In March 2016, ICMS ran a Modelling Camp. The students were from the Maxwell Institute CDT and public applicants. Public Applicants came from across Scotland, North of England and Europe. The MI‐NET COST Action TD1409 funding enabled us to be meet the bulk of the travel and accommodation costs of the non‐local students as well as the costs of the instructors. The MI‐NET funding also contributed to the local catering costs.
30 PhD students considered 4 problems:
1. Forecasting periods of maximum electricity consumption ‐ societal/economic impact
2. Brewing Filter Coffee ‐ economic/societal impact
3. Bottle testing ‐ economic impact: reduction of costs
4. Optimal Resource Allocation across Advertising Budgets
Each problem team had an allocated instructor, who gave an initial presentation on the problem, and provided guidance throughout the week. The advertising budget problem was also support by the company Skyscanner, who set the problem in conjunction with Paul Johnson (University of Manchester) and provided data and guidance throughout the week. Following a structure akin to the Study Groups, students formed into small teams after a morning listening to the problem description.
The following days predominantly involved group working under the guidance of the problem instructors. In addition there was a plenary talk by Tony Mulholland (University of Strathclyde).
Students gave regular presentations/updates on progress throughout the week:
Problem Descriptions and Results
Students gave presentations on their work on the last day of the workshop. They were asked to recap the problem, outline their approach, detail any results and highlight future work options.
Electricity
Electricity companies wish to reduce energy consumption during peak times in the winter period. Electricity companies, add a surcharge to the three half‐hour periods of highest energy consumption (triads) retrospectively. These `Triads’ must be spaced by at least 10 days. Electricity companies issue warnings. Aim is to reduce the number of false warnings to electricity customers, whilst ensuring the triads are captured.
The group originally considered the Secretary Problem, and extension of the Secretary Problem using a numerical method. With the insight this provided they moved to an alternative method which used historical weather data and forecasting inputs. They created a mathematically justified algorithm which resulted in issuing fewer warning than the electricity company.
The group highlighted, the triad spacing, forecasting uncertainty and warnings producing negative feedback as areas for algorithm refinement.
Coffee
World‐wide there is a large and expanding market for filter coffee machines. This project focussed on modelling the extraction of coffee within a coffee machine, with the eventual aim of designing coffee machines that can robustly produce good coffee. Experimental data on coffee extraction was provided.
The team developed a basic model, which for a given geometry of the coffee bed predicts the quality of the coffee. The model showed more coffee is extracted at the top of the filter rather than at the bottom due to the lower pressure and lower velocity a decrease in the angle of inclination of the filter leads to an increase in the concentration of coffee in the solution a prediction that the height of the coffee bed along the filter should be in the range 0:8 < h < 1 cm
The team suggested that straightforward extensions of that weeks’ work could include 3D axisymmetric model, variable h. Further improvements to the model could consider the process of a coffee bed deformation and chemical impact.
Bottle Testing
A company’s quality control of the containers it produces involves testing for leaks. The standard initial test is noisy: about 8% fail, but only about 0.4% are judged to fail a secondary test. How can one bring down the false negatives without introducing too many false positives?
The team considered three different models for the existing problem, a Deterministic Model, a Statistical Model and a Stochastic Model. The team’s method cut the probability of accepting a bad bottle from 3/2000 to 1/2000; and, cut the probability of rejecting a good bottle from 163/2000 to 84/2000. The approach cannot eliminate the probability that the good bottle is rejected (or that a bad bottle is accepted) but the team’s model was shown to be more accurate than the existing model used by the company.
The team suggested that the statistical and stochastic model should be tested further with the input of real data.
Advertising Budgets
- Problem:
How to allocate resource to different channels for advertising budgets. Background models for investment on financial markets were highlight
ed, and an existing industry model was provided. Constraints regarding increases/decrease
s in each channel were provided and a constant budget was assumed.
With the support of the Skyscanner attendees, the team consider a series of modifications to the existing model. This included consideration of linear, log linear and quadratic model variations. The team were provided with real data and were able to assess the percentage error for the various approaches. The refinements suggested by the team appeared to reduce the error substantially and provide a better fit to the real data.
Items for further work suggested by team were changing the boundaries, adding noise to the model, allocated vs spent, risk, incorporate more data and experimenting to validate the model.
After deliberation by the instructors and ICMS Scientific director, David Abrahams, and MIGSAA Deputy Director, Dugald Duncan, the prize was awarded to the Electricity Problem Team. All teams were commended on their efforts and team working throughout the week.
Feedback and Future Modelling Camps
The modelling camp has received really strong feedback with all the students who responded to the questionnaire confirming that they had found the modelling camp useful and would recommend other students participate in a similar event. Students seemed to particularly enjoy the experience of working in teams on a shared problem. Several highlighted listening to the final presentations and seeing how each team had coped with their specific problem as very instructive.
Additionally students/instructors were asked to make suggestions for improvements.
Compiled comments/recommendations from the feedback and organisers observations are provided below.
Role of the Facilitator
On the first day during team forming some of the problems proved more popular than others. Thankfully one of the modelling camp facilitators was able to resolve this and allocate people across the four problems without too much dissent. Additionally, most of the instructors/facilitators had significant experience of study groups which meant that the team‐working activities required very little additional support. There was only 1 instructor who did not have much experience of these type of activities and he was able to gain support from the others. We’d recommend that the bulk of the instructor/facilitator roles are undertaken by people with relevant experience.
Timing
Scheduling of events is always tricky and we will never please everyone. It transpired that there was a conflicting deadline for many of the local students which effected their ability to fully enjoy the week. Future events (especially if we follow a similar model with a significant proportion of local students) should be mindful of these clashes.
Team Sizes
The team sizes ranged from 6‐10. Feedback varied for this. Some students recommended that group sizes be limited to 3‐4 whilst others felt the group sizes were about right. As one of the aims was to prepare students for Study Groups where the study groups are significantly larger it would be wise not to make the groups too small, however it may be wise to cap the upper limit at 10.
Future Modelling Camp and Funding
ICMS would be keen to hold further Modelling Camps. An annual event has been recommended. It also been recommended that these could be complimentary to modelling camps run at Oxford University. This modelling camp benefitted from funding from MI‐NET, MIGSAA CDT and Skyscanner. As a result we were able to support the bulk of the student costs. ICMS would plan to submit a proposal to MI‐NET to support a 2017 Modelling Camp.
Advance Material
Several students commented that they would have liked to have had material in advance regarding the problems. This will be considered, but there are disadvantages, it puts extra preparation on the instructors and it may make the distribution of people across teams more difficult if people have developed strong preferences.
Company Links
The Modelling camp proved an excellent forum/opportunity to establish links/contact with local Edinburgh company, Skyscanner. Students really seemed to appreciate having a company’s perspective. Skyscanner also commented that they found the modelling camp an excellent way of finding out different perspectives and exploring ideas, indeed we understand that one of the PhD helpers at the modelling camp has subsequently undertaken a placement at the company. Future modelling camps should aim (where possible) to have continued company involvement.
Links to Study Group
All participating students were encouraged to sign up to the 2016 Study Group at Durham. The timescales between the modelling camp and study group were relatively short, so there was enough notice for some of the students to be able to make the time commitment. Future Modelling Camps should make students aware of the Study Group timings and opportunities well in advance.
“a very enjoyable experience for me, and very well run. I would certainly be very happy to participate in future modelling camps and recommend them to my colleagues/students.” – Instructor
“I learned a lot from this Camp and I had a lot of fun as well.” – Student
XI Forum Mathematics-Industry 
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