Via the INFORMS newsletter, I found out this cool competition (trains and analytics, how much cooler can it get?): can you find the best plan to refuel the locomotives of a railroad company?

Create a cost-effective plan to fuel the locomotives that power a railroad's trains. Specify how many fuel trucks to contract at each yard and how much fuel to dispense into the locomotives of trains that run over a specified time horizon. Ensure that no locomotive runs out of fuel en route between yards. Sounds easy? We'll see about that!

Learn more about the challenge at the competition website, and register by June 15, for glory, bragging rights, a shot at a first prize of $2,500 – and help spare some poor chaps an unpleasant day:

I have been using test-driven development since I read Kent Beck’s book on the topic. I loved the book, I tried it, and adopted it, simply because it makes my life easier. It helps me think through what I am trying to achieve, and I like the safety net of having a test suite which tells me exactly what I have broken. It also fits well with the type of code I write, which is usually math-oriented, with nice, tight domain objects.

So when I decided recently to write a C# implementation of the Simplex algorithm, a classic method to resolve linear programming optimization problems, I expected a walk in the park.

(Side note:I am aware that re-implementing the Simplex is pointless, I am doing this as an exercise/experiment)

Turns out, I was mistaken. I have been struggling with this project pretty much from the beginning, and unit testing hasn’t really helped so far. Unfortunately, I didn’t reach a point where I fully understand what it is that is not flowing, but I decided I would share some of the problems I encountered. Maybe brighter minds than me can help me see what I am doing wrong!More...

I was recently inspired by an article in OR/MS mag to write 2 posts on using Excel data tables to resolve optimization problems. As it turns out, these puzzles are not only published in the magazine: they also have their online home at Puzzlor.com. So if you like optimization and math problems in general, and like puzzles, check it out!

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.

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.

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.

More...

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.

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...