# quiz2 - IE 426 Quiz #2 November 14, 2005 4:105:25 READ...

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IE 426 – Quiz #2 November 14, 2005 4:10–5:25 READ THIS! Please put your name on all the pages of the exam. If you need more space, feel free to use the backs of the sheets, just make sure that I know where you are writing your answers. The more clearly you write your answer, the better the chance that I can grade it accurately and give it full credit. When writing down an optimization model, remember to deﬁne the decision variables! The number of points for each problem is display at the end of the problem’s title. Use your time wisely. Jim will collect all the papers promptly at 5:25. In particular, I might suggest leaving Problem 2 until the end. Good luck! Don’t panic. I’m rooting for you. Name:

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Potentially Useful Jibberish Felix’s Bag Of Tricks δ = 1 X j N a j x j b X j N a j x j + M + b X j N a j x j b δ = 1 X j N a j x j - ( m - ± ) δ b + ± δ = 1 X j N a j x j b X j N a j x j + m + b X j N a j x j b δ = 1 X j N a j x j - ( M + ± ) δ b - ± How to solve one row LP’s by branch-and-bound 1. Sort the items in nonincreasing order of c j /a j (proﬁt per unit of storage consumed). 2. Put the items (in this sorted order) into the knapsack until it would be overfull. (Let x j = 1 for all these items). 3. Add the last item (at a fractional amount if necessary) so that the knapsack is just at capacity. You can use this procedure in branch-and-bound, just be sure to ﬁx all the variables that deﬁne the node of the branch and bound tree. If x j is ﬁxed at one, put the item in the knapsack and reduce its capacity If x j is ﬁxed at zero, don’t consider the item for inclusion in the knapsack.
IE426 Quiz #2 Name: 1 Which of These Things is Less Than The Other? (10) The questions in this section refer to the optimal objective function values of the following prob-

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## This note was uploaded on 02/29/2008 for the course IE 426 taught by Professor Linderoth during the Spring '08 term at Lehigh University .

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quiz2 - IE 426 Quiz #2 November 14, 2005 4:105:25 READ...

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