The I-75 Carpet Discount Store in North Georgia stocks carpet in its warehouse and sells it through an adjoining showroom. The store keeps several brands and styles of carpet in stock; however, it s biggest seller is Super Shag carpet. The store wants to determine the optimal order size and total cost for this brand of carpet given an estimated annual demand of 10,000 yards of carpet, an annual carrying cost of $0.75 per yard, and an ordering cost of $150. The store would also like to know the number of orders that will be made annually and the time between orders (i. e, the order cycle) given that the store is open 311 days annually. (a) Calculate the economic order quantity (EOQ) (namely how many orders to place very year in order to minimize total cost?) (b) The total annual inventory cost based on the optimal order quantity calculated from (a), (c) Calculate the number of order per year and the time between orders (i. e., the order cycle.

The I-75 Carpet Discount Store

a) Calculation of the economic order quantity (EOQ)

EOQ = the square root of (2 x annual demand x Ordering costs) /Holding cost

EOQ = square root of (2 x 10,000 x $150) / $7,500 = 20

Where Demand (D) = 10,000 yards

Ordering costs (S) = $150

Carrying or Holding cost = $7,500 ($0.75 x 10,000)

Therefore, the EOQ = square root of (2 x 10,000 x $150) / $7,500 = 20

b) The total annual inventory cost based on the optimal order quantity:

=TC = PC + OC + HC

= (10,000 x unit cost (p) + $150 x 10,000/20 + $0.75 x 10,000)

= 10,000p + $75,000 + $7,500

= 10,000p + $82,500

c1) Calculation of the number of order per year:

Number of order per year = Annual Demand / EOQ = 10,000/20 = 500

c2) Calculation of the time between orders or the order cycle

= Annual Demand / EOQ per year = 500/311 = 1.61 days or 2 days.

Explanation:

a) EOQ = the square root of (2 x annual demand x Ordering costs) /Holding cost

EOQ = square root of (2 x 10,000 x $150) / $7,500 = 20

b) The total annual inventory cost based on the optimal order quantity:

=TC = PC + OC + HC,

where TC is the Total Cost;

PC is Purchase Cost;

OC is Ordering Cost; and

HC is Holding Cost

= (10,000 x unit cost (p) + $150 x 10,000/20 + $0.75 x 10,000)

= 10,000p + $75,000 + $7,500

= 10,000p + $82,500

c1) Calculation of the number of order per year:

Number of order per year = Annual Demand / EOQ = 10,000/20 = 500

c2) Calculation of the time between orders or the order cycle = Annual Demand / EOQ per year = 500/311 = 1.61 days or 2 days.

d) The total cost of inventory is the sum of the purchase, ordering and holding costs.

e) Order cycles per year are calculated by dividing the annual demand D by the order quantity Qo. An order cycle is the amount of time between when an order is placed and when the next order after it is placed.

f) EOQ (Economic Order Quantity) calculates the order quantity that minimizes costs.  It is also called the optimal order quantity.