A manager is going to purchase new processing equipment and must decide on the number of spare parts to order with the new equipment.
The spares cost $195 each, and any unused spares will have an expected salvage value of $50 each. The probability of usage can be described by this distribution: Number 0 1 2 3 Probability .10 .50 .25 .15

If a part fails and a spare is not available, two days will be needed to obtain a replacement and install it. The cost for idle equipment is $550 per day. What quantity of spares should be ordered?a. Use the ratio method. (Round your answer to 2 decimal places.)
Service level is _, so we need to order _ spares.

b. Use the tabular method.___ spares

You will find the procedures, formulas or necessary explanations in the archive attached below. If you have any question ask and I will aclare your doubts kindly.

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ogorwyne ogorwyne · Answer 2 · 2021-10-28T17:11:31+02:00

The service level is 88.35%. This service level falls under the cumulative value that lies along 85% and 100%. Therefore the number that is to be ordered is 3 spares.

The formula for the service level

[tex]service level=\frac{Cu}{Cu+Co}[/tex]

Where Cu is the cost of underestimation

= [tex]550*2=1100[/tex]

Co is the overestimation cost

[tex]Co = Unitcost - Salvage cost\\= 195-50\\= 145 dollars[/tex]

Then

[tex]servicelevel= \frac{1100}{1100+145} \\\\= \frac{1100}{1245} \\\\= 0.8835[/tex]

= 88.35%

The service level is 88.35 %This service level falls under the cumulative value that lies along 85% and 100%. Therefore the number that is to be ordered is 3 spares.

The tabular method is contained in the attachment.

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