Operations management by stevenson 9th student slides supplement 8

Supplement 8The Transportation Model... Transportation Problem• Involves finding the lowest-cost plan for distributing stocks of goods or supplies from multiple origins to multiple des

Supplement 8

The Transportation Model

Supplement 8: Learning Objectives

• You should be able to:

programming format

Transportation Problem

• Involves finding the lowest-cost plan for

distributing stocks of goods or supplies from

multiple origins to multiple destinations that

demand the goods.

Demand

Demand

Demand

Demand Supply

Supply Supply

Transportation Model: 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

Transportation Problem

– Any place from which good are sent

• Factories

• Warehouses

• Departments

– Any point that receives goods

• Factories

• Warehouses

• Departments

Model: Information Requirements

• Information requirements

supply quantity per period

period

each destination

Model: Assumptions

• Transportation model assumptions

number of units shipped

being used between each origin and destination

Transportation Table

Transportation Table

Transportation Problem: Formulation

j i

x

x x

x

x x

x

x x

x

x x

x

x x

x x

x x

x x

x x

x x

x x

x x

x

x x

x x

x x

x

j i

x

ij

D D

D

C C

C

B B

B

A A

A

D C

B A

D C

B A

D C

B A

D C

B A

D

C B

A D

C B

A ij

and all

for 0

160

120

90

80

(columns) Demand 150

200

100

(rows) Supply Subject to 5 16 10 8 8

8 3 12 1 7 7 4

Minimize

D and C, B, A, j and

3 and 2, , 1 i where

warehouse to

factory from

ship to units of

number the

Variables Decision

3 2

1

3 2

1

3 2

1

3 2

1

3 3

3 3

2 2

2 2

1 1

1 1

3 3

3 3

2

2 2

2 1

1 1

1



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

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

































































Transportation: Computer Solution

• 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

Transportation Problem: Excel Template