The single-item EOQ formula finds the minimum point of the following cost function. The economic order quantity (EOQ) is the order quantity that minimizes total holding and ordering costs for the year. Even if all the assumptions. Download scientific diagram | EOQ Model Derivation related figures [10] from publication: EOQ-based Inventory Control Policies for Perishable Items: The Case.

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The amount of inventory that will be depleted or used up during this time period is determined by multiplying by the demand rate: There are several variations of the EOQ model, depending on the assumptions made about the inventory system.

ECONOMIC ORDER QUANTITY (EOQ) MODEL: Inventory Management Models : A Tutorial

No shortages are allowed. A numeric illstration of the EPQ model is given in example 2. Variations in both inventory costs will tend to offset each other, since they have an inverse relationship.

There is a fixed cost for each order placed, regardless of the number of units ordered. Given that the store is open days annually days minus 52 Sundays, Thanksgiving, and Christmasthe order cycle is.

The inventory level is gradually replenished as an order is received.

EOQ Formula Derivation

The I Carpet Discount Store in North Georgia derivatioh carpet in its warehouse and sells it through an adjoining showroom. The required parameters to the solution are the total demand for the year, the purchase cost for each item, the fixed cost to place the order and the storage cost for each item per year. The model formula is derived under eos set of simplifying and restrictive assumptions, as follows: The Economic Order Quantity. This situation is most commonly found when the inventory user is also the producer, as in a manufacturing operation where a part is produced to use in a larger assembly.


Note that the number of times an order is placed will also affect the total cost, though this number can be determined from the other parameters. The average inventory carried per year is. This value is substituted into the following formula to determine total minimum annual inventory cost: For instance, in Example As a result, the maximum amount of inventory on hand is the order size minus the amount depleted during the receipt period, computed as Since this is the maximum inventory level, the average inventory level is determined by dividing this amount by 2: As a result, the EOQ model is relatively resilient to errors in the cost estimates and demand, or is robust, which has tended to enhance its popularity.

In EOQ model supply was instantaneous, which may not be the case in all industrial applications. The function of the EOQ model is to determine the optimal order size that minimizes total inventory costs.

Additionally, the economic order interval [8] can be determined from the EOQ and the economic production quantity model which determines the optimal production quantity can be determined in a similar fashion. Derifation presence of a strategic customer, who responds optimally to discount schedule, the design of optimal quantity discount soq by the supplier is complex and has to be done carefully.

In a continuous, or xerivation, system when inventory reaches a specific level, referred to as the reorder point, a fixed amount is ordered. An interesting effect called the “reverse bullwhip” takes place where an increase in consumer demand uncertainty actually reduces order quantity uncertainty at the supplier.


The ordering cost, C ois the cost of setting up the production process to make Super Shag carpet.

EOQ applies only when demand for a product is constant over the year derivatino each new order is delivered in full when inventory reaches zero. Demand is known with certainty and is constant over time. In practice it is acceptable to round the Q values off to the nearest whole number.

International Journal of Production Economics. The graph in Figure This enables us to determine the optimal value of Q by equating the two cost functions and solving for Q: The total minimum cost is determined by substituting the value for the optimal order size, Q optinto the total cost equation: They consider an inventory problem in which. As we mentioned, the economic order quantity is the order size that minimizes the sum of carrying costs and ordering costs.

The order is received all at once just at the moment when demand depletes the entire stock of inventory–the inventory level reaches so there will be no shortages.

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The slope of replenishment line will thus be P-D. As the order size increases, fewer orders are required, causing the ordering cost to decline, whereas derivatkon average amount of inventory on hand will increase, resulting in an increase in carrying costs. This page was last edited on 31 Decemberat