EOQ MODELS

Presentation By: Shashank

Shekhar

Economic Ordering Quantity

EOQ is the amount of inventory to be ordered at one time for purposes of minimizing annual inventory cost.

Formula for Economic Ordering Quantity :

◦ Ordering Cost: Cost of placing single order.◦ Holding Cost: Cost to hold one unit inventory for a

year

EOQ ASSUMPTIONS

Known & constant demand

Known & constant lead time

Instantaneous receipt of material

No quantity discounts

Only order (setup) cost & holding

cost

No stockouts

Various EOQ Models

Economic Production Quantity (EPQ)

Quantity Discount ModelPlanned Shortage With

Backorders

1.Economic Production Quantity

EPQ determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost.

Assumptions :◦ Demand for items from inventory is continuous and at a

constant rate.◦ The production of items is continuous and at a constant rate.◦ Ordering cost is fixed (independent of quantity produced).◦ The purchase price of the item is constant i.e. no discount is

available.◦ The replenishment is made incrementally.

Derivation of EPQ FormulaHolding Cost Per Year = Q/2*(F(1-x))

Q/2 is average inventory & F(1-x) is the average holding cost.

 F(1-x) is the average holding cost. Ordering Cost per Year =D/Q*(K)

◦ K = ordering/setup cost◦ D = demand rate◦ F = holding cost◦ Q = order quantity◦ P=Production Rate◦ x=D/P

How TO Get EPQ Formula ?Holding Cost = Ordering Cost

So, We get:

2. Quantity Discount Model   Quantity discounts are price reductions designed to

induce large orders.  The buyer's goal in this case is to select the order

quantity that will minimize total costs, where total cost is the sum of carrying cost, ordering cost, and purchase cost.

Two approach are there:◦ With the Incremental Approach, we would pay

$65 for the first 100 units and $60 for rest of the 150 units.

◦ But, with the All Units Approach, we would pay $60 a piece for all the 250 units.

Understanding Quantity DiscontQUANTITY PRICE

1 - 49 Rs.1,400

50 - 89 1,100

90+ 900

Co = Rs.2,500

Ch = Rs.190 per unit

D = 200

Qopt = = = 72.5 PCs2CoD

Ch

2(2500)(200)190

TC = + + PD = Rs.233,784 CoD

Qopt

ChQopt

2

For Q = 72.5

TC = + + PD = Rs.194,105CoD

Q

ChQ

2

For Q = 90

3.Planned Shortage WithBackorder

Continued.. Shortage: when customer demand cannot be

met.Shortage may result into:

◦ Lost of goodwill.◦ Reduction in future orders.◦ Unfavorable Changes in the market share.◦ Loss of customers.

In some situation customer may not withdraw order and wait till next shipment arrives.

Planned Backorder Formula