Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows:
Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the computer at its main office using special phone lines with telecommunications devices. The phone line from a branch office need not be connected directly to the main office. It can be connected indirectly by being connected to another branch office that is connected (directly or indirectly) to the main office. The only requirement is that every branch office be connected by some route to the main office. The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles) between every pair of offices is as follows:
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Transcribed Image Text:Q1. The Premiere Bank soon will be hooking up computer terminals at each of its branch offices to the
computer at its main office using special phone lines with telecommunications devices.
The phone line from a branch office need not be connected directly to the main office. It can be connected
indirectly by being connected to another branch office that is connected (directly or indirectly) to the main
office. The only requirement is that every branch office be connected by some route to the main office.
The charge for the special phone lines is $100 times the number of miles involved, where the distance (in miles)
between every pair of offices is as follows:
Distance between Pairs of Offices
Main
В.1
В.2
В.3
В.4
В.5
Main office
Branch 1
Branch 2
Branch 3
190
70
115
270
215
160
190
100
110
50
70
100
140
120
220
115
110
140
175
80
Branch 4
Branch 5
270
215
120
175
310
160
50
220
80
310
The management wishes to determine which pairs of offices should be directly connected by special phone lines
in order to connect every
branch office (directly or indirectly) to the main office at a minimum total cost.
Describe the problem as a network problem and solve it with an appropriate algorithm that you have seen in the
course
Transcribed Image Text:Q2. The Quick Company has leamed that a competitor is planning to come out with a new kind of product with
a great sales potential. Quick has been working on a similar product that had been scheduled to come to market
in 20 months. However, research is nearly complete and Quick's management now wishes to rush the product
out to meet the competition
There are four nonoverlapping phases left to be accomplished, including the remaining research that currently is
being conducted at a normal pace. However, each phase can instead be conducted at a priority or crash level to
expedite completion, and these are the only levels that will be considered for the last three phases. The times
required at these levels are given in the following table. (The times in parentheses at the normal level have been
ruled out as too long.)
Time
Initiate
Production
Remaining
Research Development
Design of
Manufacturing
System
and
Level
Distribution
Normal 5 months
Priority 4 months
Crash
(4 months)
3 months
2 months
(7 months)
5 months
3 months
(4 months)
2 months
1 month
2 months
Management has allocated $50 million for these four phases. The cost of each phase at the different levels under
consideration is as follows:
Cost
Initiate
Design of
Manufacturing
System
Production
Remaining
Research Development
and
Level
Distribution
Normal $5 million
Priority $9 million $10 million
Crash $14 million $15 million
$14 million
$19 million
$6 million
$9 million
Management wishes to determine at which level to conduct each of the four phases to minimize the total time
until the product can be marketed subject to the budget restriction of $50 million. Formulate and solve this
problem as a shortest-path problem.
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