A North Face retail store in Chicago sells 500 jackets each month. Each jacket costs the store $100 and the company has an annual holding cost of 25 percent. The fixed cost of a replenishment order (including transportation) is $100. The store currently places a replenishment order every month for 500 jackets. What is the annual holding and ordering cost? On average, how long does a jacket spend in inventory? If the retail store wants to minimize ordering and holding cost, what order size do you recommend? How much would the optimal order reduce holding and ordering cost relative to the current policy?

1) What is the annual holding and ordering cost?

annual ordering cost = $100 x 12 = $1,200

annual holding cost = ($100 x 25%) x [500 x 1/2(average inventory)] = $6,250

total $7,450

2) On average, how long does a jacket spend in inventory?

= 30 days / 2 = 15 days

3) If the retail store wants to minimize ordering and holding cost, what order size do you recommend?

economic order quantity (EOQ) = √[(2 x annual demand x order cost) / annual holding cost per unit]

EOQ = √[(2 x 6,000 x 100) / 25] = √48,000 = 219.09 units ≈ 219 units

4) How much would the optimal order reduce holding and ordering cost relative to the current policy?

EOQ = 219

total number of orders = 6,000 / 219 = 27.4 per year

average inventory = 219 / 2 = 109.5 units

annual ordering cost = $100 x 27.4 = $2,740

annual holding cost = ($100 x 25%) x 109.5 = $2,737.50

total $5,477.50

annual savings = $7,450 - $5,477.50 = $1,972.50