Operation Research Techniques in Transportation

Welingkar’s Distance Learning Division

CHAPTER-8

Operation Research Techniques in
Transportation

We Learn – A Continuous Learning Forum

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

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


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


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.


North West Corner Rule Figure-2
Destinations/
origins

D1

D2

D3

D4

D5

Supply

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


• 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.


• 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


Deploying vehicles-Listing Method

C

D

A

G

E

B

F


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


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


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


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


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


Listing Method
A=0

B=9

D

E

F

G

DC=14

EB=14

FD=10

GD=15

DE=7

BE=14

C=18

EC=11

FE=10

GF=11

CD=14

DF=10

ED=7

FG=11

CE=11

DG=15

EF=10


Next we observe that from C E is a shorter
route hence
A=0

B=9

C=18

D

E=29

BE=14

CD=14

ED=7

DG=15

GD=15

FE=10

DF=10

G

FD=10

DE=7

F

GF=11

FG=11

EF=10


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


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


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


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


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


Preparing a flow chart
• The project events joined by lines (activities)
• The activities are depicted by lines illustrate
project relationships and inter dependences


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


PERT network

7

3

1

2

5

4
Real Activites
Dummy Activites

6

8

9

10


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

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

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


Activity

(a)

(b)

(c)

Expected
mean time

1.Studying the existing system in
details and documenting all the current
procedures

1

3

1.5

1.7

2.Customizing the system to suit the
organizational requirement

2

4

3

3

.25

.1

.5

.75

4. Making application to exercise
authorities

1

4

1.5

1.9

5. Training staff for new system

1

2

1

1.2

1.5

3

2

2.1

3.Configuring the hardware
requirement

6. Preparing new master data
7. Setting date for change over
8.Uploading old data on new server


Network Representation
4
2
5

1

3

6
Real Activites
Dummy Activites

8

7

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


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


Operation Research Techniques in Transportation

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