Respuesta :
Answer:
The expected no. of shortage will be "0.27".
Explanation:
The given values are:
Ordering cost,
O = $250
Holding cost (i),
= 1% (per week)
= 52% (a year)
Cost of goods (C),
= $2.75
The average annual demand is:
[tex]=\frac{600+500}{2}\times 52 \ weeks[/tex]
[tex]=28600 \ units[/tex]
Now,
⇒ [tex]EOQ=\sqrt{(2\times D\times \frac{O}{C}\times i)}[/tex]
[tex]=\sqrt{2\times 18600\times \frac{250}{2.75}\times 52 \ percent}[/tex]
[tex]=\sqrt{10000000}[/tex]
[tex]=3162.27[/tex]
In a year, the number of orders will be:
⇒ [tex]\frac{D}{EOQ}=\frac{28600}{3162.27}[/tex]
[tex]=9.04 \ i.e., \ 9 \ orders[/tex]
Demand mean will be:
= [tex]\frac{500+600}{2}[/tex]
= [tex]550 \ units \ Demand \ SD[/tex]
= [tex]max[\frac{(Upper \ limit - Mean)}{3} , \frac{(mean-lower \ limit)}{3} ][/tex]
= [tex]max [\frac{50}{3} ,\frac{50}{3} ][/tex]
= [tex]16.66 \ units[/tex]
So, in a year, the expected number of the shortages will be:
⇒ [tex]Number \ of \ orders \ in \ a \ year\times fill \ rate[/tex]
⇒ [tex]9\times (1-97 \ percent)[/tex]
⇒ [tex]0.27[/tex]
