Summation notation and sizing the kanban bus route

Σ or Sigma is the Greek upper case capital letter S and is used in mathematics to represent summation or addition of a series of elements or set of data values.
x1, x2, x3, ... xn is a set of numbers. x1 is the first number in the set, xi is the 'i'th number, xn is the last of n numbers.
Elements can be simply adding up a set, or more involved such as summing squares or other algebraic equations.

summation notation

Example - in kanban or point of use replenishment planning it's important to make sure that the material handler or water spider has enough time to travel from point to point and complete an entire circuit or bus route in a predictable period of time. It may not be possible, practical, or even necessary for parts to be delivered to or removed from the production cell or point of use every single takt cycle, but we do want to be regular and predictable, and so we will make deliveries and pickups in a multiple of takt time, otherwise known as a pitch.

Pitch = Takt Time * N

T = transport or walk time, A = number of stops
R = replenishment picking time, B = number of pick points
P = point of use restocking time, C = number of restock points
N = number of takt that elapse during water spider’s circuit or route

Pitch might be every 45 minutes, or twice a shift, or however long it takes to empty or fill a container.  The Lean Lexicon defines pitch as the amount of time needed in a production area to make one container of products.  We'll expand that definition to be simply a multiple of takt.

Other factors: shopping cart (or train) size, number of different parts being picked, demand or replenishment time variation.

bus route

Translated in to English ... add up the time T that it takes to travel from stop to stop, then add up the times R in the supermarket that it takes to pick each part for each stop, and the same with the times P to restock every item needed at each stop, and finally make sure the total time is less than the Pitch Time.

 Footnote:  This formula is for a coupled route.   For a decoupled route just eliminate the Rjsummation.