POQ: An item has the following information: Setup cost/setup, S = $200/order Ann

ID: 360022 • Letter: P

Question

POQ:

An item has the following information:

Setup cost/setup, S = $200/order Annual demand, D = 630,000 units/year

Carrying cost/unit-year, H = $0.60/unit-yr Production rate = 3,000/day

Assume 300 working days in a year.

Determine:

(1) The POQ.

(2) Number of orders per year.

(3) Number of days between orders.

(4) Ordering cost per year.

(5) Carrying cost per year.

(6) Total cost per year.

(7) Average inventory.

(8) Inventory turnover.

(9) The production cost/unit if the carrying cost %/year = 40%.

(10) The production lead time.

Explanation / Answer

PLEASE FIND ANSWERS TO QUESTIONS 1 TO 8:

The Economic Production Quantity ( EPQ ) will be determined as :

EPQ = Square root ( 2 x Co x D / Ch x ( 1 – d/p))

Co = Set up cost = $ 200 / order

D = Annual Demand = 630,000 units/ year

Ch = Annual unit holding cost = $0.60

.d = Daily demand = 630,000/ 300 working days = 2100 /day

.p = Daily production rate = 3000/day

Therefore ,

EPQ = Square root ( 2 x 200 x 630000 / 0.60 x ( 1 – 2100/3000))

= Square root ( 2 x 200 x 630000/0.60 x 0.3)

= 37416.57 ( 37417 by rounding to nearest whole number )

Number of orders per year = Annual demand / EPQ = 630000/37417 = 16.84 Orders per year

( rounded to 2 decimal places )

Number of days between orders

= EPQ/annual demand x 300 days

= 37417/ 630000 x 300 days

= 17.82 days ( rounded to 2 decimal places )

Ordering cost per year = Ordering cost per order x Number of orders/year = $200 x 16.84 = $3368

Carrying cost per year

= Annual unit holding cost x EPQ ( 1 – d/p)/ 2

= 0.60 x 37417x ( 1 – 2100/3000)/2

= $3367.53

Total cost per year

= Annual ordering cost + Annual carrying cost

= $ 3368 + $3367.53

= $6735.53

Average inventory = EPQ/2 X ( 1 – d/p ) = 37417/2 x ( 1 – 2100/3000) = 5612.50

Inventory turnover = annual demand/ Average inventory = 630,000/5612.50 = 112.25

POQ = 37417

Number of orders per year = 16.84 orders per year

Number of days between orders = 17.82 days

Ordering cost per year = $3368

Carrying cost per year = $3367.53

Total cost per year = $6735.53

Average inventory = 5612.50

Inventory turnover = 112.25