Question

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 $179 each, and any unused spares will have an expected salvage value of $49 each. The probability of usage can be described by this distribution: Number 0 1 2 3 Probability .05 .60 .20 .15 Click here for the Excel Data File If a part fails and a spare is not available, 2 days will be needed to obtain a replacement and install it. The cost for idle equipment is $640 per day. What quantity of spares should be ordered

Answer 1

service level is 90.78% ( it falls on cumulative probability of 1.00 or 100%)

Therefore the quantity of spares that should be ordered is 3

Explanation:

Given that;

spares cost = $179 each

salvage value = $49 each

distribution of the probability of usage;

Number Probability cumulative Probability

0 0.05 0.05

1 0.60 0.65

2 0.20 0.85

3 0.15 1.00

Now

the cost of stock-out (underestimation) Cu

= $640 per day × 2 days = $1,280

the cost of excess inventory (overestimation) Co

= Unit cost - salvage value = $179 - $49 = $130

Therefore Service Level = Cu / ( Cu + Co )

we substitute

Service Level = $1,280 / ( $1,280 + $130 )

= $1,280 / $1410

= 0.9078 or 90.78%

so service level is 90.78% ( it falls on cumulative probability of 1.00 0r 100%)

Therefore the quantity of spares that should be ordered is 3