Chapter $6$ Problems $1$&$2$

An assembly line with $17$ tasks is to be balanced. The longest task is $2\mathrm{.}4$ minutes, and the total time for all tasks is $18$ minutes. The line will operate for $450$ minutes per day.

a$)$ What is the minimum number of workstations needed if the output rate is to be $180$ units per day?

b$)$ What cycle time will provide an output rate of $125$ units per day?

c$)$ What output will result if the cycle time is $($i$)9$ minutes? $($ii$)15$ minutes?

A manager wants to assign tasks to workstations to achieve an hourly output rate of $33$ units. Assume that the shop works $60$ minutes per hour $($i$.$e$.$ no breaks$).$

a$)$ Assign the tasks shown in the following precedence network $($ times are on the nodes and are in minutes$)$ to workstations using the following heuristic rules:

i$)$ Assign the task with the most followers.

ii$)$ Tiebreaker: assign the task with the longest time.

b$)$ What is the efficiency?