A single machine is needed to perform a specified function for the next four yea
ID: 3281960 • Letter: A
Question
A single machine is needed to perform a specified function for the next four years, after which the function and machine will no longer be needed. The purchase price of a machine varies over the next four years according to the following table.
Year
Now
One Year from Now
Two Years from Now
Three Years from Now
Purchase Price
$ 25,000
$ 33,000
$ 38,000
$ 47,000
The salvage value of a machine depends only on its length of service and is given by the following table.
Length of Service
1 Year
2 Years
3 Years
4 Years
Salvage Value
$ 17,000
$ 6,000
$ 3,000
$ 1,000
The annual operating cost varies with length of service, as follows
Length of Service
New
1 Year
2 Years
3 Years
Annual Operating Cost
$ 3,000
$ 5,000
$ 8,000
$ 10,000
The objective of the problem is to find the best policy to minimize the total cost of purchasing, operating, and salvaging over the next four years. Model this problem using the appropriate network technique. Give the network representation of this problem with all the information needed to solve it.
Year
Now
One Year from Now
Two Years from Now
Three Years from Now
Purchase Price
$ 25,000
$ 33,000
$ 38,000
$ 47,000
Explanation / Answer
Purchased in year 1 -25000
operating for 1 year – +17000-3000=14000
operating for 2 years – +6000-5000-3000=-2000
operating for 3 years – +3000-8000-5000-3000=-13000
operating for 4 years – +1000-10000-8000-5000-3000=-25000
Purchased in Year 2 -33000
operating for 1 year – +17000-3000=14000
operating for 2 years – +6000-5000-3000=-2000
operating for 3 years – +3000-8000-5000-3000=-13000
Purchased in Year 3 -38000
operating for 1 year – +17000-3000=14000
operating for 2 years – +6000-5000-3000=-2000
Purchased in Year 4 – operating for 1 year – -47000+17000-3000=-33000
So here it can be seen that while comparing operating cost for same year over purchasing new, if cumulative operating cost is lesser than purchasing then we will go with operating the same machine and vice versa, Purchase in year 1 and operate for 5 years, Answer will be -25000-25000=-50000
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