Question

what is the formula of minimum total cost in the EOQ model with quantity discount .I want examples and definitions of this

Answer 1

The Formula for Economic Order Quantity (EOQ)

​EOQ=

where:

S=Setup costs (per order, generally includingshipping and handling)

D=Demand rate (quantity sold per year)

H=Holding costs (per year, per unit)​

Definition:

Economic Order Quantity (EOQ) is a production formula used to determines the most efficient amount of goods that should be purchased based on ordering and carrying costs. In other words, it represents the optimal quantity of inventory a company should order each time in order to minimize the costs associated with ordering and holding inventory.

Economic order quantity (EOQ) is the ideal order quantity a company should purchase to minimize inventory costs such as holding costs, shortage costs, and order costs. This production-scheduling model was developed in 1913 by Ford W. Harris and has been refined over time. The formula assumes that demand, ordering, and holding costs all remain constant.

Example

BIKO is a bike retailer located in the outskirts of Paris. BIKO purchases bikes from PMX in orders of 250 bikes which is the current economic order quantity. PMX is now offering the following bulk discounts to its customers:

• 2% discount on orders above 200 units
• 4% discount on orders above 500 units
• 6% discount on orders above 600 units

BIKO is wondering if the EOQ model is still the most economical and whether increasing the order size would actually be more beneficial. Following information is relevant to forming the decision:

• Annual demand is 5000 units
• Ordering cost is $100 per order
• Annual holding cost is comprised of the following:
  • 5% insurance premium for the average inventory held during the year calculated using the net purchase price
  • Warehousing cost of $6 per unit
• Purchase price is $200 per unit before discount

Solution

We need to compare the total inventory cost of the order quantities at the various discount levels with that of the economic order quantity.

Since the holding cost is partially determined on the basis of purchase price, we need to re-calculate the EOQ by applying a discount. As the EOQ seems likely to fall within the 200 to 400 units range, we should use 2% discount in our calculation.

EOQ = √(2 x 100 (Order Cost) x 5000 (Annual Demand)) / (0.05x( 200×0.98) + 6 (Holding Cost))

≈ 252 units

Order Quantity	252 units	500 units	1,000 units
Number of orders (Annual demand ÷ Order Quantity)	5,000 ÷ 252 = 19.84	5000 ÷ 500 = 10	5,000 ÷ 1,000 = 5
Ordering Cost (number of orders × $100)	19.84 x 100 = $1,984	10 x 100 = $1,000	5 x 100 = $500
Warehousing Cost ($6 × Average number of units)	6 × 252/2 = $756	6 × 500/2 = $1,500	6 × 1000/2 = $3,000
Insurance Cost (5% × Purchase Price × Average Inventory)	0.05 × (200×0.98) × (252/2) = $1,235	0.05 × (200×0.96) × (500/2) = $2,400	$0.05 × (200×0.94) × (1000/2) = $4,700
Cost of Purchase (Purchase Price × Annual Demand × (100 - discount%)	200 × 5000 × (1.0-0.02) = $980,000	200 × 5000 × (1.0-0.04) = $960,000	200 × 5000 × (1.0-0.06) = $940,000
Total Inventory Cost	$983,975	$964,900	$948,200

Based on the above analysis, the optimum order quantity is 1000 units.