$11$ Problem $1$: Electronics Assembly Line

An electronics factory assembles circuit boards with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $3\mathrm{.}2$

B $2\mathrm{.}1$ A

C $1\mathrm{.}8$ A

D $4\mathrm{.}0$ B$,$ C

Additional Information:

$$ Target: $150$ circuit boards in an $8-$hour shift $(480$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:

a$)$ Calculate the cycle time required to meet the production goal. Round to two

decimal places.

b$)$ Determine the minimum number of workstations needed within the cycle time.

$2$ Problem $2$: Furniture Manufacturing

A furniture factory produces chairs with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $5\mathrm{.}0$

B $3\mathrm{.}5$ A

C $2\mathrm{.}8$ A

D $4\mathrm{.}2$ B

E $3\mathrm{.}0$ C$,$ D

Additional Information:

$$ Target: $100$ chairs in a $10-$hour shift $(600$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:

a$)$ Calculate the cycle time required to meet the production goal. Round to two

decimal places.

b$)$ Determine the minimum number of workstations needed within the cycle time.

$3$ Problem $3$: Toy Production Line

A toy factory manufactures dolls with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $2\mathrm{.}5$

B $1\mathrm{.}9$ A

C $3\mathrm{.}3$ A

D $2\mathrm{.}7$ B$,$ C

Additional Information:

$$ Target: $200$ dolls in a $7-$hour shift $(420$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:

a$)$ Calculate the cycle time required to meet the production goal. Round to two

decimal places.

b$)$ Determine the minimum number of workstations needed within the cycle time.

$4$ Problem $4$: Automotive Parts Assembly

An automotive factory assembles car components with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $4\mathrm{.}5$

B $2\mathrm{.}0$ A

C $3\mathrm{.}8$ A

D $5\mathrm{.}1$ B

E $2\mathrm{.}9$ C$,$ D

Additional Information:

$$ Target: $90$ components in a $9-$hour shift $(540$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:

a$)$ Calculate the cycle time required to meet the production goal. Round to two

decimal places.

b$)$ Determine the minimum number of workstations needed within the cycle time.

$5$ Problem $5$: Packaging Line

A packaging facility prepares boxes with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $1\mathrm{.}5$

B $2\mathrm{.}2$ A

C $1\mathrm{.}8$ A

D $3\mathrm{.}0$ B$,$ C

E $2\mathrm{.}5$ C

Additional Information:

$$ Target: $180$ boxes in an $8-$hour shift $(480$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:

a$)$ Calculate the cycle time required to meet the production goal. Round to two

decimal places.

b$)$ Determine the minimum number of workstations needed within the cycle time.

$6$ Problem $6$: Food Processing Line

A food processing plant prepares meals with the following tasks:

Task Time

$($min$)$

Immediate

Predecessor$($s$)$

A $3\mathrm{.}0$

B $2\mathrm{.}5$ A

C $4\mathrm{.}0$ A

D $3\mathrm{.}2$ B

E $2\mathrm{.}8$ C$,$ D

Additional Information:

$$ Target: $120$ meals in a $6-$hour shift $(360$ minutes$).$

$$ Optimize the production line to use the minimum number of workstations.

Tasks:$2$

a$)$ Calculate the cycle time required to meet the production goal. Ro