te State College is considering building o dorms to house 40 students. In order

Question

te State College is considering building o dorms to house 40 students. In order to is maximize student satisfaction a survey consisting of 6 questions has been developed and administered to the students who will be staying in the dorms. The questions pertain to issues such as sleep time, smoking, etc. The following questions along with the potential response are reported below. 1. What time do you go to bed at night? 6pm 6, Midnight 12, 2am 14, etc. 2. What time do you get up in the morning? 6am 6, noon 12, 2pm 14, etc. 3. How neat are you? 1 Messy, 2 Moderate, 3 Very neat 4. Do you smoke? 0 no, 10 yes 5. How much noise do you like in your environment? 1-Little noise, 2 moderate noise, 3 lots of noise 6. How many guests do you like having over? 1 No guests, 2 some guests, 3 lots of guests The responses for each of the 40 students are reported in table 1. Formulate the problem as an optimization model and determine what is the optimal (or near optimal) arrangement for students staying two to a room. As a hint, this problem should be formulated as a TSP and the Alldifferent constraint will be used. The objective function should consist of a total root sum of squares between 20 different sets of two roommates. The evolutionary solver in Excel will also have to be used. Be creative and try to think of how you would actually try to solve this problem and what criteria you need to use. If you were a potential roommate, who would you want to be paired with. Then extend this to the entire group.

Explanation / Answer

Let an be the time at which studentn goes to bed at night

Let bn be the time at which studentn wakes up in the morning

Let cn denote how messy studentn is

Let dn denote whether studentn smokes

Let en denote how much noise a studentn likes

Let fn denote how many guests a studentn likes

The objective function for our problem is

z = minimize {square root(an+1 - an)2 + square root(bn+1 - bn)2 + square root(cn+1 - cn)2 + square root(dn+1 - dn)2 +square root(en+1 - en)2 + square root(fn+1 - fn)2 }

subject to : dn >= 0 --- constraint 1

bn > 0 --- constraint 2

an > 0 --- constraint 3

cn > 0   --- constraint 4

en > 0   --- constraint 5

fn > 0   --- constraint 6

These constraints are listed in this particular order because -

Using Evolutionary Solver in excel we find the optimal solution for this problem is the below grouping

Person -- Person

26--7

6--4 9--36 38--16 15--11 25--35

26--7

37--33 39--32 5--27 2--21 13--10 34--17 18--30 20--12 19--40 29--23 3--1 22--14 8--31 24--28

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