1. Operations Management Transportation Models
Quantitative Methods for Managerial Decision-Making
ACN 309-5

2. Quantitative Methods for Managerial Decision-Making
Outline
TRANSPORTATION MODELING
DEVELOPING AN INITIAL SOLUTION
The Northwest-Corner Rule
The Intuitive Lowest-Cost Method
THE STEPPING-STONE METHOD
SPECIAL ISSUES IN MODELING
Demand Not Equal to Supply
Degeneracy
Quantitative Methods for Managerial Decision-Making
ACN 309-5

3. Quantitative Methods for Managerial Decision-Making
Learning Objectives
After you read these notes, you should be able to
Identify or Define:
Transportation modeling
Facility location analysis
Explain or be able to use:
Northwest-corner rule
Stepping-stone method
Quantitative Methods for Managerial Decision-Making
ACN 309-5

4. Transportation Problem
DesMoines
(100 unit capacity)
Fort Lauderdale
(300 units capacity)
Cleveland
(200 units required)
Evansville
Albuquerque
(300 units required)
Boston
Quantitative Methods for Managerial Decision-Making
ACN 309-5

5. Transportation Problem
How much should be shipped from several sources to several destinations
Sources: Factories, warehouses, etc.
Destinations: Warehouses, stores, etc.
Transportation models
Find lowest cost shipping arrangement
Used primarily for existing distribution systems
Quantitative Methods for Managerial Decision-Making
ACN 309-5

6. A Transportation Model Requires
The origin points, and the capacity or supply per period at each
The destination points and the demand per period at each
The cost of shipping one unit from each origin to each destination
Quantitative Methods for Managerial Decision-Making
ACN 309-5

7. Transportation Problem Graphical Solution2 n
Supply Quantity
Source
Quantity Shipped
Destination ai i x mn j bj a1 1 b1
x11 a2
x22 b2 : 2n am
xmn bn
x1n
x12
x21
Demand Quantity m
xm2
xm1
Quantitative Methods for Managerial Decision-Making
ACN 309-5

8. Transportation Problem Solution Steps
Define problem
Set up transportation table (matrix)
Summarizes all data
Keeps track of computations
Develop initial solution
Northwest corner rule
Find optimal solution
Stepping stone method
Quantitative Methods for Managerial Decision-Making
ACN 309-5

9. Quantitative Methods for Managerial Decision-Making
Transportation Costs
From To
(Destination)
(Sources)
Albuquerque
Boston
Cleveland
Des Moines $5 $4 $3
Evansville $8
Fort
Lauderdale $9 $7
Quantitative Methods for Managerial Decision-Making
ACN 309-5

10. Quantitative Methods for Managerial Decision-Making
Transportation Table
Destination
Source
Supply
Demand 1 2 : m a
. . n b
Quantity demanded or required
Quantitative Methods for Managerial Decision-Making
ACN 309-5

11. Quantitative Methods for Managerial Decision-Making
Transportation Table
Destination
Source 1 2
. . n
Supply x 11 c 12 1n a 21 22 2n : m m1 m2 mn
Demand b
Cost of supplying 1 unit from sources to destinations
Quantitative Methods for Managerial Decision-Making
ACN 309-5

12. Quantitative Methods for Managerial Decision-Making
Transportation Table
Destination
Source
Supply
Demand 1 2 : m a
. . n b x 11 12 1n 21 22 2n m1 m2 mn
Quantity supplied from sources to destinations
Quantitative Methods for Managerial Decision-Making
ACN 309-5

13. Quantitative Methods for Managerial Decision-Making
Transportation Table To
Albuquerque
Boston
Cleveland
Factory
From
(A)
(B)
(C)
Capacity
Des Moines 5 4 3
100
(D)
Evansville 8 4 3
300
(E)
Fort Lauderdale 9 7 5
300
(F)
Warehouse
300
200
200
700
Requirements
Quantitative Methods for Managerial Decision-Making
ACN 309-5

14. Initial Solution Using the Northwest Corner RuleTo
From
Albuquerque
(A)
Boston
(B)
Cleveland
(C)
Factory
Capacity
Des Moines
(D)
100
Evansville
(E)
200
300
Fort Lauderdale
(F)
Warehouse
Requirements
700 5 8 9 7 4 3
Quantitative Methods for Managerial Decision-Making
ACN 309-5

15. The Stepping Stone Method
Select any unused square to evaluate
Begin at this square. Trace a closed path back to the original square via squares that are currently being used (only horizontal or vertical moves allowed)
Place + in unused square; alternate - and + on each corner square of the closed path
Calculate improvement index: add together the unit cost figures found in each square containing a +; subtract the unit cost figure in each square containing a -.
Repeat steps 1-4 for each unused square
Quantitative Methods for Managerial Decision-Making
ACN 309-5

16. Stepping-Stone Method: Tracing a Closed Path - Des Moines to Cleveland
From
Albuquerque
(A)
Boston
(B)
Cleveland
(C)
Factory
Capacity
Des Moines
(D)
100
Evansville
(E)
200
300
Fort Lauderdale
(F)
Warehouse
Requirements
700 5 8 9 7 4 3
Start + -
Quantitative Methods for Managerial Decision-Making
ACN 309-5

17. The Intuitive Lowest Cost Method
Identify the cell with the lowest cost. Arbitrarily break any ties for the lowest cost.
Allocate as many units as possible to that cell without exceeding the supply or demand. Then cross out that row or column (or both) that is exhausted by this assignment.
Find the cell with the lowest cost from the remaining cells.
Repeat steps 2 & 3 until all units have been allocated.
Quantitative Methods for Managerial Decision-Making
ACN 309-5

18. Initial Solution Using the Intuitive Lowest-Cost Method
Second, cross out column C To
Albuquerque
Boston
Cleveland
Factory
From
(A)
(B)
(C)
Capacity
First, cross out top row
Des Moines 5 4 3
100
100
(D)
Evansville 8 4 3
Third, cross out row E
100
300
(E)
200
Fort Lauderdale 9 7 5
300
(F)
300
Warehouse
300
200
200
700
Requirements
Quantitative Methods for Managerial Decision-Making
ACN 309-5

19. Quantitative Methods for Managerial Decision-Making
Specialized Methods
Linear programming model is difficult to formulate & solve
Special purpose methods
Are easier to formulate
Are faster to compute
Give integer solutions
Methods
Stepping-stone
MODI
See your CD Tutorial
© 1995 Corel Corp.
Quantitative Methods for Managerial Decision-Making
ACN 309-5

20. Special Issues in the Transportation Model
Demand not equal to supply
Called ‘unbalanced’ problem
Add dummy source if demand > supply
Add dummy destination if supply > demand
Degeneracy in Stepping Stone Method
Too few shipping routes (cells) used
Number of occupied cells should be: m + n - 1
Create artificially occupied cell (0 value)
Represents fake shipment
Quantitative Methods for Managerial Decision-Making
ACN 309-5

21. Transportation Table Demand Not Equal SupplyTo
From
Albuquerque
(A)
Boston
(B)
Cleveland
(C)
Factory
Capacity
Des Moines
(D)
250
Evansville
(E)
300
Fort Lauderdale
(F)
Warehouse
Requirements
200
700 5 8 9 7 4 3
Dummy
150
New Des Moines capacity
Quantitative Methods for Managerial Decision-Making
ACN 309-5

22. Quantitative Methods for Managerial Decision-Making
Degeneracy To
From
Albuquerque
(A)
Boston
(B)
Cleveland
(C)
Factory
Capacity
Des Moines
(D)
100
Evansville
(E)
200
300
Fort Lauderdale
(F)
Warehouse
Requirements
700 5 8 9 7 4 3
Quantitative Methods for Managerial Decision-Making
ACN 309-5

23. Degeneracy - ContinuedTo
Albuquerque
Boston
Cleveland
Factory
From
(A)
(B)
(C)
Capacity
Des Moines 5 4 3
100
100
(D)
Evansville 8 4 3
200
100
300
(E)
Fort Lauderdale 9 7 5
200
200
(F)
Warehouse
300
100
200
700
Requirements
Quantitative Methods for Managerial Decision-Making
ACN 309-5