Operation Research involves determining an optimum solution to a distribution problem. In order to suitably plan and assign vehicles to different routes, organizations can use the listing method described in the North-West corner rule. Research methods such as PERT and CPM are useful for timely completion of a project.

1. Chapter-08
Operation Research Techniques
in Transportation

2. North West Corner Rule
• Model to determine the optimum solution to a
problem of separate demand points being
supplied from separate points
• Let us take a situation where there are 3 supply
sources S1,S2,S3 and S4 and demand sinks
D1,D2,D3,D4
• The costs associate with 12 combinations as
well as the supplies ex each supply point and
demands at each demand center are depicted in
the figure on next slide
Ch-08 - 0peration Research Techniques in
Transportation

3. North West Corner Rule fig-1
Destinations
/origins
D1 D2 D3 D4 D5 D6
S1 3 7 12 10 9 9
S2 14 20 13 6 12 4
S3 12 15 13 9 6 8
Demand
3 5 4 6 3 21
Ch-08 - 0peration Research Techniques in
Transportation

4. North West Corner Rule fig-1
• The three supply points S1,S2 and S3 can
supply 9 units, 4 units, and 8 units respectively,
whereas the three demand points D1, D2, D3,
and D4 require 3,5,4,6 and 3 units respectively
• The cost at the point of calculation will be treated
as negative figures, because they are basically
items whose negative impact the exercise is
trying to minimize, in this case the total demand
is 21units and the supply available is also 21
units
Ch-08 - 0peration Research Techniques in
Transportation

5. North West Corner Rule
• Where the supply may be more than demand,
an additional dummy demand column has to be
put with the residual supply being shown as
units required by this demand center, and in the
boxes for costs zero should be put
• Similarly, in case demand exceeds shown there
against, and again in the cost zero should be put
in the respective additional squares.
Ch-08 - 0peration Research Techniques in
Transportation

6. North West Corner Rule Figure-
2
Destinations/ Supply
origins
D1 D2 D3 D4 D5
S1 11 12 13 14 15 9
S2 21 22 23 24 25 4
S3 31 32 33 34 35 8
Demand
3 5 4 6 3 21
Ch-08 - 0peration Research Techniques in
Transportation

7. North West Corner Rule Figure-
2
• In fig2 we shall give the 15 squares
individual numbers for easier identification
• The five squares across supply point 1 will
have no. 11 to 15, against supply point 2
the numbers will be 21 to 25, and for the
3rd one the no. will be 31 to 35.
Ch-08 - 0peration Research Techniques in
Transportation

8. North West Corner Rule Figure-
2
• Allocate supplies fro the supply sources to the demand
sinks
• The process starts form the north west corner i.e. square
11, and hence the name north west corner rule
• Demand sink 1 has requirement for 3 units, and supply
source 1 can supply 9 units, the total requirement of D1
from S1, when the situation is such that after meeting the
demand of D1 from S1 , units remain, then the next
allotment should be made horizontally, i.e. the next
supply from S1 should go to D2
Ch-08 - 0peration Research Techniques in
Transportation

9. Deploying vehicles-Listing Method
C D
A G
E
B F
Ch-08 - 0peration Research Techniques in
Transportation

10. Deploying vehicles-Listing Method
• A is the starting point from where materials are
sent out for delivery to various points B,C, D,E,F
and G.
• The distance between
• A and B is 9 km, A and C is 11 km
• B & C is 9 km, C & D is 14 km
• C & E is 11 km, D & E is 7 km
• E & F is 10 km, D & F is 10 km
• D & G is 15 km, F & G is 11 km
Ch-08 - 0peration Research Techniques in
Transportation

11. Listing Method
A B C D E F G
AB=9 BA=9 CA=11 DC=14 EB=14 FD=10 GD=15
AC=11 BC=9 CB=9 DE=7 EC=11 FE=10 GF=11
BE=14 CD=14 DF=10 ED=7 FG=11
CE=11 DG=15 EF=10
Ch-08 - 0peration Research Techniques in
Transportation

12. Listing Method
• To initiate the solution procedure , a value of
zero is assigned to the starting point, in this case
A.
• Thereafter select the shortest distance from
origin A which in this case is AB as AC is longer
at 11. In case both the distances are the same
then selecting either will do
• The value of B will be the total of value for A
Zero plus the value AB which is 9 i.e.9
Ch-08 - 0peration Research Techniques in
Transportation

13. Listing Method
A=0 B=9 C D E F G
CA=11 DC=14 EB=14 FD=10 GD=15
BC=9 CB=9 DE=7 EC=11 FE=10 GF=11
BE=14 CD=14 DF=10 ED=7 FG=11
CE=11 DG=15 EF=10
Ch-08 - 0peration Research Techniques in
Transportation

14. Listing Method
• Thereafter from B we again choose the
shortest of the alternate routes
• You would have noted that under B, the
route BA has been removed because that
is no longer an option
Ch-08 - 0peration Research Techniques in
Transportation

15. Listing Method
A=0 B=9 C=18 D E F G
DC=14 EB=14 FD=10 GD=15
DE=7 EC=11 FE=10 GF=11
BE=14 CD=14 DF=10 ED=7 FG=11
CE=11 DG=15 EF=10
Ch-08 - 0peration Research Techniques in
Transportation

16. Listing Method
A=0 B=9 C=18 D E F G
DC=14 EB=14 FD=10 GD=15
DE=7 EC=11 FE=10 GF=11
BE=14 CD=14 DF=10 ED=7 FG=11
CE=11 DG=15 EF=10
Ch-08 - 0peration Research Techniques in
Transportation

17. Next we observe that from C E is a
shorter route hence
A=0 B=9 C=18 D E=29 F G
FD=10 GD=15
DE=7 FE=10 GF=11
BE=14 CD=14 DF=10 ED=7 FG=11
DG=15 EF=10
Ch-08 - 0peration Research Techniques in
Transportation

18. Listing Method
• The route becomes A-B-C-E=29 km.
proceeding this way you will finally find
that the shortest route is
• A-B-C-E-D-F-G=9+9+11+7+10+11=57
Ch-08 - 0peration Research Techniques in
Transportation

19. Listing Method
• The importance of this model is listing
• Unless they are plotted systematically and
eliminated sequentially the above
apparently simple exercise may be difficult
in real life
Ch-08 - 0peration Research Techniques in
Transportation

20. PERT & CPM
• In order to realize valid results within time
and budget expectations, one has to
schedule jobs and tasks
• Through scheduling one not only plans
tasks, but also checks that resources are
utilized optimally
• Above two techniques are very commonly
used
Ch-08 - 0peration Research Techniques in
Transportation

21. Critical Path Method
• In CPM the entire project work plan is
graphically portrayed. This graph or network
displays the interdependencies between
activities that will lead to successful completion
of the project. It must satisfy the following
objectives
– Evaluate progress towards attainment of project
completion
– Focus attention on potential and actual problems
during work
Ch-08 - 0peration Research Techniques in
Transportation

22. Critical Path Method
– Provide frequent, accurate status reports at
critical check points
– Provide a regular and updated prediction of
when the project will be completed
– Provide at any time during the project
determination of the shortest completion time
if priorities and resources are shifted
Ch-08 - 0peration Research Techniques in
Transportation

23. Preparing a flow chart
• The project events joined by lines
(activities)
• The activities are depicted by lines
illustrate project relationships and inter
dependences
Ch-08 - 0peration Research Techniques in
Transportation

24. Preparing a flow chart
• The events depict significant occurrences or
milestones in the completion of the project
• Activities may be real or dummy, when it
signifies an actual task that has be done, which
means resources to be needed whereas dummy
activities depicted in the flow chart just to show
that the dummy activity needs to be completed
before another activity can be taken up, which
means in terms of resource the dummy will not
extent any
Ch-08 - 0peration Research Techniques in
Transportation

25. PERT network
7
3
1 2 5 6
4
Real Activites 8 9 10
Dummy Activites
Ch-08 - 0peration Research Techniques in
Transportation

26. PERT
• Circles with numbers are events
• The dark continues lines depict real activities
and the hyphenated lines depict dummy
activities
• The next step is to assign time to the
activities as well as resources and costs.
• This is where CPM comes in,
• While in PERT probabilistic time estimates
are put in while preparing the flow chart, CPM
will use exact deterministic times with cost
benefit trade offs
Ch-08 - 0peration Research Techniques in
Transportation

27. Example of putting up a new systems
set up at a manufacturing location
1. Studying the existing system in details and
documenting all the current procedures
2. Customizing the system to suit the
organizational requirement
3. Configuring the hardware requirement
4. Making application to exercise authorities
5. Training staff for new system
6. Preparing new master data
7. Setting date for change over
8. Uploading old data on new server
Ch-08 - 0peration Research Techniques in
Transportation

28. This brings up the issue of
• Optimistic time
– The time estimate if activity proceeds perfectly (a)
• Pessimistic time
– The time estimate if extreme difficulties are
experienced (b)
• Most Likely Time
– The expected time (c) the expected time as a mean
can be calculated by apportioning weights to the 3
times, for instance giving weights of 1 each to (a) and
(b) and 3 to (c) one can calculate the mean time
Ch-08 - 0peration Research Techniques in
Transportation

29. Activity (a) (b) (c) Expected
mean time
1.Studying the existing system in 1 3 1.5 1.7
details and documenting all the current
procedures
2.Customizing the system to suit the 2 4 3 3
organizational requirement
3.Configuring the hardware .25 .1 .5 .75
requirement
4. Making application to exercise 1 4 1.5 1.9
authorities
5. Training staff for new system 1 2 1 1.2
6. Preparing new master data
7. Setting date for change over
8.Uploading old data on new server 1.5 3 2 2.1
Ch-08 - 0peration Research Techniques in
Transportation

30. Network Representation
4
2
5
1 3
6
Real Activites 8 7
Dummy Activites
Ch-08 - 0peration Research Techniques in
Transportation

31. Interpretation
• Linkage between (2) and (4) and (8) does not
require allotment of a resources from the
organization, save may be follow ups but non
completion of event (4) will not bring about event
(8) and finally (7) now on the basis of the
expected mean time if we track the path from (1)
to (7) via the three routes we shall get three sets
of time. The one with longest time is the critical
path, while the others are the slack paths
Ch-08 - 0peration Research Techniques in
Transportation

32. Summary
• To determine optimum solution to a
distribution problem, we need to employ
suitable operation research technique
• North-west corner rule, listing method are
suitable for planning and assigning
vehicles for different routes
• PERT and CPM are useful for timely
completion of a project
Ch-08 - 0peration Research Techniques in
Transportation