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ECONOMIC ORDER QUANTITY

Assumptions of the Model

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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

 

 

dTC    = ( - 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.

 

3D bar chart

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