Harris- Wilson EOQ/ EBQ Model

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Definition: Harris- Wilson EOQ/ EBQ Model

The economic order quantity (EOQ) is a model that is used to calculate the optimal quantity that can be purchased or produced to minimize the cost of both the carrying inventory and the processing of purchase orders or production set-ups. Economic Order Quantity is the quantity that minimizes all these costs. The model was first developed by Ford W. Harris in 1913 but R. H. Wilson, a consultant, is given credit for his in-depth analysis.


Q= √(2DS/H)


Q = optimal order quantity or economic order quantity
D = demand of the item
S = fixed ordering cost or setup cost
H = inventory holding cost per unit

The economic order-quantity model considers the trade-off between ordering cost and storage cost in choosing the quantity to use in replenishing item inventories. A larger order-quantity reduces ordering frequency, and, hence ordering cost/month, but requires holding a larger average inventory, which increases storage (holding) cost/month. On the other hand, a smaller order-quantity reduces average inventory but requires more frequent ordering and higher ordering cost/month.

Example: Suppose car manufacturer Maruti Suzuki uses radiators in installing air conditioners and orders a batch every month. The demand for AC-fitted cars is 200 in a month and the ordering cost (transportation, etc.) is Rs. 100,000. The average inventory holding cost is 2% of unit price which is Rs. 20,000. Using the EOQ formula given above, the optimal quantity of radiators to order will come as Q*=316.23 or 316. Therefore, Maruti Suzuki should order 316 radiator units in order to minimise their total inventory costs.

The Economic Batch Quantity (EBQ) model is an extension of the EOQ model where an optimum is to be calculated for the batch quantity to be produced.

Principal Assumptions:

  • The ordering cost is constant over a period
  • The demand is constant and known throughout the period
  • The new order is delivered in full when inventory reaches zero
  • Lead time is fixed
  • Purchase price of the item is fixed
  • The replenishment is made instantaneously
  • Only one product is involved

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