The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item are D = 600 units, S = $20/order and I = 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?
|
Quantity |
1 to 99 |
100 to 199 |
200 and up |
|
Price |
$8.00 per unit |
$7.00 per unit |
$6.00 per unit |
Theoretical economic order quantity ( EOQ )
= Square root ( 2 x D x S/I)
Since "i" is a function of price, I ( i.e. inventory carrying cost per unit ) will vary from one quantity slab to another. Theoretical EOQ will also change accordingly for different quantity slabs
In case such derived theoretical EOQ is out of range for the corresponding quantity slab, minimum /maximum ( as applicable ) quantity for that slab needs to be considered as Modified order quantity. For example in case theoretical EOQ works out to be 83 for quantity slab 100 to 199, modified order quantity should be considered as 100.
Basis above introduction, please find relevant data on EOQ in below- mentioned table :
|
Quantity slab |
Price/ unit |
I ( 30% of Price per unit) |
Theoretical EOQ |
Modified order quantity |
|
1 TO 99 |
$8 |
2.4 |
100 |
99 |
|
100 TO 199 |
$7 |
2.1 |
107 (rounded ) |
107 |
|
200 and up |
$6 |
1.8 |
115.47 |
200 |
Total annual cost
= Annual price value of items + Annual ordering cost + Annual inventory holding cost
= Price/unit x annual quantity + Ordering cost / order x Number of orders + Inventory holding cost per unit x Average inventory
= $600 x Price/unit + $20 x Annual quantity ( i.e. 600) / Modified order quantity + I x Modified order quantity/2
Total annual costs for different quantity slabs will be as per following :
For quantity slab 1 to 99 :
Total cost ( $) = 600 x 8 + 20 x 600/99 + 2.4 x 99/2 = 4800 + 121.21 + 118.8 = $ 5040.10
For quantity slab 100 to 199 :
Total cost ($) = 600 x 7 + 20 x 600 / 107 + 2.1 x 107/2 = 4200 + 112.15 + 112.35 = $ 4424.50
For quantity slab 200 and up :
Total cost = $600 x 6 + 20 x 600 /200 + 1.8 x 200 /2 = $3600 + $60 + $180 = $3840
Minimum total cost therefore is achieved for order quantity of 200 items.
HENCE, ORDER QUANTITY SHOULD BE 200 ITEMS IN ORDER TO MINIMIZE TOTAL ANNUAL COST
The annual demand, ordering cost, and the annual inventory carrying cost rate for a certain item...