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The Transportation
Model
McGraw-Hill/Irwin Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
You should be able to:1. Describe the nature of a transportation
problem2. Set up transportation problems in the general
linear programming format3. Interpret computer solutions
8S-2Student Slides
Involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple destinations that demand the goods.
8S-3Student Slides
The transportation model has numerous applications: Location decisions
Compare location alternatives in terms of their impact cost on the total distribution costs for the system
Involves working through a separate model for each location being considered
Production planning Capacity planning Transshipment
8S-4Student Slides
Shipping (supply) points Any place from which good are sent
Factories WarehousesDepartments
Destinations Any point that receives goods
FactoriesWarehousesDepartments
8S-5Student Slides
Information requirements1. A list of the origins and each one’s capacity or
supply quantity per period2. A list of the destinations and each one’s
demand per period3. The unit cost of shipping items from each
origin to each destination
Student Slides 8S-6
Transportation model assumptions1. The items to be shipped are homogeneous2. Shipping cost per unit is the same regardless
of the number of units shipped3. There is only one route or mode of
transportation being used between each origin and destination
Student Slides 8S-7
4 7 7 1
100
12
3 8 8
200
810
16
5
150
80 90 120 160
A B C D Supply
Demand
1
2
3
Warehouse
Factory
450
450
Factory 1 can supply 100 units per period
Total capacity per period
Cost to ship one unit from factory 1 to warehouse A
Total Demand per period
Warehouse B can use 90 units per period
Student Slides 8S-8
4 710
790
1100
12
903
1108 8
200
808
10
16
705
150
80 90 120 160
A B C D Supply
Demand
1
2
3
WarehouseFactory
450
450
8S-9Student Slides
jix
xxx
xxx
xxx
xxx
xxxx
xxxx
xxxx
xxxxx
xxxxxxx
jix
ij
DDD
CCC
BBB
AAA
DCBA
DCBA
DCBA
DCBAD
CBADCBA
ij
and allfor 0
160
120
90
80 (columns) Demand
150
200
100 (rows)Supply
Subject to
5161088
83121774 Minimize
D and C, B, A, j and 3 and 2, ,1i
where
warehouse tofactory from ship tounits ofnumber the
VariablesDecision
321
321
321
321
3333
2222
1111
33332
2221111
Student Slides 8S-10
Transportation problems can be solved manually in a straightforward manner Except for very small problems, solving the problem
manually can be very time consuming For medium to large problems, computer solution
techniques are more practical
A variety of software packages are available for solving the transportation model Some require formulating the problem as a general LP
model Others allow data entry in a more simple, tabular format
Student Slides 8S-11
8S-12Student Slides