6. NP Hard Problems
Computer Science has a concept called “NP Hard” problems.
“Non-deterministic Polynomial-time Hard”
In other words:
A computer can tell you if a given set of options works but it
would take ages to work out the “best” answer, because there’s
no shortcut other than looking at every possible combination.
8. NP Hard Problems
TL;DR
Some problems are too hard even for a computer to solve in a
reasonable timeframe and timetabling is one of them.
It’s definitely hard, but the human factor makes it worse!
10. What is the Monte Carlo Method?
“In physics-related problems, Monte Carlo methods are quite useful for simulating
systems with many coupled degrees of freedom, such as fluids, disordered materials,
strongly coupled solids, and cellular structures.
“Other examples include modelling phenomena with significant uncertainty in inputs
such as the calculation of risk in business and, in math, evaluation of multidimensional
definite integrals with complicated boundary conditions.
“In application to space and oil exploration problems, Monte Carlo–based predictions of
failure, cost overruns and schedule overruns are routinely better than human intuition
or alternative ‘soft’ methods.”
Wikipedia Definition
“In physics-related problems, Monte Carlo methods are quite useful for simulating
systems with many coupled degrees of freedom, such as fluids, disordered materials,
strongly coupled solids, and cellular structures.
“Other examples include modelling phenomena with significant uncertainty in inputs
such as the calculation of risk in business and, in math, evaluation of multidimensional
definite integrals with complicated boundary conditions.
“In application to space and oil exploration problems, Monte Carlo–based predictions of
failure, cost overruns and schedule overruns are routinely better than human intuition
or alternative ‘soft’ methods.”
11. What is the Monte Carlo Method?
TL;DR
The Monte Carlo method is way of coming up with answers to hard problems
that are:
•Better than guessing
•Probably right
•Easier and quicker than doing the math!
12. What is the Monte Carlo Method?
Define your problemDefine your problem
Randomly guess the answerRandomly guess the answer
Record the resultRecord the result
Find the best resultFind the best result
Repeat many timesRepeat many times
13. What is the Monte Carlo Method?
Important note:
The Monte Carlo method is not guaranteed to find you the best answer.
The more iterations, the more likely you are to find the best answer.
17. Current North Campus Central Teaching Room Provision
Renold Building – 28 rooms including 1 x 532, 2 x 296
George Begg Building – 5 rooms
Pariser Building – 5 rooms
Sackville Street Building – 11 rooms
The Mill – 2 rooms
(plus a big pool of School controlled rooms of various sizes)
Problem: How much space to build?
22. Problem: How much space to build?
Phrase the problem in a way which can be expressed in
numerical values:
•How many rooms of size 0 to 30 should we have?
•How many rooms of size 31 to 50 should we have?
•How many rooms of size 51 to 100 should we have?
•How many rooms of size 101 to 200 should we have?
•How many rooms of size 201 to 300 should we have?
•How many rooms of size 301 to 400 should we have?
23. Problem: How much space to build?
RANDBETWEEN(lower, upper)
=RANDBETWEEN(0,10)
24. Problem: How much space to build?
Calculated from
real demand and
random supply
Can see overall
effect of this
combination of
spaces
26. Problem: How much space to build?
Outcome:
The approach answers the question that you asked!
We thought we had asked “how many rooms should we build?”
We actually asked “how many rooms give us the most efficient use of space?”
29. Problem: How to structure an Induction event?
Requirements:
•2,000 participants
•During Welcome Week
•30 minutes in a large lecture theatre
•2 hours in small groups (flat rooms)
•30 minutes in a large lecture theatre
•Keep everything close together for logistical reasons.
30. Problem: How to structure an Induction event?
Questions:
•How many sessions?
•Where on campus?
•Efficient use of space
•How to divide the cohort?
•Who do we disrupt?
•Interdependencies between all these.
31. Problem: How to structure an Induction event?
We can simplify the problem a bit (“local knowledge” of best rooms)
…but there are simply too many variables to explore every possibility.
32. Problem: How to structure an Induction event?
One column for
each room, each
possible session
Use RANDBETWEEN to populate each cell with
either zero or the capacity of the room
=RANDBETWEEN(0,1) x 470
33. Problem: How to structure an Induction event?
Sum how many seats are being used.
Conditional formatting highlights
those close to 2,000 target
Highlight in amber when this
combination cannot be condensed
into 2 or fewer sessions
36. Conclusions – Positives!
It’s a powerful tool for complex problems.
It impresses academics!
Surprisingly simple to do with some Excel skills.
37. Conclusions – Negatives!
Sometimes hard to phrase the question.
You get the answer to what you ask:
…make sure you ask the right question.
…you may not like the answer.
Hard physics questions may follow.
