The next diagram depicts a system of aqueducts that originate at three rivers (nodes R1, R2, and R3) and terminate at a major city (node T), where the other nodes are junction points in the system. To From R1 R2 R1 R2 R3 R3 A C B Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day. To D A B C From 130 115 A B 70 90 110 140 120 с E F T DEF 110 85 - 130 95 85 130 160 To From D E F T 220 330 240 The city water manager wants to determine a flow plan that will maximize the flow of water to the city. a) Formulate this problem as a maximum flow problem by identifying a source, a sink, and the transshipment nodes, and then drawing the complete network that shows the capacity of each arc. b) Use the augmenting path algorithm described in Sec. 10.5 to solve this problem. List the augmenting path and c* for each iteration in a table. Show your final result by either listing the optimal flow assignment paths or clearly labeling the flow on the network.

The next diagram depicts a system of aqueducts that originate at three rivers (nodes R1, R2, and R3) and terminate at a major city (node T), where the other nodes are junction points in the system. To From R1 R2 R1 R2 R3 R3 A C B Using units of thousands of acre feet, the tables below show the maximum amount of water that can be pumped through each aqueduct per day. To D A B C From 130 115 A B 70 90 110 140 120 с E F T DEF 110 85 - 130 95 85 130 160 To From D E F T 220 330 240 The city water manager wants to determine a flow plan that will maximize the flow of water to the city. a) Formulate this problem as a maximum flow problem by identifying a source, a sink, and the transshipment nodes, and then drawing the complete network that shows the capacity of each arc. b) Use the augmenting path algorithm described in Sec. 10.5 to solve this problem. List the augmenting path and c* for each iteration in a table. Show your final result by either listing the optimal flow assignment paths or clearly labeling the flow on the network.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section: Chapter Questions

Problem 17RP

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