Honestly, the last bit of formal and substantive math that I worked with was back in college. Many, many years ago, I received a B.S. in Mathematics, but other than the diploma, there is little physical or intellectual (!!) evidence that would support this reality.
My former classmates might say the same was true way back when. My kids? Well, they used to hesitate before asking me to help them with their math homework.
...Which is exactly why I associate with really smart folks like my Lean MathTM blog co-founders Larry Loucka and Michael O'Connor (a.k.a. Dr. Mike - seems he has a Ph.D. in Physics).
In any event, it's tough to write about math without using mathematical symbols and notation. I know, you're probably on the edge of your seat right about now. This is going to get really, really exciting, right?!
No, obviously, it's not. But, we need to cover this sooner or later. This post will find its rightful place in the archives and the symbols are permanently posted under the "Symbols" menu tab.
So, without further ado, please check out this very cool and oh, so unique table below.
As you most likely noted in the table, certain variables were referenced, for example x, a, b, A, and B. Most Lean MathTM entries have at least one formula with multiple variables. These variables, virtually always independent variables in that they are inputs into a system, represent a value that may change within the scope of the problem or operation. For example, work content (Wc) and takt time (Tt) within the optimal staffing model are independent variables. They are what they are.
Typically variables have single-symbol names, with constants from the beginning of the alphabet (e.g., a, b, and c) and variables from the end (e.g., t, x, y, and z). You can thank the 17th French philosopher and mathematician, Rene Descartes, for that. The single symbol names are usually italicized and are often lower case. Oh, and upper case variables are traditionally used for random variables within probability and statistics. All that we can say is that we tried our best to follow these conventions, but we’re pretty sure that we broke, and will break, more than a few rules here and there.
Honestly, the easiest notation many times is no notation. For example:
Who can’t understand that?!
The problem is that more complicated formulas end up being way too long for the printed page. This requires very tiny font and/or multiple lines on a page. Not good (according to editors)!
Furthermore, there are certain variables that are used relatively frequently with this blog. It seems that a variable such as Tt for takt time, may be the least waste way. Of course, we define our variables within every post that contains a formula.
As you’ll see we have tried to keep most variables to one letter with a subscript to further identify it – like the “T” for time and “t” for takt. Of course, this convention is not always possible and not always prudent. For example, everyone knows “WIP” as work-in-process inventory. We have no desire to needlessly invent brand new variables!
Another, occasional departure from convention is the double subscript, for example Icc is inventory carrying cost...or did we change that to Ic?! Our apologies if we have offended any math purists.
Ok, there you have it. If you made it through this post, thank you for your perseverance! Now, let's do some math!
