At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 0 1 2 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem by drawing a network representation. (b) Use the Dijkstra's algorithm to solve this shortest-path problem. At what times (if any) should the tractor be replaced to minimize the total cost?
At a small but growing airport, the local airline company is purchasing a new tractor for a tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage system will be installed in 3 years, so the tractor will not be needed after that. However, because it will receive heavy use, so that the running and maintenance costs will increase rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2 years. The following table gives the total net discounted cost associated with purchasing a tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the end of year i and trading it in at the end of year j (where year O is now). i 0 1 2 1 $13,000 j 2 $28,000 $17,000 3 $48,000 $33,000 $20,000 The problem is to determine at what times (if any) the tractor should be replaced to minimize the total cost for the tractors over 3 years. (a) Formulate this problem as a shortest-path problem by drawing a network representation. (b) Use the Dijkstra's algorithm to solve this shortest-path problem. At what times (if any) should the tractor be replaced to minimize the total cost?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
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Transcribed Image Text:At a small but growing airport, the local airline company is purchasing a new tractor for a
tractor-trailer train to bring luggage to and from the airplanes. A new mechanized luggage
system will be installed in 3 years, so the tractor will not be needed after that. However,
because it will receive heavy use, so that the running and maintenance costs will increase
rapidly as the tractor ages, it may still be more economical to replace the tractor after 1 or 2
years. The following table gives the total net discounted cost associated with purchasing a
tractor (purchase price minus trade-in allowance, plus running and maintenance costs) at the
end of year i and trading it in at the end of year j (where year O is now).
i
B
012
1
$13,000
j
2
$28,000
$17,000
3
$48,000
$33,000
$20,000
The problem is to determine at what times (if any) the tractor should be replaced to minimize
the total cost for the tractors over 3 years.
(a) Formulate this problem as a shortest-path problem by drawing a network representation.
(b) Use the Dijkstra’s algorithm to solve this shortest-path problem. At what times (if any)
should the tractor be replaced to minimize the total cost?
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