OPERATIONS RESEARCH

CHAPTER V

Transportation ModelsInstructor : Lect.Volkan ÇETİNKAYA

Transportation Model The Transportation Model is a special class of

linear programs that deals with shipping a

commodity from sources (factories) to

destinations (warehouses).

The objective is to determine the shipping

schedule that minimizes total shipping cost while

satisfying supply and demand limits.

Representation of Transportation Model

POLAND

S. AFRICA

BRAZIL

AUSTRALIA

İSKENDERUN

ANTALYA

GÖKOVA

TEKİRDAĞ

TRABZON

12

10

11

15

20

15

17

20

22

28

15

22

23

25

27

25

27

30

32

35

SOURCES

Coal MineSUPPLY

DESTINATIONSThermal Power Plants DEMAND

8

6

5

2

5

4

3

5

4

21 21

?

Transportation Model Xij = Quantity of product to be delivered from i to j

Cij = Transportation cost from i to j

ai = Supply of i

bj = Demand of j

Transportation Model Min

≤ ai (Supply Constraint for each factory)

≥ bj (Demand Constraint for each customer)

≥ 0 and integer

Number of constraints=Total of Fact. + Total of Dist.Centers

Representation of Transportation Model In a transportation model, as seen previous slide,

there are m sources and n destinations, each

represented by a node. The arcs represent the routes

linking the sources and destinations.

Arc(i,j) joining source to destination j carries two

pieces of information.

The transportation cost from i to j : Cij

The transportation quantity from i to j : Xij

Representation of Transportation Model

The amount of supply at source i : ai

The amount of demand at destination j : bj

The objective : To Determine the unknowns Xij that

will minimize the total transportation cost by

satisfying all the supply and demand constraints.

EXAMPLE-1 MG Automative has 3 factories in İzmir, Edirne and Bursa and

2 distribution centers in Ankara and Mersin.

In coming 3 months term, the capacities of factories:

İzmir: 1,500pcs. Edirne: 1,000pcs. Bursa: 1,200pcs.

In coming 3 months term,the demands of centers:

Ankara: 2,300 Malatya: 1,400

The distances (km.) between factories and centers: Ankara Mersinİzmir 579 892Edirne 683 1,162Bursa 384 831

EXAMPLE-1 Transportation outsourcing company serves a price as 0.08

TL/km.

Construct the transportation model.

Balanced Transportation Model Demand = Supply , The model is BALANCED

Demand = Supply, we have to balance the model by

adding dummy demand or dummy supply points in

solution.

EXAMPLE-2 In MG Automative Model, Let’s assume that Izmir

Factory has a capacity of 1,300(instead of 1,500). In

this case Supply = 3,500pcs.and demand = 3,700pcs.

Assume that Ankara Distribution Center has a

demand of 1,900 pcs.(instead of 2,300)

HOMEWORK C1 C2 C3 Capacity

F1 15 20 18 200F2 16 22 17 300

Demand 180 150 175

Construct the transportation model.