Question

3. Continuous review inventory control is being applied to purchase motors for an electric fan manufacturer. Demand is uniformly distributed between 500 and 600 motors per week. Each order costs $250 to prepare, place and receive. Motors cost $2.75/unit and the holding cost rate is 1% per week. Management proposes using the EOQ order quantity and setting reorder points to ensure a 97% fill rate. Find the imputed(implied) cost of a shortage and the expected number of shortages per year.

Answer 1

The expected no. of shortage will be "0.27".

Step-by-step 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:

`=(600+500)/(2)* 52 \ weeks`

`=28600 \ units`

Now,

⇒
`EOQ=\sqrt{(2* D* (O)/(C)* i)}`

`=\sqrt{2* 18600* (250)/(2.75)* 52 \ percent}`

`=√(10000000)`

`=3162.27`

In a year, the number of orders will be:

⇒
`(D)/(EOQ)=(28600)/(3162.27)`

`=9.04 \ i.e., \ 9 \ orders`

Demand mean will be:

=
`(500+600)/(2)`

=
`550 \ units \ Demand \ SD`

=
`max[((Upper \ limit - Mean))/(3) , ((mean-lower \ limit))/(3) ]`

=
`max [(50)/(3) ,(50)/(3) ]`

=
`16.66 \ units`

So, in a year, the expected number of the shortages will be:

⇒
`Number \ of \ orders \ in \ a \ year* fill \ rate`

⇒
`9* (1-97 \ percent)`

⇒
`0.27`