Operations management by stevenson 9th student slides supplement 8

Supplement 8
The Transportation Model

McGraw-Hill/Irwin

Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.


Supplement 8: Learning Objectives
• You should be able to:
– Describe the nature of a transportation problem
– Set up transportation problems in the general linear
programming format
– Interpret computer solutions

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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
Supply
Demand

Supply

Demand

Supply

Demand
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Transportation Model: Applications
• 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

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Transportation Problem
• Shipping (supply) points
– Any place from which good are sent
• Factories
• Warehouses
• Departments

• Destinations
– Any point that receives goods
• Factories

• Warehouses
• Departments

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Model: Information Requirements
• Information requirements
1. A list of the origins and each one’s capacity or
supply quantity per period
2. A list of the destinations and each one’s demand per
period
3. The unit cost of shipping items from each origin to
each destination

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Model: Assumptions
• Transportation model assumptions
1. The items to be shipped are homogeneous
2. Shipping cost per unit is the same regardless of the
number of units shipped
3. There is only one route or mode of transportation
being used between each origin and destination

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Transportation Table

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Transportation Table

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Transportation Problem: Formulation
xij = the number of units to ship from factory i to warehouse j
Decision Variables

Minimize

where
i = 1, 2, and 3 and j = A, B, C, and D
4 x1 A + 7 x1B + 7 x1C + 1x1D + 12 x2 A + 3x2 B + 8 x2C
+ 8 x2 D + 8 x3 A + 10 x3 B + 16 x3C + 5 x3 D

Subject to
Supply (rows)

x1 A + x1B + x1C + x1D = 100
x2 A + x2 B + x2C + x2 D = 200
x3 A + x3 B + x3C + x3 D = 150

Demand (columns)

x1 A + x2 A + x3 A = 80

x1B + x2 B + x3 B = 90
x1C + x2C + x3C = 120
x1D + x2 D + x3 D = 160
xij ≥ 0 for all i and j
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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

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Transportation Problem: Excel Template

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