A manager wants to assign tasks to workstations as efficiently as possible, and

Question

A manager wants to assign tasks to workstations as efficiently as possible, and achieve an hourly output of 4 units. The department uses a working time of 56 minutes per hour. Assign the tasks shown in the accompanying precedence diagram (times are in minutes) to workstations using the following rules 4 4 a. In order of most following tasks. Tiebreaker: greatest positional weight. Work Station Tasks Click to select) A, G F, A, G IV D, B, C b. In order of greatest positional weight. Work Station Tasks (Click to select) (Click to select) (Click to select) Click to select) IV c. what is the efficiency? (Round your answer to 2 decimal places. Omit the "%" sign in your response.) Efficiency 1%

Explanation / Answer

Demand per hour= 4 units/hr

Productive time per hour=56 mins/per

Cycle time= (Productive time/hr) / (Demand/hr)

               = 56/4= 14 mins/unit

Task Table

Task

Task time

Precedence

Following Task

No of following tasks

Positional weight

a

3

-

b,c,h,i

4

23

b

2

a

c,h,i

3

20

c

4

b

h,i

2

18

d

7

-

e,h,i

3

25

e

4

d,g

h,i

2

18

f

5

-

g,e,h,i

4

29

g

6

f

e,h,i

3

24

h

9

c,e

i

1

14

i

5

h

-

0

5

Positional weight of a task is the sum of its own time and the time of all its following tasks.

The total station time is nothing but the cycle time. So, total station time of each station is 14 mins.

a. In order of most following tasks:

               Workstation 1:

                        First task =f

                        Time left= 14-5=9

                        Second task=a

                        Time left=9-3=6

                        Third task=g

                        Time left=6-6=0

So, workstation 1: f->a->g

Workstation 2:

                        First task =d

                        Time left= 14-7=7

                        Second task=b

                        Time left=7-2=5

                        Third task=c

                        Time left=5-4=1

So, workstation 2: d->b->c

Workstation 3:

                        First task=e

                        Time left= 14-4=10

                        Second task=h

                        Time left=10-9=1

So, workstation 3: e->h

Workstation 4:

                        First task=i

                        Time left=14-5=9

Work Station

Tasks

1

f->a->g

2

d->b->c

3

e->h

4

i

b. In order of greatest positional weight:

Tasks in order of positional weight:

Task

f

d

g

a

b

c

e

h

i

P Weight

29

25

24

23

20

18

18

14

5

Task time

5

7

6

3

2

4

4

9

5

Workstation 1:

                        First task =f

                        Time left= 14-5=9

                        Second task=d

                        Time left=9-7=2

So, workstation 1: f->d

Workstation 2:

                        First task =g

                        Time left= 14-6=8

                        Second task=a

                        Time left=8-3=5

                        Third task=b

                        Time left=5-2=3

So, workstation 2: g->a->b

Workstation 3:

                        First task=c

                        Time left= 14-4=10

                        Second task=e

                        Time left=10-4=6

So, workstation 3: c->e

Workstation 4:

                        First task=h

                        Time left=14-9=5

                        Second task=i

                        Time left=5-5=0

So, workstation 4: h->i

Work Station

Tasks

1

f->d

2

g->a->b

3

c->e

4

h->i

c. Sum of task time: 45 mins

Minimum no of workstations = (sum of task time*demand per hr)/productive time/hr

Minimum no of workstations = (45*4)/56 =3.21

Efficiency= Minimum no of workstations/Actual number of workstations

               =3.21/4=80.25 %

Task

Task time

Precedence

Following Task

No of following tasks

Positional weight

a

3

-

b,c,h,i

4

23

b

2

a

c,h,i

3

20

c

4

b

h,i

2

18

d

7

-

e,h,i

3

25

e

4

d,g

h,i

2

18

f

5

-

g,e,h,i

4

29

g

6

f

e,h,i

3

24

h

9

c,e

i

1

14

i

5

h

-

0

5

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