamic contraflow with switching cost (MDCFAWSC).

	Input: two-terminal arc reversible network with reversal budget , reversal cost , and symmetric arc capacity
(1)	Transform the given dynamic network into the time-expanded network by
	capacities and costs of holdover arcs are infinity and zero, respectively
(2)	Construct an auxiliary as or with new capacity
(3)	Define the cost function by
(4)	Transform the cost and the capacity functions by
(5)	Find the optimal flow in the auxiliary network considering budget and the cost defined in Step 4 using binary search in , where
(6)	An arc is reversed with capacity if and only if the flow along is greater than or there is a nonnegative flow along the arc
(7)	Reconstruct the dynamic network flow from the static network flow according to the flow obtained in Step 5 and arc reversal in Step 6
	Output: Maximum dynamic contraflow in with respect to budget