Question

An inventory of Product A has to be maintained at NiceCare using the EOQ model, based upon the following information:   

Table 7

Inventory Information for product A
Annual Demand	456 units
Ordering Cost	$12
Our Selling Price per unit	$28
Carrying Cost percentage	0.3
Stock Out Cost per unit	$30
Lead Time from Supplier	2 months

The supplier has offered quantity discounts for bulk orders of Product A. The price brackets are as follows:

  Table 8

Bulk Discounts from Supplier
Quantity	Cost per unit
1 – 30	$11
31 – 80	$6
81 plus	$3

Under this pricing offer, what is the optimal order quantity for Product A that minimises annual total inventory costs for NiceCare?  Present your workings in a table format and also explain to the Senior Leadership Team how you reached your solution.

Answer 1

Lead Time = 2 months

Annual Demand = 456

Monthly Demand = 456/12 = 38

Demand over the Lead Time = 76

In case, when the order quantity is < 76, the demand would deplete the stock before the next batch of stock gets delivered. In such case, the steep Stock Out cost would severely damage the financial profitability of the NiceCare. Therefore, Order Quantity has to be >= 76 so as make sure that the stock out don't happen with certainty.

Order Quantity	Ordering Cost =Annual Demand*Ordering Cost/Order Quantity	Holding Cost =Order Quantity*Carrying Cost/2	Inventory Cost = Annual Demand * Unit Cost	Total Inventory Cost
76	72	68.4	2736	2876.4
80	68.4	72	2736	2876.4
81	67.56	36.45	1368	1472

It can be clearly seen that the Total Inventory Cost would reduce to a great extent if the Order Quantity is set at 81 or above. This is due to the fact that the Ordering Cost & Holding Cost are always found to be very marginal in comparison to the Unit cost of the product.

Now after evaluating the range of Ordering quantity, we shall find the exact EOQ value (considering unit cost = 3$)

EOQ = sqrt(2*Annual Demand*Ordering Cost/Holding Cost) = sqrt(2*456*12/(0.3*3)) = 110.27 ~ 110

Using the above derived EOQ value,

The Ordering Cost will be = 49.75

Holding Cost = 49.5

Inventory Cost = 1368

and the Total Inventory Cost = 1467.45

Therefore, we can say using the Order Quantity of 110, we shall be able to prevent stock chances and ensure the minimal level of Total Inventory Cost at 1467.45

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