BUSOBA 3230: Final Math Notes and Observations

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Critical Path Method and Crashing

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Steps 1-4

1. Make network diagram.

2. Determine paths and critical path (the longest).

3. Find slack. (Occasional)

4. Find Available Weeks of Crashing.

Steps 5-8

5. Find Crashing Cost Per Day.
6. Find total normal cost by adding them all together.
7. Find total project cost.
8. Fill out graph/crash.

To make network diagram, use

activity, immediate predecessor, and normal time (NT).

Normal time can be

days, weeks. Just make sure it's TIME.

To determine paths and critical path, use

network diagram.

During step 2, add all of the NTs that are in a path together. The path that's the

longest is the critical path.

During step 3, first, find EARLY start and EARLY finish. Next, find

LATEST start and LATEST finish.

EARLY start and EARLY finish is moving to the

right.

With EARLY start and EARLY finish, ALWAYS start with

0.

With LATEST start and LATEST finish, ALWAYS pick the

LARGEST number from ES and EF.

LATEST start and LATEST finish is moving to the

left.

Available Weeks of Crashing is

normal time - crash time. = NT - CT.

Crashing Cost Per Day is

• crash cost - normal cost / normal time - crash time.

• Essentially, Cost/Time.

• = CC - NC / NT - CT

After finding total normal cost, find

total project cost.

Total Project Cost =

Total Normal Cost + Indirect Cost + Penalty Cost

To find Total Project Cost, you must take the Indirect Cost given and

multiply by the Critical Path found earlier.

To find Total Project Cost, you must take the Penalty Cost given and

multiply by the Critical Path found earlier subtracted by the "if the project takes longer than _ number _"

• is

additional cost.

• is

what you save.

REALLY think of the numbers underneath + as

positive.

REALLY think of numbers underneath - as

negative.

When trying to find the Net, use the

correct signs for the numbers underneath the + and -.

Total in the graph is

Total Project Cost.

First action will ALWAYS be

DO Nothing.

After first crash, look at

• Crashing Cost Per Week.
• Then, select the activity that is the smallest/cheapest on the critical path.
• THIS is the one you will crash next. Again, this must be the SMALLEST/CHEAPEST.

After you select the activity to crash, cross out

the number associated with Available Weeks of Crashing. Make it one less.

Take $ from Crashing Cost Per Week and

write it underneath +.

Take Indirect Cost and Penalty Cost and

write it underneath -.

The same Indirect Cost and Penalty Cost will always be written underneath - until a certain point. It's related to

"if the project takes longer than _ number."

After the Critical Path reaches the number associated with "if the project takes longer than _ number" then for the next crash,

there is NO MORE Penalty.

Take PREVIOUS Total and subtract by

CURRENT Net.

Whenever crashing an activity, subtract 1 week by

ALL the paths that are affected by THAT specific activity. If it's multiple, do this as well.

Take this: "If the project takes longer than _ days." When the critical path reaches that day,

stop putting Penalty Cost underneath -.

Minimum Cost Schedule is the

last Critical Path.

Minimum Cost Schedule Savings is

FIRST Total - LAST Total.

Skim the information before

drawing the network diagram.

When finding the paths, go from the

top of the diagram to the bottom. Really follow the lines.

Duration for the project is the / "Before crashing, the project duration is _ week(s)." is the

Critical Path.

"The total cost of the project if we do nothing is $ __ " is the

Total Project Cost.

Essentially, duration is

critical path.

Must subtract both F

FINISHES. Late first.

Must subtract both S

STARTS. Late first.

LF - EF and LS - ES must be the

same.

If we were to draw Activity Time with a circle around it, ES and EF would be together at the top and

LS and LF would be together at the bottom.

The first paths in the graph are the

paths you found while trying to find the Critical Path.

When trying to figure out what to crash next, go back to the

Critical Path.

When you are down to 2 letters in the critical path OR after a while,

find a letter that impacts ALL paths and crash that one.

Look for opportunities to

crash two things at once.

When trying to figure out two things to crash at once,

pick the combination that is the smallest.

After crashing for a while, if a letter is only on ONE path, consider

stopping. There may be nothing else you can do.

STATISTICAL PROCESS CONTROL

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Mean

 is the total sum of all the values in a sample.

X-Bar

 is the mean of the sample. The average value of a set of numbers

X-Double Bar

 is the average of the means of the samples. 

R-Bar

is the average of the measurement differences R for all samples. 

R

is range.

σ

is the standard deviation of the process distribution.

“selects a random box of 5 packets” means

sample size is 5 packets. 

“decided to take random samples of 53 patients” means

sample size is 53

“concerned over the number of times patients must wait more than 30 minutes” or “to see how many in each sample had to wait more than 30 minutes” means

data is an attribute.

Steps to Find LCL R and UCL R:

1 Find data type. Attribute or Variable. This will determine what chart to 

2 Determine what chart you are making and what formula you are solving for.

3 Determine sample size (n). 

4 Find R-Bar.

5 Find either D3 or D4.

6 Solve

Steps to Find σ p

1 Find data type. Attribute or Variable. This will determine what chart to 

2 Determine what chart you are making and what formula you are solving for.

3 Determine sample size (n). 

4 Number of Defects / Sample Size (n). Do this for EACH sample in graph.

5 Add all of the PREVIOUS answers up and then divide by the number of samples ON THE GRAPH to find the average/p-bar. Focus. Find the average/p-bar

6 Use the equation inside the square root (formula sheet) to find  σ p.

*Steps to Find LCL P and UCL P

1 Find data type. Attribute or Variable. This will determine what chart to 

2 Determine what chart you are making and what formula you are solving for.

3 Determine sample size (n). 

4 Number of Defects / Sample Size (n). Do this for EACH sample in graph.

5 Add all of the PREVIOUS answers up and then divide by the number of samples ON THE GRAPH to find the average/p-bar. Focus. Find the average/p-bar

6 Use the equation inside the square root (formula sheet) to find  σ p.

7 Use equation (formula sheet) to find the control limits.

“the range in the weight of each sample has averaged 9 grams” means

the R-bar is 9.

A2, D3, and D4 are determined by

the sample size (n).

Data is attribute if it’s the following:

Categories, good/bad, # of mistakes, pass/fail, yes/no, shift #

Data is variable if it’s the following:

Weight, time, cost, length, speed, money, rate, pressure.

Equation inside the square root (formula sheet) is

σ p. It’s also known as standard deviation.

In (), lower limit first, then

upper limit.

Must use subtraction to find

lower limit.

Must use addition to find

upper limit.

LCL can never be

negative - because negative proportions don’t exist. The LCL will be 0 instead.