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# quiz2 - IE 426 Quiz#2 4:105:25 READ THIS Please put your...

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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 j N a j x j b j N a j x j + M + b j N a j x j b δ = 1 j N a j x j - ( m - ) δ b + δ = 1 j N a j x j b j N a j x j + m + b j N a j x j b δ = 1 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?

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