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Unformatted text preview: Exam: Optimization Modelling Code : 158142 Date : January 25, 2007 Preliminaries: 1. You may answer in Dutch. 2. Calculators are not allowed. 3. Every answer needs to be motivated! 1 Eitheror Constraints Consider the following model: minimize summationdisplay j ∈ J c j x j subject to : summationdisplay j ∈ J a 1 j x j ≤ b 1 (1) summationdisplay j ∈ J a 2 j x j ≤ b 2 (2) x j ≥ ∀ j ∈ J where : at least one of the conditions (1) or (2) must hold. Due to the eitherorcondition the model is not linear. Formulate a linear programming model that is equivalent to the above. Provide a short argu ment why your linear model is equivalent to the above. 2 A Fractional Objective Consider the following model: minimize ∑ j ∈ J c j x j ∑ j ∈ J d j x j subject to : summationdisplay j ∈ J a ij x j ≤ b i ∀ i ∈ I x j ≥ ∀ j ∈ J Due to the fractional objective the model is not linear. Formulate a linear programming model that is equivalent to the above, by the introduction of new variables and substitution. Under which conditions is your linear model equivalent to the above? 1 3 Sumbrero In the first lecture we constructed a linear programming model for the Su doku puzzle. An other interesting puzzle, also frequently found in the Metro newspaper, is the Sumbrero. Details on the Sumbrero puzzle is given in the figure below: Build an linear programming model for the Sumbrero problem. 4 Multiitem lot sizing Consider the Multiitem lot sizing problem which we discussed in one of the lectures. You can find the problem description and the basic linear program ming formulation in Appendix A....
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This note was uploaded on 12/03/2011 for the course SCHOOL 1 taught by Professor 2 during the Fall '07 term at Aquinas.
 Fall '07
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