041 tutoring 15053 dinner budget 14 ihtfp points

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Unformatted text preview: ooz’s problem as an integer program. 1 Let x i 0 if prize i is selected otherwise 41 Integer Programming Formulation Objective and Constraints? Max 16x1+ 22x2+ 12x3+ 8x4+ 11x5+ 19x6 5x1+ 7x2+ 4x3+ 3x4+ 4x5+ 6x6 ≤ 14 xj∈ {0,1} for each j = 1 to 6 We will solve this problem in two lectures. 42 Knapsack or Capital Budgeting You have n items to choose from to put into your knapsack. Item i has weight wi, and it has value ci. The maximum weight your knapsack (or you) can hold is b. Formulate the knapsack problem. 43 The mystery of integer programming Some integer programs are easy (we can solve problems with millions of variables) Some integer programs are hard (even 100 variables can be challenging) It takes expertise and experience to know which is which It’s an active area of research at MIT and elsewhere 44 Using Excel Solver to Solve Integer Programs Add the integrality constraints (or add that a variable is binary) Set the Solver Tolerance. (Integer optimality %) (The tolerance is the percentage deviation from optimality allowed by solver in solving Integer Programs.) – The default used to be 5%. – A 5% default is way too high – It often finds the optimum for small problems 45 Some Comments on IP models There are often multiple ways of modeling the same integer program. Solvers for integer programs are extremely sensitive to the formulation. (not true for LPs) 46 Summary on Integer Programming Dramatically improves the modeling capability – Economic indivisibilities – Logical constraints – capital budgeting – games Not as easy to model Not as easy to solve. Next lecture: more IP formulations 47 MIT OpenCourseWare 15.053 Optimization Methods in Management Science Spring 2013 For information about citing these materials or our Terms of Use, visit:
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This note was uploaded on 03/18/2014 for the course MGMT 15.053 taught by Professor Jamesorli during the Spring '07 term at MIT.

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