It is one of the oldest classical production scheduling models.
The model was developed by Ford W. Harris in 1913, but the consultant R. H. Wilson applied it extensively, and he and K. Andler are given credit for their in-depth analysis.
[1] The EOQ indicates the optimal number of units to order to minimize the total cost associated with the purchase, delivery, and storage of a product.
EOQ applies only when demand for a product is constant over a period of time (such as a year) and each new order is delivered in full when inventory reaches zero.
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 for a single item and the storage cost for each item per year.
Q* is independent of P; it is a function of only K, D, h. The optimal value Q* may also be found by recognizing that where the non-negative quadratic term disappears for
= 400 units Number of orders per year (based on EOQ)
For instance, supposing 500 units per order, then Total cost
Similarly, if we choose 300 for the order quantity, then Total cost
This illustrates that the economic order quantity is always in the best interests of the firm.
An important extension to the EOQ model is to accommodate quantity discounts.
There are two main types of quantity discounts: (1) all-units and (2) incremental.
[2][3] Here is a numerical example: In order to find the optimal order quantity under different quantity discount schemes, one should use algorithms; these algorithms are developed under the assumption that the EOQ policy is still optimal with quantity discounts.
Perera et al. (2017)[4] establish this optimality and fully characterize the (s,S) optimality within the EOQ setting under general cost structures.
In presence of a strategic customer, who responds optimally to discount schedules, the design of an optimal quantity discount scheme by the supplier is complex and has to be done carefully.
An interesting effect called the "reverse bullwhip" takes place where an increase in consumer demand uncertainty actually reduces order quantity uncertainty at the supplier.
[5] Several extensions can be made to the EOQ model, including backordering costs[6] and multiple items.
In the case backorders are permitted, the inventory carrying costs per cycle are:[7] where s is the number of backorders when order quantity Q is delivered and
In the first case the optimal lot is given by the classic EOQ formula, in the second case an order is never placed and minimum yearly cost is given by
solving the preceding quadratic equation yields: If there are backorders, the reorder point is:
A version of the model, the Baumol-Tobin model, has also been used to determine the money demand function, where a person's holdings of money balances can be seen in a way parallel to a firm's holdings of inventory.
[9] Malakooti (2013)[10] has introduced the multi-criteria EOQ models where the criteria could be minimizing the total cost, Order quantity (inventory), and Shortages.
A version taking the time-value of money into account was developed by Trippi and Lewin.
[11] Another important extension of the EOQ model is to consider items with imperfect quality.
Salameh and Jaber (2000) were the first to study the imperfect items in an EOQ model very thoroughly.
They consider an inventory problem in which the demand is deterministic and there is a fraction of imperfect items in the lot and are screened by the buyer and sold by them at the end of the circle at discount price.
[12] The EOQ model and its sister, the economic production quantity model (EPQ), have been criticised for "their restrictive set[s] of assumptions.
[13] Guga and Musa make use of the model for an Albanian business case study and conclude that the model is "perfect theoretically, but not very suitable from the practical perspective of this firm".
[14] However, James Cargal notes that the formula was developed when business calculations were undertaken "by hand", or using logarithmic tables or a slide rule.
Use of spreadsheets and specialist software allows for more versatility in the use of the formula and adoption of "assumptions which are more realistic" than in the original model.