Friends,
We all are know that QT cover a large portion in COSTING and its very eary to learn
BUT
Generaly the proublems are feel by students that they forgot again and again quantitive technique very early and when we sit to revise QT we have found only PRACTICLE QUESTION AND THEIR SOLUTIONS ONLY
TO REVISE AGAIN WE NEED THE STEPS TO SOLVE THESE QUESTION.
So Thats why I'm Posting Here some good valuable notes on QUANTITIVE TECHNIQUE.
PLEASE FIND HERE THE SAME AND REPLY HERE,
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Assignment
1) Basis of Technique used is minimization Technique
2) It can also be done in maximation Technique
3) Various steps in Assignment Problem are
Step 1: Check whether the problem is balanced or unbalanced by checking
whether row is equal to column, if unbalanced add dummy column or
row to balance the problem
Step 2: Identify Least Number in each row and subtract with all number in that
Row.
Step 3: Identify least number of each column and subtract with all number in that
column.
Step 4: Check whether solution is reached with zero selection in one row and
column, ie. Cover all the zero with minimum number of lines, solution is
reached only when selected zeros is equal to number of rows or columns
or number of lines is equal to order of matrix.
Step 5: If solution is not reached so maximum sticking
Step 6: Select the least element in within the unstriked Element
Step 7: The element selected above is
i) Subtracted with all the unstriked element
ii) Added to all the double striked element (Intersection of two lines)
Step 8: Check the solution
Step 9: If solution is not reached continue with the process from step 5.
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Linear Programming
Simplex Method:
Steps:
For minimization problem the constraints would be > sign.
For < sign – add the slack variable ie. Add S1
For > sign – subtract the slack variable and add artificial variable
ie. Subtract S1, add A1.
4. Change the Objective function
For S1 – Add ‘0S1’
For A1 – Add ‘MA1’
5. Simplex table format:


Cj 






Quantity 
Variable 
Const. 
X 
Y 
Z 
S1 
S2 
RR 

S1 








S2 









Zj 








Cj  Zj 






6. Zj is arrived by summation of constant column with X,Y,Z columns
7. Criteria for selecting the key column :
For Maxima ion Problem – Highest value of Cj – Zj
For Minimization Problem – Lowest Value of Cj – Zj
8. Divide the Quantity Column with Key column to arrive at RR
9. Criteria for Selecting the Key row :
For Maximation & Minimization Problem – Lowest Positive RR is selected
10. The Meeting Point is key Element
11. Criteria for deciding the optimal solution
For Maximation Problem – All elements in Cj – Zj row is negative or zero.
For Minimization Problem – All elements in Cj – Zj row is positive or zero
Note – For finding whether all the elements in Cj – Zj row is positive or zero
for minimization problem substitute all the ‘M’ with highest value.
12. If solution is not reached next table is formed.
13. Input for next table is
First key row in the next table is filled by dividing all the numbers in the key row of the previous table with the key element.
Remaining all the rows is arrived as follows: 
Corresponding previous _ (Value relating to that * Corresponding
Table row element row in the key column element in key row
in the 2^{nd} table as
filled in previous step)
14. Check the optimal solution, if not reached form the third table.
15. If solution is reached then answer is amount in quantity column corresponding to the variable.
Other Points : 
E.g. X + Y < 100
is converted into X  Y > 100
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Transportation
Row penalty and column penalty is calculated at (2^{nd} least – 1^{st} least) in the corresponding row or column.
Notes: 
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Network Analysis (CPM/PERT)
CPM
Crash cost per day (or) Activity cost supply
= Crash cost – Normal cost
Normal time – Crash time
Ls = Lf – Duration
Ef = Es + Duration
Notes: 
PERT : 
1 for optimistic
4 for Most likely
1 for pessimistic
Average time = 1 optimistic + 4 most likely + 1 pessimistic
6
6
= Required time(N) () Expected time (critical path duration)
Standard Deviation
[Nothing but Z = (X  Mean) / Standard deviation]
= Y (say)
= Find Z(y)
= Probability %
 If required time > Expected time then = 0.5 + Z(Y)
 If required time < Expected time then = 0.5 – Z(Y)
Learning Curve
Learning is the process of acquiring skill, Knowledge, and ability by an individual. According to learning curve theory the productivity of the worker increases with increase in experience due to learning effect. The learning theory suggests that the best way to master a task is to “learn by doing”. In other words, as people gain experience with a particular job or project they can produce each unit more efficiently than the preceding one.
The speeding up of a job with repeated performance is known as the learning effect or learning curve effect.
The cumulative average time per unit produced is assumed to fall by a constant percentage every time the total output is doubled. So generally learning effect is found in the multiples of 2. If learning curve effect is asked between two even numbers then Learning curve equation is formed ie. Learning curve effect is expressed mathematically as follows:
Learning curve equation =
Y = a(x)^{ b }Where Y = Average time per unit
a = Total time for first unit
x = Cumulative number of units manufactured
b = the learning curve index
Learning curve index (b) = log (1 % decrease)
Log 2
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