Ingeniero

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Quantitative Module

Transportation Models

C

Module Outline
TRANSPORTATION MODELING
DEVELOPING AN INITIAL SOLUTION

USING SOFTWARE TO SOLVE TRANSPORTATION
PROBLEMS

The Northwest-Corner Rule

SOLVED PROBLEMS

The Intuitive Lowest-Cost Method

INTERNET AND STUDENT CD-ROM EXERCISES

THE STEPPING-STONE METHODDISCUSSION QUESTIONS

SPECIAL ISSUES IN MODELING

PROBLEMS

Demand Not Equal to Supply

INTERNET HOMEWORK PROBLEMS

Degeneracy

CASE STUDY: CUSTOM VANS, INC.

SUMMARY

ADDITIONAL CASE STUDIES

KEY TERMS

L EARNING O BJECTIVES
When you complete this module you
should be able to

BIBLIOGRAPHY

IDENTIFY OR DEFINE:
Transportation modeling
Facility location analysis
EXPLAIN ORBE ABLE TO USE:
Northwest-corner rule
Stepping-stone method

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T R A N S P O RTAT I O N M O D E L S

The problem facing rental companies like Avis, Hertz, and National is cross-country travel. Lots of it. Cars rented in
New York end up in Chicago, cars from L.A. come to Philadelphia, and cars from Boston come toMiami. The scene
is repeated in over 100 cities around the U.S. As a result, there are too many cars in some cities and too few in
others. Operations managers have to decide how many of these rentals should be trucked (by costly auto carriers)
from each city with excess capacity to each city that needs more rentals. The process requires quick action for the
most economical routing; so rentalcar companies turn to transportation modeling.

Because location of a new factory, warehouse, or distribution center is a strategic issue with substantial cost implications, most companies consider and evaluate several locations. With a wide
variety of objective and subjective factors to be considered, rational decisions are aided by a number of techniques. One of those techniques istransportation modeling.
The transportation models described in this module prove useful when considering alternative
facility locations within the framework of an existing distribution system. Each new potential plant,
warehouse, or distribution center will require a different allocation of shipments, depending on its
own production and shipping costs and the costs of each existing facility. The choiceof a new location depends on which will yield the minimum cost for the entire system

TRANSPORTATION MODELING
Transportation
modeling
An iterative procedure for
solving problems that
involves minimizing the
cost of shipping products
from a series of sources to
a series of destinations.

Transportation modeling finds the least-cost means of shipping supplies from several origins toseveral destinations. Origin points (or sources) can be factories, warehouses, car rental agencies like
Avis, or any other points from which goods are shipped. Destinations are any points that receive
goods. To use the transportation model, we need to know the following:
1.
2.
3.

The origin points and the capacity or supply per period at each.
The destination points and the demand per periodat each.
The cost of shipping one unit from each origin to each destination.

The transportation model is actually a class of the linear programming models discussed in
Quantitative Module B. As it is for linear programming, software is available to solve transportation problems. To fully use such programs, though, you need to understand the assumptions that
underlie the model. To illustrateone transportation problem, in this module we look at a company
called Arizona Plumbing, which makes, among other products, a full line of bathtubs. In our
example, the firm must decide which of its factories should supply which of its warehouses.
Relevant data for Arizona Plumbing are presented in Table C.1 and Figure C.1. Table C.1 shows,
for example, that it costs Arizona Plumbing $5 to...