There is a feature of F# this is incredibly powerful and rarely talked about: The Object Expression. It is such a simple idea that it is almost boring but the implications of it are profound. We often define an interface to abstract the implementation of an object so that we can code against different implementations. By programming against an IEnumerable or IDictionary, we can write algorithms which work against a host of different backing data structures....

There are few things I love more than a fresh mathematical planning challenge so I was delighted when Kevin Avignon reached out to me and asked me to look at a question he had posted on the Software Engineer Stack Exchange site. He wanted to know whether the question was a candidate for Mathematical Planning. The question is a really interesting problem of pairing Mentors and Mentees. Mentors have a set of skills they can teach....

Recently I was asked if it would be possible to add the log function to the Flips library. Flips is a library for modeling and solving Linear and Mixed-Integer Programming problems. Both classes of problems are constrained to only having linear (i.e. straight) lines. You may ask, “What do you mean by straight?” The following are examples of linear functions. $$ \displaylines{ \text{Linear Functions}\\ y=1.0x+2.0 \\ y=2.0x_{1}+3.0x_{2} \\ y=1.2x_{1}+1.7x_{2}+x_{3} } $$...

I was recently asked by someone, “What do I need to do to get into Machine Learning and Finance industry?” I told them that I would think about it and get back to them. I have been in many interviews for Machine Learning Engineers and I do have a set of questions that I frequently use to get a feeling for where someone is in their career and where they are hoping to go....

I am on a bit of a quest to bring Mathematical Optimization to the masses, or at least to Software Developers. I often come across problems where people are wanting to find the best plan for their problem but they lack to tools to express the problem. Typically the way this is “solved” is by some domain expert coming up with a laborious heuristic in Excel which involves outrageous amount of copying and pasting....

Previously I described how we can perform Discrete Optimization using the Branch and Bound technique. Today I want to describe another foundational technique for Discrete Optimization, Cutting Planes. Cutting Planes is like the Branch and Bound technique in that it uses a series of LP Relaxations to search for solutions. Where it is different from Branch and Bound is in how it refines the LP Formulations. Branch and Bound would subdivide the solution space by branching on a decision variable and creating two new subproblems....

If you have spent any time with me you will know that I am passionate about Optimization. Now, you may pass this off as a bit of geekiness on my part but the reason I care about Optimization is that it has profound implications for how we care for people. When I get a moment to describe Optimization to someone the way I start off is by saying, “Optimization is the mathematics of caring for people....

One of the reasons that I love F# is that is makes it incredibly easy to model domains. By creating a Domain Model which represents the business domain it becomes relatively easy to create workflows and algorithms which streamline business processes. In this post I show how to create types for a domain which are summable, a feature I use frequently in my work. The Value of Restricting Values When I have to create a new Domain Model one of the first things that I do is define a single case Discriminated Union of decimal for the basic building blocks that I am going to work with (Costs, Items, Sales Rates, Days of Inventory, etc....

I recently attended a training event hosted by Gurobi. For those who don’t know, Gurobi produces one of the best mathematical solvers in the industry. It was a great event and we were able to spend ample time with engineers and experts in the field. Using a mathematical solver requires the ability to formulate models and at this time one of the easiest languages for doing that is Python. Python is a great language for many use cases....

I am a huge fan of Domain Driven Design and I have been trying to apply it more and more. I ran into a problem last week that kept beating me over the head though. I kept using a bottom up approach and kept coming up with terrible solutions. Finally, I took a more outside to in approach which cleaned up the solution. I credit Mark Seemann for the idea to work from the outside in....