Problem $3$

The assembly of a dresser requires $9$ tasks. The tasks, their precedence relationships, and the task times in minutes are given in the following table:

$\backslash$table$[[$Tasks$,\backslash$table$[[$Immediate$],[$Predecessor$]],$Task Time $($in minutes$)],[$A$,$NONE,$10],[$B$,$A$,2],[$C$,$B$,4],[$D$,$B$,6],[$E$,$B$,4],[$F$,$C$,$ D$,8],[$G$,$F$,7],[$H$,$E$,$ F$,6],[$I$,$G$,$ H$,5],[$Total$,,52]]$

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

b$.$ If $200$ dressers are to be assembled in a $40-$hour work week, 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$).$