A PRODUCTION ORDER QUANTITY MODEL. Nathan Manufacturing, Inc., makes and sells specialty hubcaps for the retail automobile aftermarket. Nathan’s forecast for its wire-wheel hubcap is 1,000 units next year, with an average daily demand of 4 units. However, the production process is most efficient at 8 units per day. So the company produces 8 per day but uses only 4 per day. The company wants to solve for the optimum number of units per order. ( Note: This plant schedules production of this hubcap only as needed, during the 250 days per year the shop operates.)
APPROACH \blacktriangleright Gather the cost data and apply Equation (12-7):
Annual demand = D = 1,000 units
Setup costs = S = $10
Holding cost = H = $0.50 per unit per year
Daily production rate = p = 8 units daily
Daily demand rate = d = 4 units daily
Q^*_p = \sqrt{\frac{2DS}{H[1 - (d/p)]}} (12-7)