Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 5.4, Problem 19P
Summary Introduction
To determine: The restriction cost that is relative to the original optimal cost.
Introduction: In linear programming, unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints then it is said to be unfeasible solution.
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Greenstreets Recycling, Inc., collects used motor oil from several collection sites around the Greater Stanford area. To minimize the use, and thereby the cost, of its labor, vehicle, and energy resources, the company is interested in locating the shortest route that will allow its collection vehicle to visit each collection site exactly once. The following table provides the travel distances in miles between each site. Note that the company’s recycling facility is located at site A.
From/To
A
B
C
D
E
F
A (depot)
–
25
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48
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60
B
25
–
35
22
23
43
C
50
35
–
25
47
65
D
48
22
25
–
24
40
E
41
23
47
24
–
21
F
60
43
65
40
21
–
Provide an efficient route for the collection vehicle.
In the original Gorman Construction Company problem, we found the shortest distance from the office (node 1) to the construction site located at node 6. Because some of the roads are highways and others are city streets, the shortest-distance routes between the office and the construction site may not necessarily provide the quickest or shortest-time route. Shown here is the Gorman road network with travel time rather than distance. Find the shortest route from Gorman’s office to the construction site at node 6 if the objective is to minimize travel time rather than distance.
Abu Dhabi municipality is given an assignment to ensure provision of enough water for residents of the Abu Dhabi city. The water is purified in a large water treatment plant (node
1) and then is sent via a water supply network to the Abu Dhabi city (node 14). As shown in the below water supply network, the capacity of each water pipeline (arc) is shown in million liters per hour. For example, the hourly water flow from node 1 to node 2 is four million liters, and from node 2 to node 1 is zero million liters.
a) The municipality is interested to find out how much water (in million liters per hour) can be sent from the water treatment plant to the Abu Dhabi city via this water supply network. Determine it.
b) Due to a maintenance problem both nodes 10 and 11 need to be taken offline.
Therefore, these nodes cannot flow any water in and out. How this problem impacts the network maximum flow capacity?
Please include algebraic method and excel solver.
Chapter 5 Solutions
Practical Management Science
Ch. 5.2 - Prob. 1PCh. 5.2 - Prob. 2PCh. 5.2 - Prob. 3PCh. 5.2 - Prob. 4PCh. 5.2 - Prob. 5PCh. 5.2 - Prob. 6PCh. 5.2 - Prob. 7PCh. 5.2 - Prob. 8PCh. 5.2 - Prob. 9PCh. 5.3 - Prob. 10P
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