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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 Either-or 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 either-or-condition 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 Multi-item lot sizing Consider the Multi-item 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