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Homework4

# Homework4 - construction described in the handout to...

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ENGRI 1101 Engineering Applications of OR Fall 2008 Homework 4 The Maximum Flow Problem Due date: 4:00pm on Friday, September 26, 2008 in the ENGRI 1101 box at the west end of the corridor on the second floor of Rhodes Hall, where it connects to Upson. Reading assignment: Handout 5 on the maximum flow problem. Make sure to put your name on the first page and staple the problems in order. 1. (50 points) The following figure gives an input to the maximum flow problem, and a feasible flow that has been computed by the Ford-Fulkerson algorithm. 6 2 5 f 6 1 2 3 5 1 5 1 8 4 6 10 1 2 9 5 3 u KE 0 2 2 1 4 3 5 6 (a) (30 points) Finish the execution of this algorithm to produce a maximum flow. (b) (10 points) Use the Ford-Fulkerson algorithm to produce a cut of minimum capacity. Be sure to explain your work. (c) (10 points) What is the value of the flow that you have found? What is the capacity of the cut that you have found? 2. (a) (20 points) For the input for the advisor assignment problem given in Handout 5, apply the

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Unformatted text preview: construction described in the handout to formulate this problem as a maximum ±ow problem. 1 (b) (30 points) It turns out that half of the faculty have left FUN. Now each advisor will take at most two new advisees, and the students have given their choices from among the remaining ±ve advisors. Once again, we wish to maximize the number of students assigned to one of their two choices. Take the data given below, and formulate this new problem as a maximum ²ow problem. (Hint: in this new formulation not all of the arc capacities will be 1.) Student # Choice #1 Choice #2 1 A C 2 B D 3 A C 4 D A 5 A C 6 B A 7 D A 8 E B 9 B A 10 B E Be sure to explain why your formulation is correct; in this explanation, be sure to explain how the integrality property is important. 2...
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