PracticeAnswers - Practice questions for OEM DMOR Final...

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Practice questions for OEM DMOR Final Exam Question 1. A company is pursuing a project that requires three phases: (i) data collection, (ii) model development, and (iii) implementation. Phases i and ii can be done simultaneously by the team. After those phases are complete, phase (iii) can begin. We anticipate that phase (i) will require 20 weeks, phase (ii) will require 22 weeks, and phase (iii) will require 16 weeks. We have three ad-hoc teams, A, B, and C, that can work on phases i, ii, and iii, respectively. Every week that team A works reduces the number of weeks required by phase (i) by 0.7. Every week that team B works reduces the number of weeks required by phase (ii) by 0.8, and every week that team C works reduces the number of weeks required by phase (iii) by 0.6. However, there are three restrictions that govern the team assignment process: 1: The total amount of weeks worked by these three teams is no more than 20. 2: Due to project accounting limits, we cannot allocate more than $80,000 to teams A, B, and C, combined. Team A gets paid $5,000 per week, Team B gets paid $8,000 per week, and Team C gets paid $6,000 per week. 3: Because of overlaps in team members, the sum of weeks worked by Team B and Team C must be no more than 8. The objective is to minimize the time that the entire project is finished. The following is the model: Minimize t subject to t t 1 t 3 0 (Constraint 1) t t 2 t 3 0 (Constraint 2) t 1 + 0.7 x A = 20 (Constraint 3) t 2 + 0.8 x B = 22 (Constraint 4) t 3 + 0.6 x C = 16 (Constraint 5) x A + x B + x C 20 (Constraint 6) 5000 x A + 8000 x B + 6000 x C 80000 (Constraint 7) x B + x C 8 (Constraint 8) t , t 1 , t 2 , t 3 , x A , x B , x C 0 Part a: Give a brief (one line) interpretation of each variable. t is the time at which the entire project finishes t 1 is the time at which phase i finishes (similarly for t 2 and t 3 ) x A is the number of weeks that team A works on this project (similarly for x B and x C ). Part b: Modify the problem as follows. Team C can also be assigned to help out in phase (ii) if required. Every week of Team C’s effort on phase (ii) reduces the number of
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weeks required for that phase by 0.5. Team C can work on a combination of phase (ii) and phase (iii). (You may need an extra variable, perhaps two, for this modification.) Now, we need to know not just how many weeks team C works, but how many hours team C works on phase ii, and how many they work on phase iii. Remove variable x C , and replace it with two new variables: x C 2 (weeks worked on phase ii by team C) and x C 3 (weeks worked on phase iii by team C). t 2 + 0.8 x B + 0.5 x C 2 = 22 (New constraint 4) t 3 + 0.6 x C 3 = 16 (New constraint 5) x A + x B + x C 2 + x C 3 <= 20 (New constraint 6) 5000 x A + 8000 x B + 6000 x C 2 + 6000 x C 3 <= 80000 (New constraint 7) x B + x C 2 + x C 3 <= 8 (New constraint 8) Also, both new variables are nonnegative. The next few parts are all independent of all other questions.
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This note was uploaded on 02/25/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.

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PracticeAnswers - Practice questions for OEM DMOR Final...

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