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ps10 - ORIE 3300/5300 Prof Bland Problem Set 10 Fall 2011...

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ORIE 3300/5300 Fall 2011 Prof. Bland Problem Set 10 Due 11/22/2011, 11:40 a.m. Submit hardcopy in Hollister B14 at the beginning of lecture on 11/22 . Only 1 sub- mission from each group. Problem 1 is a continuation of Recitation Exercise 10. Problem 2 will be continued as Recitation Exercise 11. 1. Finish recitation Exercise 10. For each of the two approaches, submit a summary of the optimal values of the decision variables, yield and risk as functions of the relevant parameter. Show your analysis beginning from the point where the recitation solutions ended. 2. Twenty-five students will each be taking one of ten different tutorial courses next semester. Each tutorial will have at most three students. The file Prefer- ences.txt shows for each student a ranking of her first through fifth choices. An entry of 6 in row i and column j indicates that course i was not ranked in the top 5 by student j; it is not really student j’s sixth choice, it is one of her 20 unranked courses. As explained briefly in class on 11/17, this looks like a transportation problem, except we have not yet established an objective function. For now, we are going to assign a cost (penalty) of k for assigning student j to her kth most preferred course i and minimize the total cost. (This is NOT a good choice of a cost func- tion, but we will use it for now, and return to the choice of objective function coefficients later.) CPlex solver. You will want to use the CPlex solver (on all parts of this problem and future variations on this problem)– use the option solver cplex command. The print command and conditional indexing . See AMPL book pp.238-239. The AMPL command display is somewhat lim- ited. The print command functions like the display command. Among the features that make the print command useful is it takes conditional indexing – e.g., the command

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print { i in ORIG, j in DEST: cost[i,j] = 0 } : i, j; would print a line of output only for those choices of i and j in the appropri- ate sets which satisfy the condition after the colon – i.e., the cost of assigning destination j to origin i is zero. Conditioning on the decision variables could be pretty handy in reducing and organizing your output. In each part, use the print command to display a list of all courses and the students assigned to them. If you would like to have tab separated entries on each line (recommended), see the end of the next-to-last paragraph on p. 238 of the AMPL book. This will make your output a little prettier and a little easier for the eye to scan, and will also make it easier to import into a spreadsheet, if you wish to do that.
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