Question

Our home construction company consumes nails from our warehouse in 15-pound boxes. We use an average of 1414 boxes a year. The warehouse can provide nails at 42 boxes per day while our usage is 19 boxes per day. It costs $0.90 to place the typical order. Annual carrying costs are $0.65 per box. What will be our average number of boxes on hand if we order the EPQ boxes in each order

Answer 1

23.155 units

Explanation:

Economic Production Quantity (EPQ) helps to sustain the equilibrium between the ordering cost and carrying costs and it is given by the expression:

`EPQ=\sqrt{(2DS)/(H) }*\sqrt{(P)/(P-u) }`

where;

D = Annual demand

P = production rate

u = usage rate

S = setup cost

H = holding cost

Given that:

We use an average of 1414 boxes a year; D = 1414 boxes/year

The warehouse can provide nails at 42 boxes per day; P = 42 boxes/day

our usage is 19 boxes per day; u = 19 boxes/day

It costs $0.90 to place the typical order; S = $ 0.90/ order

Annual carrying costs are $0.65 per box; H = $0.65/ order

replacing our given parameters into the above formula; we have:

`EPQ=\sqrt{(2*1414*0.90)/(0.65) }*\sqrt{(42)/(42-19) }`

`EPQ= 62.57549287*1.351327849`

`EPQ= 84.56000618`

`EPQ=84.56 units`

Maximum average number of boxes
`I_{max` =
`(EPQ)/(P)(P-u)`

`I_{max` =
`(84.56)/(42)(42-19)`

`I_{max` = 46.31 units

average number of boxes on hand if we order the EPQ boxes in each order;

=
`(I_(max))/(2)`

=
`(46.31)/(2)`

= 23.155 units