$1$ Warehouse Order Picking Optimization

A warehouse processes orders with the following tasks, their times, and dependencies:

Additional Information

The warehouse needs to process $60$ orders in a $10-$hour shift $(600$ minutes$).$

The goal is to balance the picking process using the minimum number of workers while

respecting task dependencies.

Formulas

Cycle Time $($CT$)=$ Total shift time $-$: Orders per shift

Minimum number of workers $=$ Total task time $-$: Cycle time $($rounded up$)$

Tasks

a$)$ Calculate the cycle time required to meet the order processing rate. Round to two decimal

places.

b$)$ Determine the minimum number of workers needed without exceeding the cycle time.

$2$ Electronics Assembly Line

An electronics manufacturer assembles a gadget with the following tasks:

Additional Information

The production target is $500$ units per $6-$hour shift $(21,600$ seconds$).$

The assembly line must be balanced to minimize workstations while maintaining task order.

Formulas

Cycle Time $($CT$)=$ Total available time $-$: Units per shift

Minimum workstations $=$ Total task time $-$: Cycle time $($rounded up$)$

Tasks

a$)$ Compute the cycle time needed to achieve the production target. Round to one decimal

place.

b$)$ Find the minimum number of workstations required without violating the cycle time.

A bakery produces cakes with the following tasks and dependencies:

Additional Information

The bakery aims to produce $80$ cakes during a $12-$hour shift $(720$ minutes$).$

The goal is to balance the production line with the fewest workstations possible.

Formulas

Cycle Time $($CT$)=$ Total shift time $-$: Cakes per shift

Minimum workstations $=$ Total task time $*$ Cycle time $($rounded up$)$

Tasks

a$)$ Determine the cycle time required for the production goal. Round to two decimal places.

b$)$ Calculate the minimum number of workstations needed to stay within the cycle time.

$4$ Automotive Parts Assembly

An automotive supplier assembles a component with the following tasks:

Additional Information

The target is to assemble $100$ components in an $8-$hour shift $(480$ minutes$).$

The assembly process must be optimized to use the minimum number of stations.

Formulas

Cycle Time $($CT$)=$ Available shift time $-$: Components per shift

Minimum stations $=$ Total task time $*$ Cycle time $($rounded up$)$

Tasks

a$)$ Calculate the cycle time needed to meet the production target. Round to two decimal

places.

b$)$ Determine the minimum number of stations required without exceeding the cycle time.

$5$ Furniture Manufacturing Line

A furniture company builds chairs with the following tasks:

Additional Information

The goal is to produce $50$ chairs in a $10-$hour shift $(600$ minutes$).$

The production line must be balanced to minimize workstations while respecting task or$-$

der.

Formulas

Cycle Time $($CT$)=$ Total shift time $-$: Chairs per shift

Minimum workstations $=$ Total task time $-$: Cycle time $($rounded up$)$

Tasks

a$)$ Compute the cycle time required to achieve the production rate. Round to two decimal

places.

b$)$ Find the minimum number of workstations needed without violating the cycle time.

$6$ Packaging Line Optimization

A packag$2$