average $85\%.$ They notes that there are $30,000$ pencil blanks in work$-$in$-$process inventory between the Cutting and Inserting.

Insert Department

In the Insert Department, the operator inserts a graphite rod into the center of the pencil blank. There is no setup required for this operation. After watching the Insert Department for $20$ minutes, $375$ pencils were processed through the department. One person works in this department. There are $18,000$ pencils are sitting in an inventory staging area waiting to have erasers attached. Uptime is on average $95\%.$

Eraser Department

In the Eraser Department, the pencils are banded with a metal band and an eraser is crimped into place. There is no setup required for this process. Currently, six eraser installers work in this department; each operating one of six eraser installing machines. After watching one of the operators work at this process, they observe that it takes an average of $17$ seconds for each pencil to be processed through this machine. Victoria knows that she has $6$ operators, each one installing erasers in $17$ seconds. The team notices that there are $60,000$ pencils in an inventory staging area waiting to be boxed. Uptime is on average $100\%.$

Boxing and Printing Department

The Boxing and Printing Department boxes the pencils into custom imprinted boxes. Each day, the workers receive a list of orders that should be packaged that day. Fifteen $(15)$ people work simultaneously during the shift, but only $3$ are printing and boxing for this product family of wood pencils. After watching the department for $20$ minutes, the improvement team notes that one of the average workers has boxed $60$ pencils. Victoria calculates the Cycle Time for this operation by dividing $1,200$ seconds $[20$ minutes x $60$ seconds$]$ by $60$ pencils resulting in $20$ s econds per pencil. Uptime is on average $100\%.$

Finished Goods Storage Area

CWI maintains boxed products in the finished goods storage area for customers that order on a routine basis. Victoria and her team note that there are currently $60,000$ pencils in finished goods storage.

C$/$O $=$ Changeover or Setup time

C$/$T $=$ Cycle time

Questions

$1)$ Use the data provided above to calculate: a$)$ takt time; b$)$ total production lead time; c$)$ total processing time; d$)$ the capacity of each process step and the capacity of the whole the value stream.

$2)$ Victoria decides to re$-$distribute the work among the employees at the Printing and Boxing area to achieve a cycle time that would be enough for an increase in daily demand to $6,000$ pencils a day, working $8$ hours per day. Use the Work elements table at the answer sheet to: a$)$ calculate cycle time; b$)$ define how many employees are needed for this assembly line; c$)$ calculate efficiency of the assembly stations; and d$)$ determine the work balance per station.

FOR the Value Stream Mapping and questions $1$a$,1$b and $1$c$,$ please answer and fill out the Excel document. Upload both documents. Show math in all your answers!

$1.$d$)$ Capacity of each process and the capacity of the whole value stream

$1.$d$\mathrm{.}1)$ Capacity of Cutting

$1.$d$\mathrm{.}2)$ Capacity of Insert

$1.$d$\mathrm{.}3)$ Capacity of Erasing

$1.$d$\mathrm{.}4)$ Capacity of Boxing and Printing

$1.$d$\mathrm{.}5)$ What is the Capacity of the whole value stream?

$2)$ Work balance $$ Theory of Constraints

$2.$a$)$ Calculate Cycle time

$2.$b$)$ Define how many employees are needed for this assembly line

$2.$c$)$ Calculate the efficiency of the assembly line

$2.$d$)$ Determine the work balance per station