Operations Research MBA-024
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 1/153
Operations Research
MBA-024
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 2/153
TRANSPORTATION PROBLEM
UNIT II
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 3/153
Transportation Model/Problem
TP is essentially an LPP.
But because of certain special characteristics
associated with the problem, we have aspecial algorithm to solve a TP.
It is not solved by applying the simplex
method.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 4/153
Transportation Model/Problem
Although in principle it can be solved by the
simplex method but its application would
make the problem very unmanageable.
The TP, along with the assignment problem is
a special type of LPP, therefore we have
special purpose algorithms for them.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 5/153
TP: Important Features
TP normally used for minimising
transportation cost, although the algorithm
can be applied on some other types of
problems also.
A TP deals with problems related to
minimisation of cost when goods have to be
transported from different points of supply todifferent points of demand.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 6/153
TP: Important Features
The amounts available at different points of
supply and amounts required at different
points of demand are known to us.
The unit cost of transportation is also known
to us.
In a general TP we may assume m points of
supply and n points of demand.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 7/153
TP: Important Features
We have to design a transportation plan which
would minimise the total cost of
transportation.
Total number of variables = m x n.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 8/153
TP: Formulation
General notation of variable: xij (amount of goodstransported from ith point of supply to jth point of demand).
Cij = cost coefficient attached with xij. Total number of constraints = m+n.
There would be m supply and n demandconstraints.
Availability at supply points: b1, b2, b3, , bm.
Requirement at demand points: d1, d2, d3, , dn.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 9/153
TP: Formulation
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 10/153
TP: Formulation
This is a balanced TP because total supply is equalto total demand.
Because total supply = total demand, thereforeone constraint becomes redundant.
T
otal number of effective constraints = m+n-1. Number of basic variables = number of constraints = m+n-1
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 11/153
There are 3 coalieries which can supply coal in
the following quantities:
a: 14 tonnes, b: 12 tonnes, c: 5 tonnes.
There are 3 consumers who require coal in the
following quantities:
A: 6 tonnes, B: 10 tonnes, C: 15 tonnes.
The cost of transporting 1 tonne of coal from
any one point a, b or c to any other point A, B orC are as follows:
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 12/153
The problem is to minimise total cost of
transportation.
6 4 1 a8 9 2 b
4 3 6 c
A B C
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 13/153
North West Corner Rule
1. Select the north-west (upper left) corner cell.
2. Allocate as many units as possible.
3. Adjust supply and demand figures in therespective row and column.
4. If row supply is exhausted, move down one row.
5. If column demand is exhausted, move right onecolumn.
6. Repeat steps 2-5 till total available quantity isfully allocated.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 14/153
Least Cost Method
1.Select the cell with the lowest transportation
cost.
2.Allocate as many units as possible.3.Adjust supply and demand figures in the
respective row and column.
4.Repeat steps 1-3 till total available quantity is
fully allocated.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 15/153
Vogels Approximation Method
Best method of obtaining initial solution.
Consists of determining (row and column)penalties.
Row penalty is calculated by subtracting theminimum cost element from the second leastcost element in the row.
Column penalty is calculated by subtractingthe minimum cost element from the secondleast cost element in the column.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 16/153
Stepping Stone Method
Determine an initial basic feasible solution
using any of the above three methods.
Make sure that the number of occupied cellsis m+n-1.
Select an unoccupied cell.
Beginning at this cell, trace a closed path.
Move only horizontally or vertically.
Turn only at occupied cells.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 17/153
Stepping Stone Method
The cells at the turning points are called the
stepping stones.
Assign plus and minus signs alternatively toeach stepping stone, starting with a plus sign
at the unoccupied cell to be evaluated.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 18/153
Stepping Stone Method
Compute the net change in cost along theclosed path by finding the algebraic sum of the unit costs of the stepping stones,
considering the plus/minus signs assigned inthe previous step.
A negative sum indicates a decrease intransportation cost.
Repeat these steps for all the unoccupiedcells.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 19/153
Modified Distribution Method
Determine an initial basic feasible solution.
Compute the values of the row and column
variables (ui and v j). Compute the improvement index for each
unoccupied cell,
If all improvement indices are positive or zero,
the optimum solution has been reached.
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 20/153
Factory Warehouse Capacity
(Supply)W1 W2 W3 W4
F
1 21 16 25 13 11F2 17 18 14 23 13
F3 32 27 18 41 19
Requirement
(Demand)
6 10 12 15 43
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 21/153
W1 W2 W3 W4
F121 16 25 13
11
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15 43
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 22/153
N
orth West Corner Rule
NWCR
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 23/153
W1 W2 W3 W4
F121 16 25 13
11
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 24/153
W1 W2 W3 W4
F121 16 25 13
116
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 25/153
W1 W2 W3 W4
F121 16 25 13
56
F2 17 18 14 23 13X
F3
32 27 18 41
19X
0 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 26/153
W1 W2 W3 W4
F121 16 25 13
56 5
F2 17 18 14 23 13X
F3
32 27 18 41
19X
0 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 27/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 13X
F3
32 27 18 41
19X
0 5 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 28/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 13X 5
F3
32 27 18 41
19X
0 5 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 29/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 8X 5
F3
32 27 18 41
19X X
0 0 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 30/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 8X 5 8
F3
32 27 18 41
19X X
0 0 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 31/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 0X 5 8 X
F3
32 27 18 41
19X X
0 0 4 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 32/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 0X 5 8 X
F3
32 27 18 41
19X X 4
0 0 4 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 33/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 0X 5 8 X
F3
32 27 18 41
15X X 4
0 0 0 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 34/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 0X 5 8 X
F3
32 27 18 41
15X X 4 15
0 0 0 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 35/153
W1 W2 W3 W4
F121 16 25 13
06 5 X X
F2 17 18 14 23 0X 5 8 X
F3
32 27 18 41
0X X 4 15
0 0 0 0
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 36/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 37/153
Least Cost Method
LCM
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 38/153
W1 W2 W3 W4
F121 16 25 13
11
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 39/153
W1 W2 W3 W4
F121 16 25 13
1111
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 40/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 41/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 1312
F3
32 27 18 41
19
6 10 12 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 42/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 112
F3
32 27 18 41
19X
6 10 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 43/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 11 12
F3
32 27 18 41
19X
6 10 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 44/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
19X
5 10 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 45/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
1910 X
5 10 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 46/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
910 X
5 0 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 47/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
95 10 X
5 0 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 48/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
45 10 X
0 0 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 49/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
45 10 X 4
0 0 0 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 50/153
W1 W2 W3 W4
F121 16 25 13
0X X X 11
F2 17 18 14 23 01 X 12 X
F3
32 27 18 41
05 10 X 4
0 0 0 0
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 51/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 52/153
Vogels Approximation Method
VAM
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 53/153
W1 W2 W3 W4
F121 16 25 13
11
F2 17 18 14 23 13
F3
32 27 18 41
19
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 54/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13
F332 27 18 41
19
6 10 12 15 43
Column
Penalty
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 55/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19
6 10 12 15 43
Column
Penalty
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 56/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 57/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 58/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 59/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 60/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 61/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 3
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 62/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
11 311
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 63/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 311
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 15 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 64/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 311
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 4 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 65/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 3X X X 11
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 4 43
Column
Penalty 4 2 4 10
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 66/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
13 3
F332 27 18 41
19 9
6 10 12 4 43
Column
Penalty 15 9 4 18
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 67/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
13 34
F332 27 18 41
19 9
6 10 12 4 43
Column
Penalty 15 9 4 18
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 68/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
9 34
F332 27 18 41
19 9X
6 10 12 0 43
Column
Penalty 15 9 4 -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 69/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
9 36 4
F332 27 18 41
19 9X
6 10 12 0 43
Column
Penalty 15 9 4 -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 70/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
3 46 4
F332 27 18 41
19 9X X
0 10 12 0 43
Column
Penalty - 9 4 -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 71/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
3 46 4
F332 27 18 41
19 9X X
0 10 12 0 43
Column
Penalty - 9 4 -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 72/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
3 46 3 4
F332 27 18 41
19 9X X
0 10 12 0 43
Column
Penalty - 9 4 -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 73/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
0 -6 3 X 4
F332 27 18 41
19 9X X
0 7 12 0 43
Column
Penalty - - - -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 74/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
0 -6 3 X 4
F332 27 18 41
19 -X 7 X
0 7 12 0 43
Column
Penalty - - - -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 75/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 76/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
0 -6 3 X 4
F332 27 18 41
12 -X 7 12 X
0 0 12 0 43
Column
Penalty - - - -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 77/153
W1 W2 W3 W4 Row
Penalty
F121 16 25 13
0 -X X X 11
F2
17 18 14 23
0 -6 3 X 4
F332 27 18 41
0 -X 7 12 X
0 0 0 0 43
Column
Penalty - - - -
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 78/153
W1 W2 W3 W4
F121 16 25 13
1111
F2 17 18 14 23 136 3 4
F3
32 27 18 41
197 12
6 10 12 15
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 79/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 80/153
Stepping Stone Method
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 81/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 82/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 83/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 84/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 85/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 86/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 87/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 88/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 89/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 90/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 91/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
F1W2F1W4F3W4F3W2 16-13+41-27=17
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 92/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 93/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 94/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 95/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 96/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 97/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 98/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
F1W2F1W4F3W4F3W2 16-13+41-27=17
F
1W3F
1W4F
3W4F
3W1F
2W1F
2W3 25-13+41-32+17-14=24
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 99/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 100/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 101/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 102/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 103/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
F1W2F1W4F3W4F3W2 16-13+41-27=17
F1W3F1W4F3W4F3W1F2W1F2W3 25-13+41-32+17-14=24
F2W2F3W2F3W1F2W1 18-27+32-17=6
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 104/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 105/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 106/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 107/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 108/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
F1W2F1W4F3W4F3W2 16-13+41-27=17
F1W3F1W4F3W4F3W1F2W1F2W3 25-13+41-32+17-14=24
F2W2F3W2F3W1F2W1 18-27+32-17=6
F2W4F3W4F3W1F2W1 23-41+32-17=-3
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 109/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 110/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 111/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 112/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 113/153
F1W1F1W4F3W4F3W1 21-13+41-32=17
F1W2F1W4F3W4F3W2 16-13+41-27=17
F1W3F1W4F3W4F3W1F2W1F2W3 25-13+41-32+17-14=24
F2W2F3W2F3W1F2W1 18-27+32-17=6
F2W4F3W4F3W1F2W1 23-41+32-17=-3
F3W2F3W1F2W1F2W3 18-32+17-14=-11
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 114/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 115/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5- 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 116/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1+ 12
F332 27 18 41
5- 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 117/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 118/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1+ 12-
F332 27 18 41
5- 10 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 119/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 120/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 121/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 122/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 123/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 124/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 125/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 126/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 7
F332 27 18 41
10 5 4
F1W1F1W4F3W4F3W3F2W3F2W1 21-13+41-18+14-17=28
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 127/153
F1W1F1W4F3W4F3W3F2W3F2W1 21-13+41-18+14-17=28
F1W2F1W4F3W4F3W2 16-13+41-27=17
F1W3F1W4F3W4F3W3 25-13+41-18=35
F2W2F2W3F3W3F3W2 18-14+18-27=-5
F2W4F3W4F3W3F2W3 23-41+18-14=-14
F3W1F2W1F2W3F3W3 32-17+14-18=11
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 128/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 129/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F332 27 18 41
10 9
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 130/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 131/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F332 27 18 41
10 9
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 132/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 133/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
10 9
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 134/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
10 9
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 135/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
10 9
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 136/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
10 9
F1W1F1W4F2W4F2W1 21-13+41-32=17
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 137/153
F1W2F1W4F2W4F2W3F3W3F3W2 16-13+23-14+18-27=3
F1W3F1W4F2W4F2W3 25-13+23-14=21
F2W2F2W3F3W3F3W2 18-14+18-27=-5
F3W1F2W1F2W3F3W3 32-17+14-18=11
F3W4F3W3F2W3F2W4 41-18+14-23=14
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 138/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3- 4
F3 32 27 18 41
10- 9+
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 139/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
7 12
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 140/153
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 141/153
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 142/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
7 12
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 143/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
7 12
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 144/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
7 12
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 145/153
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 146/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
6 3 4
F3 32 27 18 41
7 12
F1W1F1W4F2W4F2W1 21-13+41-32=17
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 147/153
F1W2F1W4F2W4F2W2 16-13+23-18=8
F1W3F1W4F2W4F2W2F3W2F3W3 25-13+23-18+27-18=26
F2W3F3W3F3W2F2W2 14-18+27-18=5
F3W1F2W1F2W2F3W2 32-17+18-27=6
F3W4F3W2F2W2F2W4 41-27+18-23=9
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 148/153
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 149/153
W1 W2 W3 W4
F121 16 25 13
11
F217 18 14 23
1 12
F332 27 18 41
5 10 4
W1 W2 W3 W4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 150/153
W1 W2 W3 W4
F121 16 25 13
u111
F217 18 14 23
u21 12
F332 27 18 41
u3
5 10 4
v1 v2 v3 v4
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 151/153
Degeneracy
A manufacturing company has three plants X Y
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 152/153
A manufacturing company has three plants X, Y
and Z, which supply to the distributors locatedat A, B, C, D and E. Monthly plant capacities are
80, 50 and 90 units respectively. Monthly
requirements of distributors are 40, 40, 50, 40
and 80 units respectively. Unit transportationcosts are given below in rupees:
F T
8/9/2019 Unit-II-2-TP
http://slidepdf.com/reader/full/unit-ii-2-tp 153/153
Determine an optimal
distribution for the
company in order tominimise the total
From To
A B C D E
X 5 8 6 6 3
Y 4 7 7 6 6
Z 8 4 6 6 3
Related Documents
