OM II - Class 5

7/29/2019 OM II - Class 5

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7/29/2019 OM II - Class 5


Simple linear regression takes the formy = a + bx + e

y is the dependent variable

x is the independent or explanatory variable

Constants „a‟ and „b‟ represent the intercept and slope,

respectively, of the regression line

Term „e‟ represents an “error” term or “residual”

In other words, we may think of the relationship between xand y as if it follows the straight line formed by the function y

= a + bx, subject to some unexplained factors captured in

error term

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Regression is a means to find the line that most closely

matches the observed relationship between x and y.

Most common approach is to minimize the sum of

squared differences between the observed values and

the model values

Sum of squared differences SS: 22

1 1

n n

i i i

i i

SS e y a bx

1 1 1

2

2

1 1

n n n

i i i i

i i i

n n

i i

i i

n x y x y

b and a y bx

n x x

7/29/2019 OM II - Class 5


7/29/2019 OM II - Class 5


Much of the information in the regression tables is quite

detailed and beyond the scope of our coverage

Focus on five measures of how well the regression model is

supported by the data: R2, Standard error, F-statistic, p-

statistics, and confidence intervals

First three of the measures apply to the regression model

as a whole

Last two apply to individual regression coefficients

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Having found the values of the constants a and b that give

the best fit of the model to the observed data, we might

wonder, how good a fit is the best fit?

Goodness can be interpreted as the extent to which all of the variation in y-values is completely accounted for (or

explained) by their dependence on x-values.

In order to quantify the outcomes and to provide a measureof how well the regression equation fits the data, we

introduce the coefficient of determination, known as R2

Its square root is the coefficient of correlation, „r‟

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Values of R2 must lie between zero and one.

Closer R2 to one, the better the fit

When R2 is relatively large, then the model explains much of

the variation in observed y-values

When R2 is equal to one, the regression equation is perfect – it

explains all of the observed variation

When R2 is zero, the regression equation explains none of the

observed variation

Unexplained variation could be because of “noise” or other

systematic factors that were not considered in the regression

equation

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If the standard error of estimate (Se) is small, the fit isexcellent and the linear model should be used for

forecasting

If it is large, the model is poor But, what is small and what is large?

Judge the value of Se by comparing it with the sample mean

of the dependent variable In this example, Se is 32.165 and sample mean is 783.9

Hence, in this case, the linear regression model developed

is good

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The significance level of F answers this question: Howlikely is it that we would get the R2 we observe (or

higher) if, in fact, all the true regression coefficients

were zero? In other words, if our model really had no explanatory

power at all, how likely is it that, sampling at random, we

would encounter the explained variation we observed?

Precisely, what is the probability of getting a coefficient

of determination of R2 by fluke or by chance?

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p-statistic or p-value is somewhat akin to thesignificance level of the F-statistic.

It answers this question: How likely is it that we would

get an estimate of the regression coefficient at least thislarge (either positive or negative) if, in fact, the true

value of the regression coefficient were zero?

In other words, if there really was no influence of this

particular explanatory variable on the response variable,

how likely is it that we would encounter the estimated

coefficient we observed?

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The most useful way to determine the range of uncertainty in a regression coefficient is to form a

confidence interval

A confidence interval for the coefficient will tell uswhether the actual parameter is likely to lie between two

numbers

This information, along with the point estimate of the

coefficient itself and our judgment, will help us to select

a final parameter value for the coefficient in our model

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7/29/2019 OM II - Class 5


Value of R2

is about 0.745, which suggests that themodel fits the data rather well

Probability under Significance of F is about 6 percent,

which suggests that it is unlikely that this value R2

couldhave arisen by chance

a = 708 and b = -27.7, indicating the average y value

drops by almost 28 points each round

p-value for the intercept is very small, suggesting that

this estimate would be unlikely by chance

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However, the p-value for X variable 1 is 6 percent, whichsuggests that we cannot be so sure that this estimate

could not have arisen by chance

The 95% confidence interval for X variable is extremelywide, from -57 to +2. This suggests that our point

estimate, from which we concluded that the average y

value drops by almost 28 points each year, is ratherimprecisely estimated

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Demand Forecasting

Capacity Planning

Aggregate Planning

Inventory Control

Scheduling

Quality Control & Maintenance

7/29/2019 OM II - Class 5


Demand Forecasting

Capacity Planning

Aggregate Planning

Inventory Control

Scheduling

Quality Control & Maintenance

7/29/2019 OM II - Class 5


Capacity refers to a system‟s potential for producing goods or

delivering services over a specified time interval

Goal of capacity planning is to achieve a match between long-

term supply capabilities and the predicted level of long-term

demand

Basic questions in capacity planning:

- What kind of capacity is needed?

- How much is needed?

- When is it needed?

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Capacity often refers to an upper limit on the rate of

output

In selecting a measure of capacity, it is important to

choose one that does not require updating (capacity of

$30 million a year)

When only one product or service is involved, capacity

may be expressed in terms of that item When multiple products are involved, capacity is often

expressed in terms of inputs

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Type of BusinessInput Measures of

Capacity

Output Measures

of Capacity

Car manufacturer Labor hours Cars per shift

Hospital Available beds Patients per month

Pizza parlor Labor hours Pizzas per day

Retail storeFloor space in

square feet Revenue per foot

No single measure of capacity will be appropriate in everysituation. Rather it must be tailored to the situation

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Design capacity:

◦ Maximum output rate under ideal conditions

Effective capacity:

◦

Design capacity minus allowances such as personaltime, maintenance, and scrap

Actual output cannot exceed effective capacity and is

often less because of machine breakdowns,absenteeism, shortage of materials, and quality

problems

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Actual outputEfficiency =

Effective Capacity

Actual outputUtilization =

Design Capacity

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Facilities – Location, Size, Provision for expansion etc.,

Product and service factors – Design similarities

Process & human factors – Quality considerations

Policy factors – Overtime, second or third shifts

Operational factors – Scheduling, inventory, purchasing

Supply chain factors – Suppliers, warehousing, logistics

External factors – Safety, Unions, Pollution control etc.,

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1. Estimate future capacity requirements

2. Evaluate existing capacity

3. Identify alternatives

4. Conduct financial analysis

5. Assess key qualitative issues

6. Select one alternative7. Implement alternative chosen

8. Monitor results

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1. Design flexibility into systems (capacity cushions)

2. Take stage of life cycle into account

3. Take a “big picture” approach to capacity changes

4. Prepare to deal with capacity “chunks”

5. Attempt to smooth out capacity requirements

6. Identify the optimal operating level

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100% –

80% –

60% –

40% –

20% –

0 –

N i s s a n

C h r y s l e

r

H o n d a

G M

T o y o t a

F o r d

Percent of North American Vehicles Made on Flexible Assembly Lines

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(a) Leading demand withincremental expansion

D e m a n d

Expecteddemand

Newcapacity

(b) Leading demand withone-step expansion

D e m a n d

Newcapacity

Expecteddemand

(c) Capacity lags demand withincremental expansion

D e m a n d

Newcapacity

Expecteddemand

(d) Attempts to have an averagecapacity with incrementalexpansion

D e m a n d

Newcapacity Expected

demand

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Demand exceeds capacity Curtail demand by raising prices, scheduling

longer lead time

Long term solution is to increase capacity

Capacity exceeds demand

Stimulate market

Product changes

Adjusting to seasonal demands

Produce products with complementary demandpatterns

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4,000 –

3,000 –

2,000 –

1,000 –

J F M A M J J A S O N D J F M A M J J A S O N D J

S a l e s i n

u n i t s

Time (months)

Air-conditioners

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4,000 –

3,000 –

2,000 –

1,000 –


S a l e s i n u n i t s

Time (months)

Air-conditioners

Room heaters

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4,000 –

3,000 –

2,000 –

1,000 –


S a l e s i n u n i t s

Time (months)

Air-conditioners

Room heaters

Combining both demandpatterns reduces the variation

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BOLis the output that results in the lowest average unit

cost

Economies of Scale:

◦ Where the cost per unit of output drops as volume of output

increases

◦ Spread the fixed costs of buildings & equipment over multiple

units, allow bulk purchasing & handling of material

Diseconomies of Scale:

◦ Where the cost per unit rises as volume increases

◦ Often caused by congestion (overwhelming the process with too

much work-in-process) and scheduling complexity

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7/29/2019 OM II - Class 5


Cost-volume analysis

◦ Break-even point

Financial analysis

◦ Cash flows

◦ Present value

Decision theory

Waiting-line analysis

Simulation

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-$90,000Market unfavorable (.6)

Market favorable (.4)$100,000

Market favorable (.4)

Market unfavorable (.6)

$60,000

-$10,000

Medium plant



$40,000

-$5,000

$0

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$60,000

-$10,000

Medium plant



$40,000

-$5,000

$0

EMV = (.4)($100,000)+ (.6)(-$90,000)

Large Plant

EMV = -$14,000

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-$14,000

$13,000

$18,000





$60,000

-$10,000

Medium plant



$40,000

-$5,000

$0

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OM II - Class 5