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Chapter 5 - Capacity Management
Operations Management (The University of the South Pacific)
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CHAPTER 5
5.1. A work center consists of 4 machines each working a 16-hour day for 5 days a week. What is the
weekly available time?
Available time = 4 machines * 16 hour per day * 5 days a week
= 320 hours per week
5.2. The work center in problem 5.1 is utilized 75% of the time. What are the hours per week actually
worked?
Rated capacity = 320 * 0.75 = 240 standard hours. We can expect to get 240 standard hours of work
from that work center in an average week.
5.3. If the efficiency of the work center in problem 5.1 is 120%, what is the rated capacity of the work
center?
Rated capacity = 320 * 0.75 * 1.2 = 288 standard hours per week
5.4. A work center consisting of 7 machines is operated 16 hours a day for a 5-day week. Utilization
is 80%, and efficiency is 110%. What is the rated weekly capacity in standard hours?
Available time = 7 * 16 * 5 = 560 hours per week
Rated capacity = 560 * 0.80 * 1.1 = 492.8 standard hours per week.
5.5. A work center consists of 3 machines working 8 hours a day for a 5-day week. If the utilization
is 75% and the efficiency is 120%, what is the rated capacity of the work center?
Available time = 3 * 8 * 5 = 120 hours per week
Rated Capacity = 120 * -.75 * 1.2 = 108 standard hours per week.
5.6. Over a period of 4 weeks, a work center produced 50, 45, 40, and 55 standard hours of work.
What is the demonstrated capacity of the work center?
Demonstrated capacity = 50 + 45 + 40 + 55 / 4 =
= 190 / 4
= 47.5 standard hours of work per week
5.7. In an 11-week period, a work center produces 1050 standard hours of work. What is the
measured capacity of the work center?
Measured capacity of the work center produces 1050 standard hours of work;
= 1050 / 11
= 95.45 standard hours
5.8. In 1 week, a work center produces 85 standard hours of work. The hours scheduled are 80, and
75 hours are actually worked. Calculate the utilization and efficiency of the work center.
Capacity required = 85 standard hours
Efficiency = 85 / 75 = 1.133 * 100 = 113.33%
Utilization = 75 / 80 * 100 = 93.75%
Answer. Utilization is 93.75%; efficiency is 113.33%
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5.9. A work center consisting of 3 machines operates 40 hours a week. In a 4-week period, it
actually worked 355 hours and produced 475 standard hours of work. Calculate the utilization and
efficiency of the work center. What is the demonstrated weekly capacity of the work center?
Available time = 3 * 40 * 4 = 480 standard hours per week
Demonstrated capacity = 355 + 475 / 2
= 830 / 2
= 415 standard hours
5.10. A firm wishes to determine the efficiency and utilization of a work center composed of 3
machines each working 16 hours per day for 5 days a week. A study undertaken by the materials
management department found that over the past year the work center was available for work
12,000 hours, work was actually being done for 10,000 hours, and work was performed 11,480
standard hours. Calculate the utilization, efficiency, and demonstrated weekly capacity. Assume a
50-week year.
Work center = 12,000 hours
Hours actually worked = 10,000 hours
Standard hours = 11,480 hours
Available time = 3 * 16 * 5 = 240
Utilization = hours actually worked / available hours * 100%
= 10,000 / 240 *100%
= 41.67 *100%
= 4,166.67 %
Efficiency = standard hours produced / hours actually worked * 100
= 11,480 / 10,000 * 100%
= 1.148 * 100%
= 114.8%
Rated Capacity = 240 * 41.67 * 1.15 = 11,500.92
Demonstrated Capacity
= 12,000 + 10,000 + 11,480 / 3
= 33,480 / 3
= 11,160 standard hours
5.11. How many standard hours are needed to run an order of 200 pieces if the setup time is 1.3
hours and the run time 0.3 hours per piece? How many actual hours are needed at the work center
if the efficiency is 130% and the utilization is 70%?
Total standard time = set up time + run time
= 1.3 + (200 * 0.3)
= 1.3 + 60
= 61.3 standard hours (capacity required)
Actual time = capacity required / (efficiency) (utilization)
= 61.3 / (1.3) (0.7)
= 61.3 / 0.91
= 67.36 ~ 67.4 actual hours
Answer. 61.3 standard hours; 67.4 actual hours
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5.12. How many standard hours are needed to run an order of 500 pieces if the setup time is 3.0
hours and the run time 0.2 hours per piece? How many actual hours are needed at the work center
if the efficiency is 125% and the utilization is 85%? 5.13. A work center has the following open and
planned orders for week 4. Calculate the total standard time required (load).
Order
Setup Time (hrs) Run time (Hours / Total Time (Hours)
Quantity
piece)
Released Orders 120 300
1.00
0.10
31 standard hours
340
200
2.50
0.30
62.5 standard hours
Planned orders 560 300
3.00
0.25
78 standard hours
780
500
2.00
0.15
77 standard hours
Total Time (Standard time)
248.5 standard hours
Released orders – 120 Total time = 1.00 + (300 * 0.10) = 31 standard hours
– 340 Total time = 2.50 + (200 * 0.30) = 62.5 standard hours
Planned orders – 444 Total time = 3.00 + (300 * 0.25) = 78 standard hours
– 555 Total time = 2.00 + (500 * 0.15) = 77 standard hours
Total time = 31 + 62.5 + 78 + 77 = 248.5 standard hours
5.14. A work center has the following open and planned orders for week 4. Calculate the total
standard time required (load).
Order
Setup Time (hrs) Run time (Hours / Total Time (Hours)
Quantity
piece)
Released Orders 125 200
0.25
0.12
24.25
standard
hours
345
70
0.70
0.05
4.2 standard hours
Planned orders 565 80
1.00
0.25
21 standard hours
785
35
1.50
0.15
6.75 standard hours
Total Time (Standard time)
56.2 standard hours
Released orders
Total time =0.25 + (200 * 0.12) = 24.25 standard hours
Total time = 0.70 + (70 * 0.05) = 4.2 standard hours
Planned Orders
Total time = 1.00 + (80 * 0.25) = 21 standard hours
Total time = 1.50 + (35 * 0.15) = 6.75 standard hours
Total time = 24.25 + 4.2 + 21 + 6.75 = 56.2 standard hours
5.15. Using the information in the following route file, open order file, and MRP planned orders,
calculate the load on the work center.
Routing
Part 123:
Setup time
= 2 standard hours
Run time per piece
= 3 standard hours per piece
Part 456:
Set up time
= 3 standard hours
Run time per piece
= 1 standard hour per piece
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Open orders for parts
Week
1
2
123
12
8
456
15
5
Load Report
Week
Released load
1
3
5
5
2
Planned orders for parts
1
2
3
0
5
10
0
10
15
3
123
456
Planned Load 123
456
Total Load
Week 1:
Released order 123 = 2 + (12 * 3) = 38
456 = 3 + (15 * 1) = 18
Planned order 123 = 2 (0 * 3) = 2
456 = 3 + (0 * 1) = 3
Total time = 38 + 18 + 2 + 3 = 61 standard hours
Week 2:
Released order 123 = 2 + (8 * 3) = 26
456 = 3 + (5 * 1) = 8
Planned order 123 = 2 + (5 * 3) = 17
456 = 3 + (10 * 1) = 13
Total time = 26 + 8 + 17 +13 = 64 standard hours
Week 3:
Released order 123 = 2 + (5 * 3) = 17
456 = 3 + (5 * 1) = 8
Planned order 123 = 2 + (10 * 3) = 32
456 = 3 + (15 * 1) = 18
Total time = 17 + 8 + 32 + 18 = 75 standard hours
Load Report
Week
Released load
Planned Load
Total Load
123
456
123
456
1
3
8
18
2
3
61
2
3
26 17
8
17
13
6
4
8
32
18
75
5.16. Complete the following load report and suggest possible courses of action
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Week
18
19
Released
150
155
Load
Planned Load 0
0
Total Load
150
155
Rated
150
150
Capacity
(Over)
/ 0
5
Under
Total Load calculations as follows:
Week 18 = 150 + 0 = 150
Week 19 = 155 + 0 = 155
Week 20 = 100 + 80 = 180
Week 21 = 70 + 80 = 150
Total load = 150 + 155 + 180 + 150 = 635
20
100
21
70
Total
475
80
180
150
80
150
150
160
635
600
30
0
35
Total calculation for over capacity: Total Load – Rated Capacity
Week 18 = 150 – 150 = 0
Week 19 = 155 – 150 = 5
Week 20 = 180 – 150 = 30
Week 21 = 150 – 150 = 0
5.17. Back schedule the following shop order. All times are given in days. Move time between
operations is 1 day, and wait time is 1 day. Due date is day 150. Assume orders start at the beginning
of a day and finish at the end of a day.
Total
Operation
Work
Operation
Queue
Wait
Move
Arrival
Finish
Number
Center
Time
Time
time
time
date
date
(days)
(days)
(Days) (days)
10
111
2
4
1
1
126
132
377
20
130
4
5
1
1
134
143
418
30
155
1
2
1
1
145
148
453
Stores
150
Since the due date of 150 is given, we will start here.
Finish date of operation number 30 = 150 – wait time – move time
- 30 = 150 -1 -1 = 148
Arrival date of operation 30 = Finish date – operation time – queue time
- 30 = 148 -1 -2 = 145
Finish date of operation number 20 = 145 – 1 – 1 = 143
Arrival date of operation number 20 = 143 – 4 – 5 = 134
Finish date of operation number 10 = 134 – 1 – 1 = 132
Arrival date of operation number 10 = 132 – 2 – 4 = 126
Answer: The order must arrive at work center 111 on day 126
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5.18. Back schedule the following shop order. All times are given in days. Move time between
operations is 1 day, and wait time is 1 day. Due date is day 200. Assume orders start at the beginning
of a day and finish at the end of a day.
Wait
Move
Operation
Work
Operation Queue
Arrival
Finish
time
time
Number
Center
Time (days) Time
date
date
(days)
(days) (days)
10
110
4
3
1
1
176
183
20
120
2
4
1
1
185
191
30
130
3
2
1
1
193
198
Stores
200
Since the due date of 200 is given, we will start here.
Finish date of operation number 30 = 200 – wait time – move time
- 30 = 200 -1 -1 = 198
Arrival date of operation 30 = Finish date – operation time – queue time
- 30 = 198 -3 -2 = 193
Finish date of operation number 20 = 193 – 1 – 1 = 191
Arrival date of operation number 20 = 191 – 2 – 4 = 185
Finish date of operation number 10 = 185 – 1 – 1 = 183
Arrival date of operation number 10 = 183 – 4 – 3 = 176
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