# Transportation Model

```CHAPTER V
Transportation Models
Instructor : Lect.Volkan &Ccedil;ETİNKAYA
 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.
SOURCES
SUPPLY
DESTINATIONS
Thermal Power Plants
Coal Mine
12
8
İSKENDERUN
DEMAND
5
15
POLAND
15
10
ANTALYA
4
17
S. AFRICA
6
22
25
27
20 11
15
30
25
22
27
28 20
32
AUSTRALIA
2
21
3
23
BRAZIL
5
G&Ouml;KOVA
35
TEKİRDAĞ
TRABZON
5
4
21
 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
 Min
𝑖∈𝐼
𝑗∈𝐽 X𝑖𝑗
. C𝑖𝑗

𝑗∈𝐽 𝑋𝑖𝑗
≤ ai (Supply Constraint for each factory)

𝑖∈𝐼 𝑋𝑖𝑗
≥ bj (Demand Constraint for each customer)
 𝑋𝑖𝑗 ≥ 0 and integer
 Number of constraints=Total of Fact. + Total of Dist.Centers
 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
 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.
 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:
İzmir
Edirne
Bursa
Ankara
579
683
384
Mersin
892
1,162
831
 Transportation outsourcing company serves a price as 0.08
TL/km.
 Construct the 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.
 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)
F1
F2
Demand
C1
C2
C3
Capacity
15
16
180
20
22
150
18
17
175
200
300
Construct the transportation model.
```