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hw8 - AMS/MBA 546(Fall 2010 Estie Arkin Network Flows...

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AMS/MBA 546 (Fall, 2010) Estie Arkin Network Flows Homework Set # 8 Due Thursday, November 18, 2010. Suggested reading Chapters 9, 12 and Section 11.12 (Unimodularity Property) of [AMO]. 1). [9.30] With respect to an optimal solution x of a minimum cost flow problem, suppose that we redefine arc capacities u as follows: u ij = braceleftbigg u ij if x ij = u ij otherwise Show that x is also an optimal solution of the minimum cost flow problem with the arc capacities as u . 2). [12.4] The Bin Packing paroblem is as follows: There are n items of weight a 1 ,a 2 ,...,a n (assume that 0 a i 1). What is the minimum number of Bins each of total weight at most 1, are needed to pack all
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