Economic batch size

Economic batch size (economic order quantity) - is a method of inventory management in the supply chain. It assumes fixed quantity of each order of products whose amount is determined by the price, the characteristics of demand and the cost of maintaining inventory and the cost of re-ordering. Using the EOQ in practice managers should also designate a point of reorder i.e. critical volume of stocks, which if reached, causes ordering od a certain size. The size of the order depends on the time required to receive the goods after placing the order, as well as on demand/volume of sales.

Fig.1. Economic batch size

The simple EOQ model assumes:

• continuous constant known amount of demand,
• full satisfying demand,
• constant, well-known cycle of replenishment, time of delivery,
• unlimited availability of capital,
• infinite planning horizon,
• no stock in transit,
• homogeneity of goods,
• fixed price or cost, which shall be independent of the size of the contract or time (purchase price, transport costs)
• R - Total volume of demand in the period (year or during the period)
• Q - The size of the order in units
• A - the cost of ordering
• V - cost per unit of inventory
• W - The percentage of maintenance costs of inventory in an annual inventory,
• S = V x W - the cost of inventory per unit per year (or test period)
• t - time in days
• TAC - total annual cost
• $TAC={1 \over 2}QVW+{AR \over Q}={1 \over 2}QS+{AR \over Q}\,$

The first part of the equation is the cost of maintaining inventory, the second refers to the cost of ordering. Optimal order quantity must minimize the costs per unit of the product. By differentiating the equation designating the total cost after Q and equating to zero, we get the following equation:

• $Q={\sqrt {{2RA} \over {VW}}}$ or $Q={\sqrt {{2RA} \over {S}}}$

Solving the above equation, we get the optimal order size.

See also:

• Types of logistics costs

Examples of Economic batch size

• Businesses with a high cost of inventory and a large demand for their goods often use the economic batch size to determine the optimal order size. For example, a restaurant chain may use the economic batch size to determine how much of each ingredient they need to order each month.
• A manufacturing company may use the economic batch size to determine the optimal quantity of parts to order from a supplier. For example, a company that produces bicycles may need to order a certain number of wheels and tires each month.
• A retailer may use the economic batch size to determine the optimal quantity of items to order from a wholesaler. For example, a clothing store may need to order a certain number of shirts, pants, and shoes each month.
• A logistics company may use the economic batch size to determine the optimal quantity of items to ship. For example, a company that ships packages across the country may need to order a certain number of boxes and packing materials each month.

Advantages of Economic batch size

Economic batch size is an inventory management system which helps to determine the optimal order quantity of products to be purchased. It has the following advantages:

• It helps to reduce the carrying costs associated with inventory maintenance. The lower the inventory, the lower the costs.
• It helps to reduce order costs as larger orders will be more cost-effective.
• It can help to maintain a stable supply of goods, preventing stock-outs and potentially reducing customer dissatisfaction.
• It helps to reduce the time needed to place orders as well as the time needed to receive them.
• It helps to improve the inventory control system by determining the optimal order quantity and the point of reorder. This increases overall efficiency.

Limitations of Economic batch size

• One of the main limitations of Economic batch size is that it does not take into account the variable costs associated with production. This includes costs such as labor, materials, and overhead costs that can fluctuate from order to order.
• Another limitation is that it does not consider other factors that can influence the cost of production, such as the availability of supplies, the quality of the supplies, or the complexity of the product being manufactured.
• Additionally, the Economic batch size ignores the potential for price increases from suppliers, which can cause a significant increase in cost for the production of an item.
• Moreover, the Economic batch size does not take into account the cost of storage and associated risks, such as spoilage, theft, and other losses that can occur in the process of storing products.
• Finally, the Economic batch size does not account for the customer's demand or preferences, which can affect the size of orders and the cost of production.

Other approaches related to Economic batch size

One approach related to Economic batch size is the Reorder Point (ROP). This approach is used to determine the point at which an order should be placed to ensure that the inventory level is maintained. The ROP is calculated by taking into account the lead time for ordering, the rate of demand, and the safety stock needed. Other approaches include:

• Just-in-time (JIT) inventory management: This approach is a system for ordering inventory that is based on the actual demand for products and eliminates the need for safety stock.
• Continuous review system: This system is used to constantly monitor and evaluate inventory levels and to adjust the order size and order frequency based on the results.
• ABC inventory analysis: This system assigns a priority level to each inventory item, based on the value of the item in terms of cost and importance to the company.

In summary, there are several approaches related to Economic batch size such as Reorder Point, Just-in-time inventory management, Continuous review system, and ABC inventory analysis. Each approach has its own advantages and disadvantages and should be carefully evaluated to determine which is best suited for a given situation.

Economic batch size — recommended articles

Optimum size of the order — Minimum stock level — Order point — Cycle stock — Reorder level — Abc inventory classification — Lot size — Stock turn — Fill rate

References

• Eilon, S. (1959). Economic batch-size determination for multi-product scheduling. OR, 217-227.
• Jamal, A. M. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at a single-stage production system. Computers & Industrial Engineering, 47(1), 77-89.