Question

Consider a retailer that sells a single type of product and all assumption of the basic economic order quantity model are valid. The annual demand is 5000 units. Each order release to the supplier incurs a fixed $50 cost and the annual holding cost is $8 per unit. The store manager has already determined the optimal order quantity for this product. (a) If we choose to use an order quantity of q = 350 units, what would be the percentage of increase in the optimal total of ordering and holding costs (the total of ordering and holding costs is also called the dependent cost component)? (b) If the store manager can tolerate only a 2% increase from the optimal total of ordering and holding costs, determine an interval for order quantities that satisfy this tolerance.

Answer 1

a)Economic Order Quantity (EOQ) =√2xAXO/H

where, A= Annual Demand=5000

O=ordering cost=$50

H=Honding cost=$8

Thus,

EOQ=√2x5000X50/8

=√500000/8

=√62500

=250 units i.e. 20 orders(5000/250)

optimal ordering cost=20*50=$1,000

Optimal holding cost=(250/2)*8=$1,000

Total optimal costs=$2,000

If we order 350 units per order we will make 15 orders thus,

ordering cost = 15*50=$750

Holding cost=(350/2)*8=$1,400

Total Cost=750+1400=$2,150

Increase in total optimal cost=2150-2000=150

%age increase in cost=(150/2000)*100=7.5%

b) If we can tolerate 2%variation in total optimal cost our optimal cost will be in the range of $2,000 -+2% i.e.

$1960 to $2040

let us assume that the order quantity to be "n" then total cost will be:

[(5000/n)*50]+[(n/2)*8)]=2040 ------eq 1

or

250000/n+8n/2=1960

Solving eq 1:

Using quadratic formula:

[(5000/n)*50]+[(n/2)*8)]=2040

250000/n+8n/2=2040

4n^2-2040n+250000=0

using quaratic formula:

[-(-2040)+-√(-2040)^2-(4)(4)(250000)]/2(4)

use excel,

n=204.75 or 305.25

Similarly eq 2

250000/n+8n/2=1960

4n^2-1960n+250000=0

[-(-1960)+-√(-1960)^2-(4)(4)(250000)]/2(4)

using excel answer is imaginary

Thus value will be between 204.75 to 305.25 (EOQ also falls in this range)

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