A national chain of tyre fitters stocks a popular tyre for which the following in on 50-week year and normally operates from Monday to Friday only wered Average usage 140 tyres per day rked out of Minimum Flag question usage Maximum 90 tyres per day 175 tyr per day usage Lead 10 to 16 days time Reorder 3.000 quantity Cost per tyre N$1 500 Holding Cost per unit 3% of unit cost Ordening Costs per order N$75.50 Calculate the average level of inventory.?

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Answer

Calculation of Average Level of Inventory

Determining the Reorder Point

To calculate the average level of inventory, we first need to determine the reorder point. The reorder point is the inventory level at which a new order should be placed. It is calculated by multiplying the lead time demand by the lead time and adding the safety stock.

Reorder point = (Lead time demand x Lead time) + Safety stock

The lead time demand is the average daily usage multiplied by the lead time. In this case, the average daily usage is (140+90)/2 = 115 tyres per day. The lead time is between 10 to 16 days. Therefore, the lead time demand ranges from 1150 to 1840 tyres. Assuming a safety stock of 500 tyres, the reorder point ranges from 1650 to 2340 tyres.

Determining the Economic Order Quantity

The economic order quantity (EOQ) is the optimal order quantity that minimizes the total inventory costs. It is calculated by taking the square root of (2 x annual demand x ordering cost per order / holding cost per unit).

Annual demand = Average daily usage x Number of working days in a year
Annual demand = 115 x 50 = 5750 tyres

Using the given values, the EOQ is calculated as follows:
EOQ = √(2 x 5750 x 75.50 / (0.03 x 1500))
EOQ = 152 tyres

Determining the Average Level of Inventory

The average level of inventory is the sum of the reorder point and the EOQ divided by 2.

Average level of inventory = (Reorder point + EOQ) / 2
Average level of inventory = (1650 + 152) / 2 = 901 tyres

Therefore, the average level of inventory for the national chain of tyre fitters is 901 tyres.

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