2012-13- assoc prof. sami fethi, emu, revision revision mgmt 405, production man. revision business...

© 2012-13- Assoc Prof. Sami Fethi, EMU, Revision

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MGMT 405, Production Man.

REVISION

Business Department

FALL 2013-14

MGMT 405, Production Man., 2012/13 © 2012-13- Assoc Prof. Sami Fethi, EMU, Revision

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2

Section B/type 1-Example- Section B/type 1-Example- Productivity Assume 40 hour weeks and an hourly wage of $12. Overhead is

1.5 times weekly labor cost. Material cost is $ 6 per pound.(a)Compute the average multi-factor productivity measure for each

of the weeks shown.(b)Calculate the productivity growth rates throughout the weeks.(c) What do the productivity figures suggest? Draw the productivity

figures and briefly explain.

Week Output (units) Workers Materials (lbs)

1 30,000 6 450

2 33,600 7 470

3 32,200 7 460

4 35,400 8 480


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Example- Example- Productivity

WeekOutput

(units)

Worker cost

12*40

Overhead

cost

Material

s cost

Total

cost

MFP

1 30,000 2880 4320 2700 9900 3.03

2 33,600 3360 5040 2820 11220 2.99

3 32,200 3360 5040 2760 11160 2.89

4 35,400 3840 5740 2880 12480 2.84


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Example- Example- Productivity

Week 1- 12*40*6 =2880= worker costWeek 1- 12*40*6 =2880* 1.5=4320= overhead costWeek 1- 450*6 = 2700=material costWeek 1- 2880+4320+2700=9900 total cost Week 1-MFP=output (units)/(labor+materials+overhead) =30000/9900=

3.03 unit per dollar input


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Section B/Type2-Example-ForecastSection B/Type2-Example-Forecast

A company records indicates that monthly sales for a twelve-month period are as follows:. Period Sales1 862 933 884 895 926 947 918 939 9610 9711 9312 95


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Example-ForecastExample-Forecast

a) Use a simple three-month moving average and single exponential smoothing technique to find the next period employing smoothing constant and 12. period forecast value are 0.5 and 94.28 respectively. b) Use a simple three-month moving average and single

exponential smoothing technique to find all periods.

c) Use RMSE error model and decide which technique is better explain the data (MA and ES).

d) Plot the monthly data, three-month moving average estimates as well as exponential smoothing estimates. Briefly explain the patterns.


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Example-ForecastExample-ForecastPeriod Sales MA03 ES(α=0.5)

1 86 862 93 863 88 89.54 89 89 88.755 92 90 88.8756 94 89.66667 90.43757 91 91.66667 92.218758 93 92.33333 91.609389 96 92.66667 92.3046910 97 93.33333 94.1523411 93 95.33333 95.5761712 95 95.33333 94.28809

Next period 95 94.64404MA03: TT4= 88+93+86/3=89 TT13=95+93+97/3=95


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Example-ForecastExample-ForecastMA03: TT4= 88+93+86/3=89 TT13=95+93+97/3=95 ***ES(α=0.5) TTt = TT (t-1)+α (GT(t-1)-TT(t-1)) TT1= 86 (it is the average of series if it is not given) TT2= 86+0.5(86-86)=86 TT3=86+0.5(93-86)=89.5 TT4=89.5+0.5(88-89.5)=88.75 TT13=94.29+0.5(95-94.29)=94.64


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period Sales MA03 ES05 EMA03 SQEMA03 EES05 SQEES05

1 86 86 0 0

2 93 86 7 49

3 88 89.5 -1.5 2.25

4 89 89.00 88.75 0 0 0.25 0.0625

5 92 90.00 88.875 2 4 3.125 9.765625

6

9489.67 90.4375 4.33 18.77778 3.5625 12.69141

7 91 91.67 92.21875 -0.67 0.444444 -1.21875 1.485352

8 93 92.33 91.60938 0.67 0.444444 1.390625 1.933838

9 96 92.67 92.30469 3.33 11.11111 3.6953125 13.65533

10 97 93.33 94.15234 3.67 13.44444 2.84765625 8.109146

11 93 95.33 95.57617 -2.33 5.444444 -2.576171875 6.636662

12 95 95.33 94.28809 -0.33 0.111111 0.711914063 0.506822 13 95 94.64404 10.67 Σ=53.77778 17.28808594 Σ=106.0967


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(A - F )2

RMSE

n

=

RMSE(MA03) = 2.44 RMSE(ES05) = 2.97 MA is better explain the pattern of the data than ES05 cause MA gives less error compared to ES.


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80828486889092949698

1 2 3 4 5 6 7 8 9 10 11 12

Sal

es

Period

SALES


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Section C/type 1-Example-Trend AnalysisSection C/type 1-Example-Trend Analysis Use the information in the following table

and construct the forecast equation. Use time series regression to forecast the

petrol consumption (mn gallons) for the next four year.

Compute the correlation coefficient, determination of coefficient and standard deviation. Briefly explain

Draw the pattern for data as well as forecasting periods. Briefly explain.


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Example-Trend AnalysisExample-Trend Analysis

YEAR 2004 2005 2006 2007 2008 2009 2010 2011

PETROLSALE(Y) 1 3 4 2 1 3 5 3


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YearTrend

(t)PETROLSALES

(Y) (t) SQ Y*t (y) SQ (Σt) SQ (ΣY) SQ

2004 1 1 1 1 1

2005 2 3 4 6 9

2006 3 4 9 12 16

2007 4 2 16 8 4

2008 5 1 25 5 1

2009 6 3 36 18 9

2010 7 5 49 35 25

2011 8 3 64 24 9

(sum) Σ 36 22 204 109 74 1296 484

a 1.678

b 0.238


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Y9=1.678+0.238(9) = 3.83 in 2012Y10=1.678+0.238(10) = 4.06 in 2013Y11=1.678+0.238(11) = 4.30 in 2014Y12=1.678+0.238(12) = 4.53 in 2015

Note:Note: PetrolPetrol sales are expected to increase by 0. sales are expected to increase by 0.238238 mn mn gallonsgallons pe per yearr year..


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Sxy = 1.36 Sxy is a measure of how historical data points have been

dispersed about the trend line. If it is large (reference point in mean of the data) , the historical data points have been spread widely about the trend line and if otherway around, the data points have been grouped tightly about the trend.


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Example-Trend AnalysisExample-Trend Analysis r=0.42r lies between -1 and 1, -1 is strong negative whereas 1 is strong positive. 0 means that there is no relationship between the two variables (x and y). In this case, there is a strong positive relationship between the two variables and if an increase in independent variable, it will be a rise in dependent variable. R2=0.18. It varies between 0 and 1.0 means that there is no relationship between the two variables whereas 1 indicates that there is a perfect relationship. 18.0% variation in dependent variable can be explained by the variation happened in the independent variable. It is worth to emphasize that 82% shows unexplained part of the relationship.


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Section C/type 2-Vogel and NWCSection C/type 2-Vogel and NWC

Use the relevant information in the following Table:

Determine the dispatch program between the factories and stores.

Calculate individual cost Calculate total minimum cost


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Given a transportation problem wıth the following costs, supply, and demand, find the optimal solution:


To (Cost)

From 1 2 3 supply

A $ 6 7 4 100

B $ 5 3 6 180

C $ 8 5 7 200

Demand 135 175 170


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Section C/type 2-Vogel and NWCSection C/type 2-Vogel and NWCTo (Cost)From 1 2 3 supplyA $ 6 7 4 100 (2)B $ 5 3/175 6 180 (2)C $ 8 5 7 200 (2)Demand 135 175 170 480\480 (1) (2) (2)

B → 2 =175*3 =525

To (Cost)From 1 3 supplyA $ 6 4/100 100 (2)B $ 5 6 5 (1)C $ 8 7 200 (1)Demand 135 170 (1) (2)

A → 3 =100*4 =400


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To (Cost)From 1 3 supplyB 5/5 6 5 (1)C 130/ 8 7/70 200 (1)Demand 130 70 (3) (1)

B → 1 =5*5 =25C → 1 =130*8 =1040C → 3 =70*7 =490Total= 2,480


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Section C/type 2-Vogel and Section C/type 2-Vogel and NWCNWCTo (Cost)

From 1 2 3 supply

A $ 6*100 7 4 100

B $ 5 *35 3*145 6 180

C $ 8 5 *30 7*170 200

Demand 135 175 170

A → 1 =6*100=600B → 1 =5*35 =175B → 2 =3*145 =435C → 2 =5*30 =150C → 3 =7*170 =1190

Total= 2,550


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2012-13- assoc prof. sami fethi, emu, revision revision mgmt 405, production man. revision business...

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