A facility that operates during $450-$minute shift per day produces a product whose manufacturing

process consists of tasks A$,...,$ J$.$ Operation times for these tasks and data on predecessor tasks is

provided in the table below. The precedence of tasks is also represented pictorially in the figure

below.

a$)(3$ Points$)$ What is the minimum possible cycle time for this process? $11\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

b$)(2$ Points$)$ What is the maximum cycle time for this process? $59\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

c$)(5$ Points$)$ What is the largest cycle time that will ensure a shift output of $16?$

$450$

$16=28\mathrm{.}125$; The cycle time is the floor of the number, or $28$

d$)(5$ Points$)$ What the number of workstations for the cycle time in part c$)?59$

$28=2\mathrm{.}107$; Ceiling is $3$

e$)(5$ Points$)$ Configure the line efficiently $($i$.$e$.$ using the fewest possible number of workstations$)$

so that the shift output in part f$)$ is ensured.

Station $1$ A$,$ B$,$ C $(5+8+9=22)$ Station $2$ D$,$ E$,$ F$,$ G$,$ H $(8+3+2+4+5=22)$

Station $3$ I, J $(11+4=15)$ Tasks assigned to Station $4\_\_\_\_\_\_\_\_\_\_\_\_$

f$)(5$ Points$)$ What is the cycle time of the configuration in part e$)?$ max$\{22,22,15\}=22$

g$)(5$ Points$)$ What is the efficiency of the configuration in part e$)?59$

$3\backslash$times $22=\mathrm{.}894$; $89\%$

Task

Operation time

in minutes

Predecessor

tasks

A $5$ N$/$A

B $8$ N$/$A

C $9$ A$,$B

D $8$ C

E $3$ D

F $2$ E

G $4$ D

H $5$ G

I $11$ F$,$H

J $4$ J

A

D

F

C

B

E

G

JI

H

A

D

F

C

B

E

G

JI

H