Question

1. Q Model with Uncertain Demand

A distributor of large appliances needs to determine the order quantities and reorder points for the various products it carries. The following data refer to a specific refrigerator in its product line:

• Cost to place an order                                  $100/order
• Holding cost                                                    10 percent of product cost per year
• Cost of refrigerator                                        $500/unit
• Expected Annual demand                           3650 units
• Standard deviation of daily demand         3 units
• Lead time                                                         3 days

Questions: Consider an even daily demand and a 365-day year.

• What is the economic order quantity?
• If the distributor wants a 97% service probability, what reorder point, R, should be used?
• What will be the safety stock?

Answer 1

1.EOQ = SQRT(2 * DEMAND * ORDERING COST / HOLDING COST)

EOQ = SQRT(2 * 3650 * 100 / 50) = 120.83

2. Daily demand = 3650 / 365 = 10

Lead time = 3

Z = 1.88 (for 97% service level)

Safety stock = Z * standard deviation * sqrt (lead time)

= 1.88 * 3 * sqrt (3) = 9.77

ROP = daily demand * Lead time + Safety stock

= 10 * 3 + 9.77

= 39.77

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