I am currently in a graduate program for operations science management, currentl
ID: 2928892 • Letter: I
Question
I am currently in a graduate program for operations science management, currently we are doing integer programming, but I am stuck.
Dr. Konur has recently completed a project for Missouri Department of Transportation, which was for
optimizing the track inspection planning on the Missouri railroad network. In this question, you are asked
to formulate a simpler version of the track inspection planning problem.
In particular, suppose that there 5 rail tracks that you can inspect. Each track has different inspection
importance and each track has different inspection times. The table below gives the importance level and
inspection time for each track.
As the inspection planner, you want to determine which tracks to inspect such that you maximize the total
importance level of the inspections. However, you have one day, i.e., 24 hours available for inspections.
That is, total inspection time cannot exceed 24 hours.
a) (10 points) Formulate a binary linear programming model for the above inspection planning
problem by defining you decision variables and writing the objective and objective function and
the constraints in terms of your decision variables. Combine everything to get the final model.
b) (10 points) Formulate a spreadsheet model for the above problem and solve it using excel solver.
c) (15 points, 3 points each) Mathematically formulate the following restrictions as constraints
independent of each other and the constraints in part a. You should formulate a single constraint
for each part.
i. If you inspect track 1, then you have to inspect track 2.
ii. You can either inspect track 3 or track 4, but not both.
iii. If you inspect both track 1 and track 2, then you have to inspect track 4.
iv. You cannot inspect track 3 unless you inspect track 4.
v. You cannot inspect track 1 unless you inspect track 3; and, you cannot inspect track 3
unless you inspect track 1.
Explanation / Answer
set up the cells in excel as follows
maximize sum(importance)
subject to
1 st constraint track1 yes/no <= track2 yes/no
2nd constraint
NAND(track3, track4) = 1
NOT(AND(track3 yes/no , track4 yes/no) = 1
3rd constraint
track1 + track2--track4 <=1
4th constraint track3 <= track4
5th constraint
track1 = track3
Solve using solver after adding these 5 constraints, sum of all track hours less than 24 and choosing the 5 track yes/no as binary
Answer is
Track 1 2 3 4 5 Hours 5 4 8 7 6 Importance 10 11 13 12 9Related Questions
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