SOM 306
Wednesday, February 19, 2014
Typewell; Dave Strong
Sirob Malkonian

Professor:   Today I will try to cover all the material you will see in the next two quizzes.  The strategy quiz read the PowerPoint or listen to the recorded lecture.  On Monday we will have a short quiz.  I will bring papers here.  

I will start the quiz at 8am and it will be 20 minutes.  So if you come late, I cannot extend the quiz.  Any questions? 

Okay, regression.  We have discussed moving average and exponential smoothing.  In those our criteria to choose the best formula was MAD.  Mean absolute derivation.  

In moving average and exponential smoothing we can only forecast for the next period.  For all other periods after the next period we assume demand is equal to the next period.  If you want to do something else in the game, you are free, there's no rigid rules.  

You will do whatever you think is the best for that specific situation.  

In linear regression, which is the only regression we will cover, we have a set of x and y values.  We claim that there is a linear relationship between these two valuables.  

We refer to x as independent variable and y as dependent variable.  We claim there's a linear relationship between them.  

The equation of the line is a variable is equal to a constant plus another constant times another variable.  y = a + bx

The variable on the right hand side is multiplied by a constant and added to another constant.  

These two are usually not zero.  But one of them can be zero.  

For example y = bx or y = a

If I have these points, I may come and say "I draw a line over there such that MAD is minimal."  No one can criticize me.  No one can criticize me.  

I draw a line [On overhead.]  And say "in my opinion, this is the best line."  I may draw a line that minimizes the MAD, add it up for different lines and select the line with minimal MAD.  Or I may draw a line where the maximum deviation from the line is minimized.  

So if this is too large [On overhead.] I may say "the best line is this line."  No one can criticize me.  However, dealing with min or max problems in math is difficult, if the objective is to minimize the maximum deviation between two variables.  Solving that problem is difficult.  Even solving math problems is difficult.  If the objective is summation of the absolute deviation divided by number of observation, solving that is difficult.  

Therefore instead of dropping the negative sign by transforming a value into absolute value, mathematicians have found another way, which dealing with it is easier.  

That is instead of absolute value they use square.  Square also drops the sign.  Therefore in regression the criteria is minimization of sun of the squared value.  That is a method trying to find a line for each square of the deviation is minimum 

Let's forget all of this.  You come here and say... in my opinion the best line is [writing on board.]  

It's your line.  Then in order to find the equation of this line I compute this distance.  That is a or in linear equation terminology b0

Then you will go one unit to the right and then you measure this height.  This is b or in our terminology b1

So that is the meaning of b0 and b1

b0  Is intercept.  b1 is slope.  Having said that, I will go to Excel.  [On overhead.]  

In this discussion we are talking about the relationship between demand and time.  In exponential smoothing, the same thing.  Here we translate x and y into demand of time.  For x we use time, for y we use demand.  

So our equation is demand for t is equal to b0 + b1 × t 

For period 2 is a constant times another content times time.  

So this is period 1.  [On overhead.]  This is 2 [On overhead.]   

These are my demands for different periods.  I am looking for a relationship between demand and time.  I used to teach the math behind this formula.  I wanted to know the formula is completed in order to minimize the square of the devotion.  You want to find the line for which the deviation between the y value in the line and the y value of reality, for this specific b1 , that specific b0, is minimal.  

So I go to data [On overhead.]   I look for data analysis, it's here.  If it wasn't here I go to options, Add Ins > Go > then select analysis 2

Now it isn't there, I go back.  Options > Add Ins > Go > analysis 

Now I go to data analysis and click regression.  

Then input the y values, usually the second column.  Then I input the first column for x.  

Second column is demand, first column is time.  Now I have entered my data regarding time and demand in that specific time period and then I click "okay"

Then a table pops up.  

There are a couple of outcomes in this table that are important and we focus on them.  

The first thing I look at is intercept.  That is my b0.  The next is slope, which is my b1   In excel it is called intercept and x variable 1.  

In sample linear regression we only have the relationship between 2 variables.  Independent and dependent variables.  

So demand for period t is equal to 10.29 plus 1.04 times t.  

These are two numbers I care about.  [writing on board.]  

Ft = 10.29 + 1.04t

The other thing that I will care about is R square or adjusted r2 

Usually the adjusted r2 is smaller than r2 

So the difference can be larger because adjusted r2 is adjusted for the number of variables.  Don't worry about it.  We like to see large numbers.  Large numbers mean closer to 1.  If it's close to 1 this relationship is fine.  If it's not close to 1 that relationship is not too reliable.  

For example if you have some like this [On overhead.]   When you give these numbers to Excel and try to draw the regression line your r2 will come out small.  Maybe 0.3, 0.2 

If you give points like this to Excel [On overhead.]  Or points like this [On overhead.]  

r2 comes out quite large.  Very close to 1.  That means almost 100% of the value of y can be estimated if you give me x.  That's the meaning of r2 

The fractional dependent variable which can be explained if you give me the independent value.  

Here I can find the equation of this line, as soon as you give me x I can give you within 95% of the y.  It's very close to the y you observed.  

Here [On overhead.]   No.  

I may give you a line like this [On overhead.] with large gaps between what I give you and you observe.  But this one, the gap is small.  That is the meaning of r2.   Any questions?  

Female Student:   What did you say on the first graph, r2 small?  

Professor:   Doesn't matter if it is upward or downward.  If the relationship is strict r2 is close to 1.  

In both these situations r2 is close.  [On overhead.]  

r2 in states you know it as the coefficient of determination.  When you do SOM120 or MATH120 you call it coefficient of determination.  Here we call it this.  In statistics we call it correlation coefficient.  

So this one [On overhead.]  Is this one squared.  

r2 is always positive.  Multiple r can be positive or negative.  If relationship is like this, correlation coefficient is positive, if like this it is negative.  In both coefficient of determination is this.  

It's between -1 and 1 

Male Student:   You just answered my question.  

Professor:   Oh.  We had a chairman at this university, when I asked him a question he would not reply for one hour.  Once he said "I am aware what you ask you find the answer in one hour"

Any questions? 

One other thing I will look at is standard error.  We can never forecast with precision.  Usually the number we give as our forecast is average forecast.  It should be accompanied with standard deviation of forecast.  In smoothing the standard deviation was 1.25 MAD.  

Here it is 3.  If I'm forecasting for next period I say 10.3 + 1.04t  But actual demand has normal distribution with this average and this standard deviation.  Any questions? Having said that, suppose the first period that we started to collect data for this study was period 1.  Right?  

What would be our forecast for the next period?  Using regression analysis.  

Regression line is Ft 

What is your forecast for the next period?  

Male Student:   11.34 

Professor:   That would be your forecast for the first period.  If you put t = 1 we assume we are in the first period.  

What is your forecast for the next period.  If you started collecting data from the first period.  

Male Student:   29.01.  

Professor:   Can you loudly explain how you did that?  

Male Student:   That's the formula you have for 17 observations, you plug in 18 for t.  

Professor:   Because the data started for period 1, we have 17 periods.  Next period is period 18.  Therefore if I want to computer the forecast for the next period, I replace t with 18.  

But I should have told you we started with period 1.  Maybe we started from 1990.  So observation 1 is 1990, 2 is 1991 etc.  But because the first observation is in period 1, we see there are 17 observations, so we put 17 observations behind and the next period is period 18.  Make sense?  

One other thing in this table is P value for variable 1.  

Did you make sure everyone is enrolled?  

Female Voice:    Yes.  

Professor:   Thank you.  

In statistics when they taught you linear regression they taught you test of hypothesis.  After doing regression your professor in statistics says let's assume there's no relationship.  If there's no relationship that means b1  Should be equal to 0.  Then you prepare test of hypothesis.  

You computed T value and compared it with α  Which was 0.1, 0.5, 0.05 etc.  So this P value should be smaller than α to reject the null hypothesis.  We need to see P value less than 0.05, less than 0.025 or less than 0.005 

If it is small we can stay with the regression line.  

Here P value is 4 times E-6

So the number in front means n to the power of that number.  So 10-6 means 1 divided by 10 to the power of 6.  

So this is 4 ... this is a small number, much less than 0.05, less than 0.005.  

We look at b1 , b0, coefficient of determination or adjusted coefficient of determination, adjusted value, P value of b1   

If we look at these numbers.  The only way to see if the relationship is positive or negative, if I don't give you this number, then you look at multiple R.  If it's positive the relationship is positive.  Otherwise it is negative.  Any questions?  

We are trying to also record our class discussions.  But we take out unnecessary discussion.  For example at the beginning of the class I may have explanation that may take 5 minutes.  We take that out.  Also now I am explaining something not related to regression, so we take that out.  Out of 1 hour 15 minutes we have about 45 minutes on our website.  If you miss something during class discussion you may watch those.  

But easier is the PowerPoint.  They are scripts for my lecture.  So the assignment part.  

So these are the important points that we will look at.  Correlation coefficient is between -1 and 1.  We like it to be close to 1 or -1.  

Coefficient of determination we want to close to 1.  Standard devotion of forecast we want small.  The least squared method tries to minimize.  

If the first period is 1, the next period is n + 1

Is these are b0 and b1  This is the regression line.  Any questions?  

Our forecast has average of 431.7 and standard devotion of 22 ...

This is very simple, this is our data [On overhead.]   This is the regression equation, we look at these numbers.  Forecast is this one plus this one times t.  

7 + 1 = 8.  So next period is 8.  Standard devotion forecast is this one [On overhead.]   What is the answer to the first question?  

I just explained it.  It tells us that percentage of y can be explained by x.  

So 0.85 means 85% of variation in y can be explained in variation of x.  

What is the answer to the next question?  What?   Negative numbers are as important as positive numbers.  B.  -0.9 is better than the others.  Any questions? 

[Teacher reading:   Question 3.]  Small.  

Now I go and for quiz 2 you need to listen to the performance measure lecture.  So for quiz 2 you need to listen to recording 2 on strategy and you need to listen or read the PowerPoint of exponential smoothing.  Also today's discussion on regression and what I will cover in a minute regarded job and flow shop.  Any questions?  

Female Student:   [Can't hear/can't understand.]  

Professor:   Yes.  

Okay on quiz 2 you need to read the PowerPoint of exponential smoothing, listen to the lecture.  Also pay attention to what I covered today on regression and what I will cover on job shop and flow shop.  

So you need to listen to the second part of the chapter 1 and 2 recording.  Plus job and flow shop, plus performance measures, plus regression.  

Female Student:   What is it?  

Professor:   Everything we have covered but easy version.  It's to see if you are getting very basic concepts Any questions? 

Basically by Monday you are expected to know everything I have put before Monday in our class.  

Now we will talk about two arrangements of departments.  Physical arrangements.  Could be department of finance, accounting, management.  Or physical arrangement of department that makes energy, the department that makes transmission.  Or physical arrangement of accounts receivable, accounts payable, asset accounting.  Or lathe machine, welding machine, grinding machine in a machine shop.  

In job shop concept we arrange the departments based on similarity of their operations.  We put account table in one department, asset accounting in one accounting, cost accounting in another department.  Based on similarity of operations.  

We put department of management on one floor, department of accounting on another floor.  Physical arrangement of departments is based on the similarity of the operations.  

So product 1 comes to department A, then D, then B, then output.  

Product 2 comes to department C, then B, then A, then output.  As you see it is complicated.  They are not based on the processes but the similarity of the processes.  

In a system like this, it's good for low volume, high variety customized products.  Flexible resources, multi-purpose machines, cross trained workers.  Multi-purpose machines are machines that can do many things.  

Special purpose machines are machines that can do a small number of operations.  But we assume any small purpose machine is a general purpose machine but the set up time is high, maybe infinity.  

In other words, we can differentiate general purpose and special purpose machines based on the time they need to go from one product to another.  

A general purpose machine needs a little set up time to go from one product to another.  A special purpose machine needs a long time.  

So to move to flexibility we need to reduce set of time of our machines.  

Male Student:   For our game, is it more job shop or what?  

Professor:   Physical arrangement of the department in the game is fixed.  Department 1 is here, department 2 is here, department 3 is here.  

Products come from department 1 and we only produce one table.  So 75% flow shop, 25% job shop.  We have one material comes to department 1, then go to 2, then go to 3, then go back to 2, then goes.  That's fixed.  

As I told you in operations management, we talk about extreme points, job shop and flow shop.  In reality we have neither job shop and flow shop but we stand somewhere in the continuum between them.  

[ reading from the overhead ] 

In flow shop we have flexible resources.  Flexible resources means in a reasonable set of time we can switch from one product to another.  We have cross trained knowledgeable workers who can do a variety of jobs, so more expensive than production line workers.  

In production lines we benefit from division of labor.  We take a complex job and divide it by 1000 piece.  Each piece is simple to be done by 1 person.  But we need more expert persons to do more complex jobs.  Work flow, the most difficult of job shop is work flow.  Departments are not close, there is a lot of working process.  That makes the variable cost much higher than flow.  

Flow time is high, takes longer than flow shop to pass a product to a job shop.  Information system is complicated to make sure what product is in which state and what should be done.  In job shop initial investment is low, fixed is low, variable is high.  

Mainly because there's lots of inventory process and lots of material handling.  This is the main reason.  Fixed cost is low because we don't have expensive machines and we don't do duplications, as I explained here.  

In a flow shop we arrange the department not based on the similarity of the department but based on the sequence they are needed in production of a product or process.  

If product 1 [On overhead.] goes to A and then D and then B and out.  Then I put D between A and B.  Therefore product 1 comes in, goes to D, then go B and then out.  

Product 2 goes to C, B and A, I arrange like this [On overhead.]   

Look I have two Bs and two As.  Therefore I need more machines in flow shop.  That's why the fixed cost is high.  Okay?  

Flow shop is for mass production.  No one for low production will create a flow shop.  

[ reading from the overhead ] 

We have already discussed when we use flow shop, when we use job shop.  If my alternatives are flow or job shop I write the cost functions, equal them and find the break-even point between job and flow shop.  

In any institute we need strategic fit between processes and product attributes.  Variety is one product attribute.  Flexibility is a process capabilities.  We need to match these together.  If in a market I need products with high variety I should have a process with high flexibility.  

If I have a product which cost is important, variety isn't important and mass production will make cost low, I don't need flexibility.  

While fixed cost is lower, but variable cost is high it's high.  

So this is something we call product process matrix [On overhead.]   This is product attribute.  The attribute we are considering here is variety.  Here is low, here is high.  As I move on the horizontal dimension, I am in Walmart [On overhead.]   Here I am a private jet manufacturer.  

Here in Walmart they don't need variety.  

Here is flexibility of the process [On overhead.]   This is process capability, which can be flexibility, cost, quality or time.  Right?  If I'm here my process needs a little flexibility.  If I'm there my process needs a lot of flexibility.  

Do I need job or flow shop?  [On overhead.]  

Female Student:   Flow 

Professor:   Who says job?  Who says flow?  You can't remain indifferent.  These people are waiting for your decision.  

Male Student:   You said earlier you need a little of both.  

Professor:   No!  Am I closer to job or flow?  Flow shop!  Here I have low variety, I need low flexibility.  So flow shop.  

There, job or flow?  Job.  So if I'm talking about physical, if I'm here I need flow, there I need job.  Here I need something between job and flow, which could be group or batch processing.  Here I need more flow shop than flow shop [On overhead.]   

Okay.  Now, if I am here and if I bring job shop here, what will happen?  I need a little variety, but I bring a very capable process, a process system that can deliver high variety of products in an environment that doesn't need variety.  What will happen?  

Let me give you a better example.  Suppose we are in McDonalds and bring a top chef there who can produce lots of meals.  But we give him responsibility of assembling Big Macs.  What will happen?  

The cost is opportunity cost.  That chef could have done a lot of other things, he isn't doing it right now.  He could produce 20 types of high class meals but he isn't doing it.  

The opportunity of producing the high value meals is gone.  

Now suppose we are in a very top restaurant and we go there for fried chicken, we create a production line with a high value chef in that production.  For sirloin steak we have production line, for pasta we have production line.  We have 20 there for each meal where we don't need that many meals.  

The chef we brought here could do that.  

If I go here [On overhead.] in the environment that needs job shop, if I create flow shop they call it opportunity cost.  We lose the opportunity of using that high value chef.  

In an environment which ... needs flexibility.  Here we need flexibility, we have created production lines for each of those products.  That is what we call out of pocket costs.  If I bring a flow shop in environment needs job shop, that is out of pocket.  

Here, if I take a flow shop ... this is product variety is low.  Here product variety is low.  I have created a process which is flexible.  Are you with me?  

In this region, variety is low.  But I have created a process which has high flexibility.  That process with high flexibility cannot benefit from producing different types of product.  It is restricted to a low variety of products.  The top chef is there are produce one kind of product.  The opportunity of selling the high value meals is gone.  

In this environment [On overhead.] variety is high and producing tens of hundreds of products.  But I brought a process with low flexibility.  By itself it cannot produce all of those products.  For each of those I should have a separate process with low flexibility.  So I need a hundred processes.  That makes it expensive and I put in more investment out of my pocket to create 100 production lines.  Because one single production line cannot produce thousands of products.  Any questions? 

Here if I bring a process that is capable of producing hundreds of products, and I am producing 2 or 3 products, the opportunity of producing other products is gone.  So opportunity costs.  

Here, flexibility is high.  If I bring a process which has high variety but the process has low flexibility it can't produce many products.  So I'd need hundreds of processes.  That's out of pocket.  

So as we have this slide, if this is variety and this is flexibility, when variety goes up flexibility should go up.  Right?  When the customer want hundreds of varieties of products the system cannot be rigid.  The system for a Rolls Royce cannot be rigid.  So I need to increase my flexibility.  Process competency.  

Let's look at another process competency.  Suppose I will compare these two [On overhead.]   Here is product variety, here is process competency.  If variety of my product goes up.  If my customers want hundreds of models and colors of the product when I move from low to high variety does cost of process go up or down?  

Male Student:   Up.  

Professor:   What??  UP.  Cost goes up, I need to produce more variety and cost goes up.  

What about time?  If I draw the line for flow time, what does it look like?  As variety goes up, flow time goes up.  Look at the process that produces one product.  Raw material comes, goes through station 1, 2 and 3 and goes out.  I can standardize the process.  

Suppose hundreds of products come through.  This goes here, here, there, here ... I'm more knowledgeable in product 1 but not in product 2, 3, 4, 5,  ... 

Right?  

Therefore flow time is high.  What about quality?  For flow time the line looks like this [On overhead.]   

What about quality?  How does quality line look?  We don't know.  We can't say if it is coming up or down.  You can have a product with high variety and high quality, or low quality.  You can have a low variety product with high or low quality.  

So the relationship between product attribute variety with the 4 process competences of cost, flexibility, time and quality.  The relationship with 3 of them is upward, positive.  That is cost, time and flexibility.  But with the other one, quality, we don't know.  

I think I have covered everything you need for the next 2 quizzes.  Listen to the recordings and solve the problems.  

[End of class.]