UofA MCM/ICM Qualification Competition

Fall semester 2012

Choose one of the two problems.
Solve and write a PDF report.
Submit electronic solutions (report and if applicable e.g. Matlab code and data you uses) by 2pm on Sat Nov 17 2012 to pass@ualberta.ca, jag@cs.ualberta.ca

You can work where you like (at home or in the library), and be alone or in groups of up to three. For groups we ask that you identify in the report who did what aspect.

Q1: Pizza places often have a maximal delivery radius or a delivery area. Having a larger radius results in more customers; on the other hand, longer deliveries cost the company more money.

Suppose you are planning to open a pizza place located on the U of A campus. What should your delivery radius or area be?

There are many different factors to consider with this problem. For example, you might start by assuming that the production capacity (that is, the number of pizzas that you can produce in a one day) is fixed, and try to determine the minimal delivery radius so that capacity is exhausted (ie, all the pizzas you can make get bought). However, in the real world, you can increase your production capacity, for a cost (for example, by buying more ovens or hiring more cooks).

Other factors you may wish to consider: is there a certain distance beyond which it is not profitable to deliver pizzas? Should the delivery area be the interior of a circle, centred at the pizza place, or is there a more beneficial shape? What about delivery fees?

Q2: In winter what is best practice to start your car? Many turn the engine on and let it sit idling until warm. Some use an electric block heater. Considerations may be comfort of occupants (car should be warm when entering), wear or drive-ability issues with the engine (particularly on older engines or Diesels). Idling and electric preheating of course uses energy. (and also contributes to engine wear)
Things you may consider:

There may be many types of priorities, models and conclusions. What might be a "best practice" procedure considering both the energy used and comfort of occupants? You may tolerate more than your grandmother.