Question

The purchasing manager for Alpa Enterprises requested the following data from the accounting department:

Annual demand = 15,500; Cost of placing an order = £180; Annual inventory holding costs = 20 percent; Unit cost = £753

Assume Alpha’s demand for an item during the lead time is normally distributed with a mean of 5,000 and a standard deviation of 50. What reorder point should be used in order to average no more than one stock out every 20 re-order cycles? If safety stock is 70, how often will a stock out occur during a re-order cycle?

Answer 1

Given,

Annual demand = 15500

Cost of placing an order = 180/-

Annual inventory holding cost = 20%

Unit cost = 753/-

Mean = 5000 units

Standard deviation = 50 units

Safety stock = 70 units

Lets assume the lead time for an order is 10 days and also the number of working days of the enterprise are 300 days per year

then the average daily sales will be 15500/300 = 52 units per day

lead time = 10 days

then the Reorder point will be Average daily sales multiplied by the lead time plus the safety stock = 52*10+70 = 590 units

Reorder point = Lead time demand + Safety stock

Safety stock = Service level(Not mentioned in the question) * Standard deviation of lead time

So 20 reorder cycles = 590 * 20 =11800 units should be used to average no more than one stock of every 20 reorder cycles.