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Solving The Brachistochrone Problem in Construction

Posted by Jerry Chabot on Oct 26, 2018 1:21:34 PM
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The brachistochrone execution plan Has A slow start but a fast finish

Because you clicked on a blog with a title like "Solving The Brachistochrone Problem in Construction," you must be naturally inquisitive. That’s great, because you're the kind of people we need in construction if we are going to solve the time, labor, and cost problems that we all wrestle with every day. Inquisitive people are always looking to learn new tricks and evaluate new approaches. 

Hopefully I will be able to reward your curiosity by explaining the Brachistochrone Problem and how to solve it in the construction process with a well-executed Virtual Design and Construction (VDC) approach combined with an aggressive prefabrication plan.

The Brachistochrone Curve


If I have lost you already but you are still interested in “building better-smarter-faster” then just skip to the end for the punchline.

As an engineer, I had to take a lot of math in college. A lot of math. Oddly, just like that manual drafting course, I don’t actually get the opportunity to apply the advanced calculus at work as often as you might think. When I do discover a corollary between the mathematical model of the world around us and what we do for work in advanced construction, I get pretty excited. The brachistochrone curve is one of those times.  

On the off chance that you are not already familiar with the concept of a brachistochrone curve, it is the fastest path between two points down which a theoretically frictionless ball, acting under the forces of gravity, will travel. It turns out that the shortest path is not the fastest path, and in fact, the shortest duration of travel follows a cycloid (the black curve). Pretty cool, eh?

Ok, that's interesting if you are a math nerd, but what does it have to do with construction? The Engineer – Procure – Construct (EPC) process that we do every day is actually attempting to solve this very Brachistrochrone Problem.

Solving the Brachistochrone Problem in construction requires determining the path with the shortest duration from point A to point B given the parameters of A and B in your specific case. Think of that case as your project, and points A and B are the start and end date your client has demanded.

How the heck are you going to pull that (usually unreasonable) schedule off with the skilled labor shortage and constrained site conditions you currently face? And oh, by the way, the project is underfunded by about 20%. You need to find that brachistochrone curve for the project and map that out in a schedule and execution plan to arrive at the best achievable schedule. “But teacher, I will never use math in real life!”

Working at a project-based company in the construction industry, every day is a deadline or a path towards a deadline. My job as the president of a construction engineering firm is to look at the problem and lay out a plan to meet the need in the time allotted. I like to think we are innovators in advanced construction technology.

We focus on construction productivity measures and apply more detail engineered, standardized, well planned methods and logistics to achieve successful outcomes for our clients and construction partners. We find the brachistochrone curve for complex projects and develop the tools and methodologies during programming to create a detailed project execution plan that allows us to follow that path of least duration.

Seems great right? Who would not be on board with that!? Interestingly enough, one of the biggest challenges that we face is often the client. Take another look at that cycloidal path that we are following:

Brachistochrone Problem Infographic-1Point A is project kick off. Point B is substantial completion of the actual construction activities. That bright red line sure looks like the fastest solution to point B, but in fact, the cyan curve is the shortest duration.

Managing the client during the first third of the project as you head off on what appears to be the slower path can be a challenge. Once we have “issued for construction” drawings or an awarded contractor, the Owner wants to see work happening on the job-site right away. After all, the schedule is really aggressive!

Our experience has proven to us that without a doubt the fastest way to get the project built is to go to BIM and start construction modeling and undertake a robust 3D coordination process. Great, I can sell that to the Owner. Some weeks go by and then we have an approved, coordinated model approved. The Owner again expects to see services going into the building and trade subcontractors running all over the place welding and cutting and fabricating. Well, that is still not what happens!

Instead, we take the coordinated model and start fabrication detailing. We break the services down into either detailed spool drawings that can be fabricated off-site, or perhaps even large scale modular sub-assemblies that can be partially erected off-site and brought to the job with all those labor hours already completed elsewhere...not where the Owner can see them! This can be a challenging “sell” to the guy paying your invoices or heatedly pointing to the looming schedule completion dates. They have to trust you and trust that we are on the brachistochrone curve.

It is worth mentioning, of course, that you also can’t get too hung up on CAD tools and process. You need to be both smart and pragmatic. You can’t let perfection get in the way of progress. That would put you on one of the longer and slower curves. You need the experience and knowledge to optimize those processes.

Slow Start, Fast Finish

The brachistochrone execution plan has a slow start but a fast finish, and often is still accelerating across the line as construction proficiency improves. It can be quite disruptive to the traditional “stick built in place” project schedule, and you have to build that trust in all the stake holders. It can get pretty uncomfortable in those first few project status meetings. We succeed by holding to our pragmatic plan and not bending to the pressure to "do a thing to look like we are doing a thing" because we trust in our process. We've proven it - it’s simple math!

Topics: construction productivity