The document discusses three methods for allocating goods in transportation problems: the North-West Corner method, Least-Cost method, and Vogel's Approximation Method. It also discusses the Assignment Method for solving assignment problems. The North-West Corner method allocates goods starting from the upper-left corner based on row and column totals. The Least-Cost method allocates goods to the lowest cost cell without exceeding supply/demand. Vogel's Approximation Method considers cost differences and allocates to the highest difference cell. The Assignment Method solves assignment problems by subtracting costs and covering entries to find the optimal assignment.

2. To use the VAM
method to obtain
an initial basic
feasible solution to
a problem.
To recognize
problems that have
alternative least-cost
solutions.
To find alternate
least-cost solutions
when they exist.

3. Math 132
Quantitative
Techniques for
Business

4. Topics to be discussed:
Ways of
Allocating
Goods
Assignment
Method
Let’s do
This!

5. Initial allocation entails assigning
numbers to satisfy supply and
demand constraints.
In order to allocate and assign
goods, there are three (3) ways
available.
The Initial Basic Feasible Solution

6. Different
WAYS of
Allocating
Goods
1. THE NORTH-WEST CORNER METHOD
2. THE LEAST-COST METHOD OF
ALLOCATION
3. VOGEL’S APPROXIMATION METHOD

7. North-West Corner method of
Allocation

8. The north-west corner
method for finding
an initial feasible
solution involves the
following steps:

9. NORTH-WEST CORNER
METHOD
a) Start in a cell at the upper-left
corner, place a quantity of goods
in this cell that equals the smaller
of the row total or the column total
in the transportation
b) If the smaller number is the row
total, the 1st row is exhausted. Go
to the 2nd. If the smaller number is
the column total, the 1st column is
exhausted. Go to the 2nd column.

10. NORTH-WEST CORNER
METHOD
c) If you have gone to the 2nd row, allocate
enough goods to the cell in row 2,
column 1, to exhaust the column
d) Continue this manner, utilizing the smaller
of the row total and the column total,
until you reach the lower right-hand
corner. You should place numbers in a
number of cells equal to the number of
columns + the number of rows -1(C+R-1);
unless the problem is degenerated.

11. Sample Problem: Let’s do this!

12. Sample Problem: Let’s do this!

13. Sample Problem: Let’s do this!

14. Sample Problem: Let’s do this!

15. Least-Cost method of Allocation

16. how?
it’s easier than you think.

17. INTUITIVE LOWEST-COST
METHOD
The intuitive method makes initial allocations
based on lowest cost. This straightforward
approach uses the following steps:
1. Identify the cell with lowest cost. Break
any ties for the lowest cost arbitrarily.
2. Allocate as many units as possible to
that cell without exceeding the supply
or demand. Then cross out that row or
column (or both) that is exhausted by
this assignment.

18. 3. Find the cell with the lowest cost
from the remaining (not crossed
out) cells.
4. Repeat steps 2 and 3 until it has
been allocated
 Rule being applied: Least cost method

19. Sample Problem: Let’s do this!

20. Sample Problem: Let’s do this!

21. Sample Problem: Let’s do this!

22. Third method ?
Vogel’s
Approximation
method of Allocation

23. This method also costs into account. In
allocation, five steps are involved in
applying this heuristic.

24. Steps to follow:
1. Determine the difference
between the lowest two cells
in all rows and columns
(including dummies if they are
unbalanced).
2. Identify the row column with
the largest difference ties that
may be broken arbitrarily.

25. 3. Allocate as much as possible to the
lowest-cost cell in the row or column
with the highest difference.
4. Stop the process if all row and
column requirements are met. If not,
go to the next step.
5. Recalculate the difference between
the two lowest cell remaining in all
rows and columns. Any row and
column with zero supply or demand
should not be used in calculating
further differences. Then go to step 2.

26. The Vogel’s Approximation Method (VAM)
usually produces an optimal or near-optimal
starting solution. One study found that VAM
yields an optimum solution in 80% of the
sample problems tested.

27. Sample Problem: Let’s do this!

28. Sample Problem: Let’s do this!

29. Sample Problem: Let’s do this!

30. Sample Problem: Let’s do this!

31. Linear
Programming:
Assignment
Method

32. how?
it’s easier than you think.

33. Assignment Method
Another type of purpose is
the algorithm used in linear
programming.
It is concerned in allocating
the jobs to each of the
workers for minimum cost.

34. 1) The assignment problem is
the problem of assigning n
workers to n jobs. In such a
way that only one worker
is assigned to each job,
each job has one. The
workers assigned to it and
the cost of completing all
of the jobs are minimized.

35. 2. The assignment method is the
standard procedure for
solving the assignment
problem on the basis of the
assignment table.

36. There are three main steps to follow in
solving an assignment problem:
1. Subtract the smallest cost from each entry in
each row. If each zero can now be assigned
in a one to one correspondence with the
“workers”, an optimal solution is obtained. If
cannot, go to step 2.
2. Subtract the smallest cost in each column. If
the zero entries can now be distributed in a
one to one correspondence with the
“workers”, an optimal solution is obtained or
reached. If not, go to step 3.

37. 3. Cover the zero entries by vertical or
horizontal lines, using the least number of
lines possible. (This can be done by
covering first the row or column having the
most number of zeros). Subtract the
smallest uncovered cost from each
uncovered cost but add it to the entry
found at the intersection of the lines. If the
assignment is already possible an optimal
solution is reached. If not, repeat step 3. An
assignment is optimum if the number of
lines is equal to the number of rows or the
number of columns.

38. Sample Problem: Let’s do this!

39. Sample Problem: Let’s do this!

40. Sample Problem: Let’s do this!

41. Sample Problem: Let’s do this!

42. Sample Problem: Let’s do this!

43. Jessica MagadiaEtrataJ E M
Submitted To:

44. THE END
THANK YOU FOR
LISTENING!
GROUP 5