ENGRI 115
Engineering Applications of OR
Fall 2007
The Transportation Problem
Lab 8
Name:
Objectives:
•
Introduce students to the transportation problem.
•
Further use of AMPL.
•
Give an application of the transportation problem to the “caterer’s problem”.
Key Ideas:
•
supply point and supply constraint
•
demand point and demand constraint
•
balanced transportation problem
•
bipartite graph
•
integrality properties
•
sensitivity analysis
Reading Assignment:
Winston 7.1
Prelab Exercise:
Please write your answer on this sheet.
The following problem is called the
Caterer’s Problem
. The goal of this prelab exercise is to formulate it as
a transportation problem (we will solve the problem in the next lab).
(From Winston, page 410, Problem 21) The Carter Caterer Company must have the following number of
clean napkins available at the beginning of each of the next four days: day 1, 15; day 2, 12; day 3, 18; day
4, 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast
service costs 10 cents per napkin, and a napkin cleaned via fast service is available for use the day after it
is last used. Slow service costs 6 cents per napkin, and these napkins can be reused two days after they are
last used. New napkins can be purchased for a cost of 20 cents per napkin. The catering company currently
has no napkins, whatsoever. We wish to meet the demand for the next four days as cheaply as possible.
First think about the demand points. What do you think is being demanded? (Hint: there are 4 demand
points.) What is the demand for each of them?
Now think about the supply points. One supply point is clearly the store from which one can buy napkins.
Observe that you can think of the source of napkins used on day
i
as the napkins used on day
i

1 (provided
1
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i

2, (provided they are laundered by the slow service).
What do you think the other supply points should be? (Hint: there are 3 other ones.) What is the supply
at each of them?
What is the unit shipping cost between each supply point and each demand point? Give a graphical
representation of this input.
Is this input balanced? Why? If it is not balanced, think about how can you convert it into a balanced
transportation problem (we will come back to this question in the lab, you don’t need to answer it right
now).
2
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 Spring '05
 TROTTER
 Cost Accounting, Supply And Demand

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