Problem $3$

A dress$-$making operation is being designed as an assembly line. The table below shows the tasks that need to be performed, their task times, and preceding tasks.

$\backslash$table$[[$Tasks$,$Description,Immediate Predecessor,$\backslash$table$[[$Task Time$],[($in seconds$)]]],[$A$,$Cut dress body,NONE,$60],[$B$,$Cut sleeves,NONE,$90],[$C$,$Cut collar,NONE,$40],[$D$,$Sew dress body,A$,120],[$E$,$Sew sleeves to dress,B$,$ D$,45],[$F$,$Sew collar to dress,C$,$ D$,75],[$G$,$Hem dress,D$,$ E$,$ F$,70],[$H$,$Package dress,G$,100]]$

a$.$ Draw a precedence diagram that shows the precedence relationships among tasks for this assembly operation.

b$.$ If $180$ dressers are to be assembled in a $8-$hour work day, what is the cycle time?

c$.$ What is the minimum number of workstations required to balance this assembly line?

d$.$ Assign tasks to workstations using the most$-$following$-$tasks rule as the primary rule and the ranked$-$positional$-$weight rule as the secondary $($breaking tie$)$ rule.

e$.$ Compute the balance efficiency and percent delay $($percent idle time$).$