Homework SourseFirst shift employees at General Motors work from 6am to 2pm
First shift employees at General Motors work from 6am to 2pm Monday through Friday. Everyone on the assembly line is allowed a 30 minute lunch and two 20 minute breaks, but other cross-trained associates cover lunches and breaks for the associates on the assembly line so the line doesn’t stop. The processes of the assembly line have the following dependencies:
Task Predecessor Average Time (sec)
A none 45
B none 90
C A 110
D B 120
E none 100
F C 15
G E 115
H F, D, G 35
The Plant Manager needs first shift to achieve an output of 100 cars.
Compute the Takt time for the line .
What is the theoretical minimum number of workstations?
Draw the precedence diagram. Then assign tasks to work stations and you must use the largest eligible task heuristic rule to break any ties. Show which tasks are assigned to each workstation.
Compute the efficiency and percent idle time for the system .
What is the maximum output that could be achieved by a single assembly line in 8 hours?
Problem 2: Forecasting
Feb Mar Apr May Jun Jul Aug
Units Sold 1507 1233 1198 1426 1629 1374 1282
Given these sales figures over the last 7 months, your boss needs you to create a forecast model that can be used to forecast sales in the future. Use three different forecasting methods (last period, 2 period moving average and 3 period moving average) to determine which forecasting method would be best to forecast future sales. For your measure of “best”, recommend the company use the method with the mean forecast error (MFE) closest to zero.
Calculate the MFE for each of the 3 forecasting techniques.
After you have selected the best forecasting method, what would you tell your boss is the forecasted sales for September?.
Problem 3: Forecast Accuracy
Your company released a new product in August. Prior to August, the Marketing Department provided their forecasted sales. The product has been on the market for 5 weeks now and the table below shows the actual sales and Marketing’s forecast of units sold.
Week
Forecasted Sales (units)
Actual Sales (units)
1
900
1,492
2
1,500
1,528
3
2,200
2,316
4
2,200
1,945
5
2,500
2,487
Calculate the MAD for the forecast.
Calculate the MAPE for the forecast.
| Week | Forecasted Sales (units) | Actual Sales (units) |
| 1 | 900 | 1,492 |
| 2 | 1,500 | 1,528 |
| 3 | 2,200 | 2,316 |
| 4 | 2,200 | 1,945 |
| 5 | 2,500 | 2,487 |
Solution
The below table shows the calculation of moving average for 3 period average of 1st 3 units sold is taken to find the forecasted of 4th value similarly forecast of others are calculated excluding the previously taken value and continuing the same similarly 2 period moving average average of 1st 2 numbers are taken to find the third one and excluding the first number to find the 3 forecasted and continuing the same way.
MFE is a measure of forecast model bias .
Ideal value = 0;
MFE > 0, model tends to under-forecast
MFE < 0, model tends to over-forecast
The mean absolute deviation, or MAD, is one of the most popular and simplest to use measures of forecast error. MAD is an average of the difference between the forecast and actual demand, as computed by the following formula:
MAD=Sum of (Dt-Ft)/n
MAD=1004/5=200.8
The MAPE (Mean Absolute Percent Error) measures the size of the error in percentage terms. It is calculated as the average of the unsigned percentage error.
Formula for MAPE = Sumof (absolute(Actual-Forcaste)/Actual Value *100 )/n
Thus MAPE = 60.15/5 = 12.03%
| Month | Units Sold | 3 Period Moving Average | 2 Period Moving Average | Last Period Moving Average |
| Feb | 1507 | |||
| Mar | 1233 | |||
| Apr | 1198 | 1370 | ||
| May | 1426 | 1312.7 | 1215.5 | |
| Jun | 1629 | 1285.7 | 1312 | |
| Jul | 1374 | 1417.7 | 1527.5 | |
| Aug | 1282 | 1476.3 | 1501.5 | |
| Sep | Forecasted Values | 1428.3 | 1328 | 1378.43 |
