At a college counselling office, an inventory of hats from each of 50 top univer

Question

At a college counselling office, an inventory of hats from each of 50 top universities is maintained so that new customers can choose a hat based on the University they seek to enter. BU hats cost the company $8.50 each. Last year, demand for BU hats was 300 per month, evenly spaced throughout the year. This demand is expected to continue in the future. The shipping and other ordering costs for the hats is $75 per order. The holding cost rate is estimated to be 25% annually. a. If the company used a fixed order quantity model, calculate the optimal economic order quantity (EOQ). Show all work. b. If management decided to order the hats on a monthly basis (one order per month), how much more would it cost the company per year (using just ordering and holding costs)? Show all work.

Explanation / Answer

Monthly demand = 300 hats

Annual demand (D) = monthly demand x 12 months = 300x12 = 3600 hats

Cost per hat = $8.50

Ordering cost(S) = $75

Holding cost (H) = 25% of cost = 25% of $8.50 = $2.13

Economic order quantity (Q) = sqrt of (2DS / H)

= sqrt of [(2x3600x75)/2.13]

= 503.5 or rounded to 504 hats

Total cost with EOQ = Holding cost + ordering cost

= [(Q/2)H] + [(D/Q) S]

= [(504/2)2.13] + [(3600/504)75]

= $536.76 + $535.71

=$1072. 47

If they order hats on monthly basis then order quantity(Q) = 300 hats

So with Q=300,total cost = Ordering cost + Holding cost

= [(D/Q) S ] + [(Q/2)H]

= [(3600/300)75] + [(300/2)2.13]

= $900 + $319.5

= $1219.5

Total cost without EOQ - Total cost with EOQ = $1219.5-$1072.47 = $147.03

So if the management orders hats on monthly basis it would cost $147.03 more

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