Mathias Brandewinder on .NET, F#, VSTO and Excel development, and quantitative analysis / machine learning.
by Mathias 24. July 2010 17:35

When I moved to California a few years back, I soon realized that to get anything done in the Silicon Valley, you pretty much have to have a car. So, I purchased my first car. Fast forward today: I live in San Francisco now, and noticed that I am driving less and less. Bicycle is very convenient in my neighborhood, and I don’t have to commute to work on a daily basis. Which got me thinking – do I really need a car? Public transportation only is not an option, because coverage is too spotty, but what about using a car sharing service?

The 2 major services available in my area are ZipCar and CityCarShare; their pricing system is largely similar: they both:

  • charge by the hour of usage,
  • charge a higher cost over the week-end,
  • offer a discount for full-day rental,
  • have a pay-as-you-go option, and better rates with minimum commitment plans.

Both include gas, with one difference: ZipCar charges by the hour, whereas CityCarShare has a hybrid pricing, with a lower per-hour cost, and a per-mile cost.

By contrast, when you own a car, you

  • pay a large upfront investment (buying the car),
  • recoup some of the upfront cost if you resell eventually.
  • pay regular fixed costs (insurance, registration taxes, garage),
  • pay by the mile (gas),
  • pay some additional costs, like maintenance, which are somewhat linked to mileage.

In addition to that, you bear the risk that your car gets damaged or totaled in an accident.

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by Mathias 3. September 2009 17:50

In my last post, I illustrated how to quickly to pick the best value from a selection to get the optimal result, by using Excel Data Tables. This time, we will see how to pick the best possible pair of values.

We are trying to figure out which 2 bridges we should build, in order to minimize the overall travel time for the inhabitants of the island.

Island

I worked out the math for one bridge last time. We will start we a similar setup, but adjust our spreadsheet so that for each islander, we compute the travelling distance for 2 bridges, and select the shortest route.

image

The ranges B1 and B2 are named Bridge1 and Bridge2. Column I now contains the formula computing the shortest route for each islander. For row 5 for instance, the formula is

=MIN(D5+E5-H5,F5+G5-H5)

Cell I10 is the total of the vertical distances travelled by each individual.

We can select from 4 bridge locations: 2, 4, 7 and 12. What we need is to find out which 2 numbers give us the lowest total travel. Let’s build our data table, this time using 2 bridge positions.

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by Mathias 28. August 2009 17:54

In the current issue of OR/MS Today, I came across this nice optimization puzzle, “Bridges to Somewhere”. There are these two islands. Five people A, B, C, D and F live on the first island, and need to commute to work to the second island. Individual A lives in the spot marked A, and needs to go to spot A on the second island – and so on for the 4 others. People can travel only vertically and horizontally (no diagonals), and will always take the shortest path available.

image

There is currently no bridge between the islands, but a budget for 2 bridges has been approved (the island just received a stimulus package). There are 4 bridge proposals to chose from (One, Two, Three and Four on the map). Which 2 bridges should be built to minimize the travel distance of the population?

Before trying to figure out which 2 bridges are best, I thought it would be interesting to investigate a simpler problem: if you could build one bridge anywhere, where should you build it?

There are a number of ways you could resolve this using Excel; I will illustrate how to find the best solution, using Excel Data Tables.More...

by Mathias 25. April 2009 11:06

Via Andew Gelman, a really cool text visualization project. It might or might not be insightful, but it’s beautiful, and the guys who put this together have really made this very cool – you can see the entire text of Alice in Wonderland scroll, simultaneously plotting the word relationships as the story progresses. Amazing.

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