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Unformatted text preview: IEOR E4007 G. Iyengar October 8th, 2008. Homework #3 Due : October 22nd, 2008. 1. Exercise 3.15 from Optimization methods for finance In this problem there is a discrepancy between the answers generated by EXCEL and AMPL/CPLEX. The issue is that there are many (at least two!) optimal corner solutions, i.e. two optimal bases. AMPL/CPLEX finds one and EXCEL finds the other. Since the sensitivity report depends on the dual variables which themselves are a function of the optimal basis, we end up with two different sensitivity reports. If you solve this problem using AMPL/CPLEX we get the following sensitivity report: x x.rc x.down c x.up 4 1 1.5 1 7 0.666667 1 1 2 1 1 1 1.5 3 7 1 1 4 1 1 1e+20 5 3 1 1.5 6 0.333333 0.666667 1 1e+20 req.dual req.down req.current req.up 0.333333 12.5 14 15.5 11e+20 13 14 2 0.333333 13.5 15 25.5 31e+20 16 19 4 0.333333 16 19 22 5 0.333333 16.5 18 19.5 6 10 11 12 The AMPL code shift.mod and shift.run that generates this report is posted on the web. Note that the days are numbered from 0,1,...,6 with Monday labeled , Tuesday labeled as 1 , etc.. (a) The total number of workers = 4 + 7 + 1 + 4 + 3 + 3 = 22. This is same regardless of how you solve the problem. (b) The Thursday constraint is slack and the allowable increase is 3 . Therefore, there is no change in the number of workers needed. 1 (c) The dual variable corresponding to the Monday constraint is 1 3 and the change in the requirement is 3 which is well within the allowable decrease for the EXCEL (i.e. Text) sensitivity report. Therefore, the net change in the objective is 3 · 1 3 = 1. For the AMPL/CPLEX report the allowable decrease is not within the RHS range. Therefore, we can only say that the decrease in the objective is within [ 1 , . 5]. (d) If the solver is EXCEL (as is the case with the book!) then the sensitivity report in the text is correct. In this case the increase of 0 . 1 is within the allowable range for the objective coefficient of the Shift4...
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 Summer '09
 OptimizationModelsandMethods
 Optimization, WI, sensitivity report, 16 19 22 16.5

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