**Economic Order Quantity(Model Assumptions)**

** **

·
Single product or item

· Demand
rate known and constant

· Item
produced in lots, or purchased in orders

· Each
lot or order received in single delivery

· Lead
time known and constant

· Inventory
holding cost based on average inventory

· Ordering,
or setup costs are constant

· No
backorders are allowed

· No
quantity discounts are allowed

**Economic Order Quantity**

Constant Demand, No Shortages

** **

TC
= DCI + D/Q * CO + Q/2 * CH

where:

TC = total annual inventory cost

D = annual demand

CI = cost of purchasing
an item

Q = order quantity

CO = cost of placing an order or setup cost

CH = annual holding cost per unit

**Economic Order Quantity**

Constant Demand, No Shortages

** **

TC = (D/Q) * CO +
(Q/2) * CH

*d*TC =
( - D/Q2) * CO + CH / 2 = 0

**Economic Order Quantity**

Constant Demand, No Shortages

** **

Number of Orders per year = D/Q *

Length of order cycle = Q*/D

TC = (D/Q*) * CO + (Q*/2) * CH

**Economic Order Quantity**

Constant Demand, Shortages Allowed

** **

* *

*TC = D/Q * CO + *__(Q-S)2
__* CH + __S2CB__

* 2Q 2Q*

* *

*where:*

*S = backorder
quantity*

*CB = annual backorder cost per unit *

** **

* *

**Economic Order Quantity**

Constant Demand, Shortages Allowed

* *

*Optimal maximum shortage level:*

* *

*S* = Q* *__CH__

* CB + CH*

* *

*Minimum total annual inventory cost:*

* *

*TC = D/Q***CO+** *__(Q* - S*)2 __* CH
+ __S* CB__

* 2Q* 2Q**

** **

* *

**Economic Order Quantity**

Uniform Replenishment Rate

**Constant Demand, No Shortages**

__ __

*Total Annual = Annual Annual *

*Inventory Setup + Holding*

*Cost Cost Cost*

* *

* *

*TC = D/Q* CS +
Q/2 * (1 - u/p) * CH *

* *

* *

*where:*

*CS = setup cost for a lot*

*u = usage rate*

*p
= production rate ** *

* *

**Economic Order Quantity**

Quantity Discounts (Solution Procedure)

** **

Step 1: Compute Q for the unit cost associated
with each discount category.

Step 2: For those Q that are too small to receive
the discount price, adjust the order quantity upward to the nearest quantity that will receive the discount price.

Step 3: For each order quantity determined
in Steps 1 and 2, compute the total annual inventory price using the unit price associated with that quantity. The quantity
that yields the lowest total annual inventory cost is the optimal order quantity.