One of my favorite concepts from science is that of the rate limiting step. Let’s say you have a process that goes A -> B -> C -> D (A is converted to B is converted to C is converted to D). The speed / yield of the entire process depends on the slowest / least efficient step.
One example of this might be cooking. If you’re making a spaghetti dish and it takes you 5 minutes to cook the chicken and 10 minutes to cook the spaghetti, it takes you at least 10 minutes to finish the whole process because you have to wait for the slowest step.
How Does This Apply to Cases?
This comes up in case interviews as well. If you have a process that goes A -> B -> C -> D the yield of that process depends on the least efficient step. This can drastically simplify calculations because the yield of the entire process A -> D depends on the yield of the least efficient step.
Example #1: Rubber Plant Investment
One great example of this is the New Rubber Plant Investment case in Darden 2012. Basically what’s going on is you’re trying to figure out how much rubber a plant can deliver to a port for sale. The process looks like this:
Raw Material (Supplier) -> Raw Materials (Factory) -> Rubber (Factory) -> Rubber (Port)
And the raw materials are transported from Supplier -> Factory and Factory -> Port by Trains. It turns out we have the following data about each of these processes:
Raw Material (Supplier) -> Raw Materials (Factory) – The train can transport 16 million tons worth of raw materials / month (note that 3 tons of raw material is converted to 1 ton of rubber, so 16 million tons of raw material / month is 5.33 million tons worth of rubber / month)
Raw Materials (Factory) -> Rubber (Factory) – Can produce up to 10 million tons of rubber / month.
Rubber (Factory) -> Rubber (Port) – Can transport up to 5 million tons of rubber / month.
So based on what we said earlier, the least efficient step is the last step, which means at most we can produce 5 million tons of rubber / month. If we try to make more it will just stockpile in the factories. The total yield is limited by the least efficient step.
Example #2: Carwash
I recently did a case where I had to figure out how many cars a carwash did per hour. See if you can use the rate limiting step concept to figure it out:
Prompt: The car washing process has 3 steps, a prewash, wash, and postwash which take 5, 10, and 12 minutes respectively. How many cars can this carwash potentially service per hour?
Example 2 Answered
The rate limiting step is step # 3, so the total number of carwashes per hour is 60 minutes * 1 carwash / 12 minutes = 5 carwashes. You could also try to draw it out if you want to prove it to yourself.
If you have a multi step process and need to figure out its speed / yield, figure out the speed / yield of the slowest step. You’ll most commonly come across these sorts of situations in process improvement cases or any sort of case that has multi step processes.
Hope it helps!