Sometimes enterprises accumulate inventory balances for the most popular positions. However, it is impossible to increase stocks indefinitely. It is necessary to determine the optimal order sizes. For this purpose, the Wilson formula is used.

Views

Remains in warehouses are divided into production and commodity ones. The first category includes purchased stocks intended for the manufacture of products. Their purpose is to ensure a smooth production process. Inventory is the balance in warehouses and those that are on their way to wholesalers and retailers.

Current stocks are designed to ensure a smooth trading or production process in between deliveries of goods. Safety stocks are accumulated for the same purpose, but in the event of unforeseen circumstances: a change in the delivery lot, an increase in demand, or delays along the way. In a normal market situation, the amount of safety stocks does not change.

Why build up inventory?

Stocks in the economy ensure the stable operation of the system. But this method is quite expensive. According to foreign sources, it costs 25 cents a year to store a $ 1 unit. Domestic economists give similar figures - 20-30% of the cost of goods. If a company has reserves worth 100 million rubles, then it spends another 25 million on their maintenance.

Risks

Inventory storage has several disadvantages. This is:

• freezing of financial resources;
• suspension of the quality improvement process, since the organization first of all eliminates stocks, and then purchases new products;
• isolation of logistics in the distribution scheme;
• expenses for the maintenance of special premises and wages of storekeepers;
• risk of losses due to damage or theft of property.

Based on how much storage costs the organization bears, the entire inventory management process is determined. Wilson's formula helps stocks to be cut. Although the storage of products is fraught with risks, entrepreneurs are forced to take them, since the lack of inventory entails a loss of profits.

The result of calculations obtained using the Wilson model, the formula for which was presented earlier, should be compared with other costs. The cost of purchasing each type of product should be less than the cost of storing it. Only then does it make sense to build up stocks.

Management problems

• The size of the order is influenced by a large number of factors: its size, uneven consumption, remoteness of the supplier, logistics.
• Inventories can be formed both for current deliveries and for seasonal sales.
• A large number of inventory control systems: from periodic to continuous.
• With the expansion of the assortment, the risk of calculating the optimal delivery schedule increases. Wilson's formula does not exclude this risk.
• Increased lead time in regions with cheap labor.

Term

Optimal size order (Wilson's formula) is a model that can be used to determine an economically feasible order size with minimal cost. It applies under the following conditions:

• The demand for products and the delivery time of the goods are clearly known.
• The receipt of the goods is carried out instantly.
• There is no shortage and no bulk discounts.

Wilson's formula

The optimal order size is TC = PR + CR / Q + PFQ / 2, where

• Q - order size;
• C - placement costs;
• R is the annual demand;
• P is the cost of purchasing 1 piece of product;
• F is the storage cost factor (usually 10-15%).
• PF is the cost of storing the goods for the year.

For whom?

Wilson's formula was developed for large industrial enterprises... It cannot be used in this form in modern trading companies. The first step is to expand it to take into account the costs of debt and wide range of products. Only then can Wilson's formula be applied on a group of weighty (ABC analysis) and stable goods (XYZ analysis).

Other indicators

For inventory management, you can use more than just the Wilson formula. IN economic theory there are a number of other factors that refine the calculation results.

Inventory turnover shows how many times a product goes through all sales cycles for a specified period of time. Using this indicator, you can calculate the possibility of obtaining gross profit from one ruble invested in the purchase of goods:

Oz = Cost of purchased goods per month (quarter, year) / Average stock of goods for the same period.

When calculating the indicator, products purchased for a specific order are not taken into account.

Stock availability - for how many days the organization's current stock will last if supplies suddenly stop:

Obes = Inventory cost x Number of days / Average inventory

Share of stocks in current and non-current assets:

Ud = Inventory value / OA (intangible assets)

ABC analysis

This calculation method identifies the most important resources of the firm. It can be applied to all kinds of organizations. It is formed according to the Pareo principle: 80% of the turnover gives 20% of the goods. Reliable control of this part of resources (reserves) will make it possible to control the system as a whole.

Within the ABC analysis, commodity items are divided into three categories:

• A - the most profitable: 20% of the assortment brings 80% of orders.
• B - intermediate: 30% of the assortment brings 15% of sales.
• С - least valuable: 50% of the assortment brings 5% of orders.

ABC analysis is a ranking by parameters. Moreover, you can sort not only products, but also buyers, the length of the sales period, and other important statistical data. The goal is to group objects according to the degree of their influence on the final result. During the analysis, a graph is also formed, which is called the Pareto curve (Lorentz or ABC curve). The same method can be used to rank customers by the number of orders in logistics. Wilson's formula is not suitable for this purpose.

The grouping of objects can be carried out according to cost indicators. In this case, the proportion of objects and overall result(for example, if products bring 50% of orders, then this value doubles). The value of the sums ranges from 0% to 200%. Groups are formed according to the following criteria: A - 100%, B - 45%, C - the rest.

XYZ analysis

Another way to determine the optimal order is to calculate the coefficient of variation (XYZ analysis). It reflects the spread of the value relative to the average (order volume, sales level, number of customers, etc.). With its help, it is possible to exclude the influence of seasonal factors on the final indicator. The calculation process uses the standard deviation percentage formula.

The information is ranked as follows:

• X - the smallest changes in the average value (0-10%);
• Y - changes in values ​​by 10-25% of the average;
• Z - change in values ​​by more than 25%.

The first two groups of indicators have the greatest influence on the final result.

Thus, before applying the Wilson formula, you should determine the most significant groups of goods for the organization, and then calculate the limit for stocks.

Economic order quantity

Application area

The optimal order size allows you to minimize the overall costs of inventory management, which allows you to reduce the rise in consumer prices, thereby positively affecting the company's competitiveness.

Description

The calculation of the most economical order size is carried out within the framework of an inventory management system with a fixed order size, which should be equal to the most economical order size. In this system, the order size is a constant value and is formed when the stock size decreases to a certain critical level. The system is based on the selection of a lot size that would minimize the overall inventory management costs, which in turn are divided into order fulfillment costs and inventory holding costs. Graphically, the dependence of total annual costs on the size of the order is shown in Figure 1.

It can be seen from the figure that the total costs are at a minimum with an order size of approximately 400 pieces, thus this order size is optimal for this case.

The Wilson formula is used to calculate the most economical EOQ order size:

$ EOQ = \ sqrt (\ frac (2 \ times S \ times C_0) (C_1 \ times i)) $,

$ S $ - annual consumption,

$ C_0 $ - cost of order fulfillment,

$ C_1 $ - unit price,

$ i $ - inventory maintenance costs (%).

Using the Wilson formula, you can calculate the optimal order size in accordance with the specific conditions of the enterprise. If stocks are replenished not instantly, but within a certain period time (for example, when restocking from our own production), then the following formula is used to calculate the most economical order size EOQ:

$ EOQ = \ sqrt (\ frac (2 \ times S \ times C_0) (C_1 \ times i \ times (1 - \ frac (S) (Q)))) $,

$ Q $ - the volume of production, due to which stocks are replenished.

In conditions of a shortage of goods that are stocks, the most economical order size EOQ is determined by the formula:

$ EOQ_ (def) = EOQ \ times \ sqrt (\ frac ((C_1 * i + h)) (h)) $,

$ EOQ $ - the most economical order size without taking into account the shortage,

$ h $ - deficit costs.

Algorithm

1. Calculate the annual storage costs per unit.
2. Calculate the optimal order size EOQ.
3. Calculate the optimal order size EOQ for your own production.
4. Calculate the optimal EOQ order size in conditions of shortage.

Calculation of the optimal order size along with the calculation of the optimal value of the safety stock will minimize storage costs, while maintaining a given level of demand.

Data Requirements

Field name	Field label	Data type	Data type
Name	Name	String	Discrete
C0	Execution costs	Real	Continuous
S	Annual consumption	Whole	Continuous
C1	Unit price	Real	Continuous
i_percent	Inventory maintenance costs (% of product unit)	Whole	Continuous
p	Annual production	Whole	Continuous
h	Deficit costs	Real	Continuous

Book: Logistics / Larina

Determining the economic size of the order

The determination of the schedule line in procurement logistics is based on the indicator of the optimal (economical) order size. This indicator expresses the power material flow directed by the supplier at the request of the consumer and providing for the latter minimum order the sum of two logistic components: transport and procurement costs and the cost of forming and storing stocks.

When determining the order size, you must match the cost of maintaining inventory and the cost of placing orders. Since the average inventory order will increase the average inventory. On the other hand, the larger batches are purchased, the less often the order has to work, and, consequently, the cost of their submission decreases. The optimal order size should be such that the total annual costs for order submission and inventory maintenance are the lowest for a given consumption volume.

The economic order quantity (EOQ) is determined by the formula obtained by F.W. Harris. However, in control theory, it is better known as the Wilson formula:

EOQ = V (2x Co x S \ Ci x U)

Where EOQ is the economical order size, units;

Co - the costs of order fulfillment, UAH;

Ci - purchase price of a unit of goods, UAH;

S - annual sales volume, units;

U is the share of storage costs in the unit price.

V - square root

Let's find the economic size of the order under such conditions. According to the accounting data, the cost of submitting one order is 200 UAH, the annual need for a component is 1550 pcs., The price of a unit of a component is 560 UAH, the cost of storing a component in a warehouse is 20% of its price. Determine the optimal order size for a component product.

Then the economical order size will be equal to:

EOQ = = 74.402 units.

To avoid a shortage of a component, you can round the optimal order size up. Thus, the optimal order size for a component product will be 75 pieces.

Therefore, 21 (1550/75) orders need to be placed during the year.

In practice, when determining the economic size of an order, more factors have to be taken into account than in the basic formula. Most often this is due to special delivery conditions and product characteristics, from which you can get some benefit, if you take into account such factors: discounts on transport tariffs depending on the volume of cargo transportation, discounts on product prices depending on the volume of purchases, and other clarifications.

Transport tariffs and the volume of cargo transportation. If transport costs are borne by the buyer, transport costs must be taken into account when determining the order size. As a rule, the larger the shipment, the lower the cost of transporting a unit of cargo. Therefore, other things being equal, enterprises benefit from such sizes of supplies that provide savings in transportation costs. However, these sizes may exceed the economic order size calculated using the Wilson formula. In this case, if the size of the order increases, the volume of stocks increases, and, as a result, the costs of their maintenance.

To make an informed decision, you need to calculate the total costs taking into account the savings in transportation costs and without taking into account such savings - and compare the results.

Let's calculate the impact of transportation costs on the economic size of the order based on the previous example with additional condition that the tariff for the transportation of a small consignment will be UAH 1. per unit of cargo, and the tariff for the transportation of a large consignment is 0.7 UAH. per unit of cargo, 85 units are considered a large batch (Table 4.6).

Table 4.6

Impact of transportation costs on the economic size of the order

	order, units
To place orders Fare	75/2 x 560 x 0.2 = 4200 21 x 200 = 4200	85/2 x 560 x 0.2 = 4760 18 x 200 = 3600 85 x 0.7 = 59.5
General expenses

Calculations show that the second option is more attractive.

Price discounts depending on the volume of purchases. Volume-based price discounts expand the economy order size formula in the same way as discounts on transport tariffs, which are determined by the volume of freight. Including discounts in the basic EOQ model amounts to calculating the total cost and the corresponding economic order size for each purchase volume (and price). If, for a certain purchase volume, the discount is sufficient to offset the increase in inventory costs, aside from the reduction in order placement costs, this option may be beneficial.

The company purchases parts at a price of 25 UAH. per unit, the annual need for parts is 4800 pieces, the cost of storing one part is 5 UAH, the cost of organizing one order is 100 UAH.

Let's find the economic size of the order:

EOQ = = 438.17 units.

Thus, the economic order size will be 439 parts, and the number of orders per year - 11 (4800/439).

Let's take into account the system of discounts (Table 4.7) and determine the total annual costs (Table 4.8).

Table 4.7

The system of discounts provided by the supplier

Order volume, units	Unit price, UAH
1000 and more

Table 4.8

Calculating total annual costs for different order volumes

Expenses, UAH	Order volume, units
organization of orders		4800/500 x 100 = 960	4800/1000 x 100 = 480
storage of one order			1000 x 5 = 5000
purchase of inventory for an annual requirement		24.8 x 4800 = 119040	24.7 x 4800 = 118560

Calculations show that the best option will be the second option (order volume 500 units), which provides the lowest annual total costs.

Other adjustments to the EOQ model. There may be other situations that require adjustments to the economic order size model:

1) Production volume. Clarification of the volume of production is necessary when the most economical size of orders is dictated by production needs and conditions.

2) Procurement of mixed lots. The purchase of mixed batches means that it finds several types of products at the same time; in this regard, discounts set in accordance with the volume of purchases and transportation should be assessed in relation to the combination of goods.

3) Limited capital. Capital constraints have to be taken into account when funds for investing in stocks are limited. Therefore, during the determination of the size of orders, limited financial resources between different kinds products.

4) Using your own Vehicle... Using your own vehicles affects the order size because in this case the transport costs associated with restocking are fixed costs. Therefore, your own transport must be completely filled, regardless of the economic size of the order.

1.	Logistics / Larina
2.	Logistics development stages
3.	Modern logistics concept
4.	Purpose, tasks and functions of logistics
5.	Logistics types
6.	The essence and types of logistics systems
7.	Logistic chains
8.	Development stages of logistics systems
9.	Material flow and its characteristics
10.	Types of material flows
11.	Logistic operations
12.

If your company belongs to a small business, then manually determining the optimal order size will seem to you a simple task. However, as your business grows, you should consider investing in to manage your inventory more efficiently.

There are many reasons why a business should invest in a system to calculate the optimal order, and they all go beyond just tracking availability. A large retail chain in the eastern region of Ukraine has recently faced the main prerequisites and reasons for investing in an automated inventory management system.

About company

A retail company in the Eastern Region with about 20 stores. The company has own production: confectionery shop, bakery. We have our own distribution center and a wholesale warehouse.

• General trade area- more than 6.5 thousand m 2
• The total number of active SKUs is over 11,000
• The number of system users is more than 30
• More than 500 promotional offers daily

Optimal order size, delivery schedule, stock level and other prerequisites

Often in companies, the optimal order size is determined manually by different interpretations of the Wilson formula:

where
S - annual consumption,
C0C0 - the cost of fulfilling the order,
C1C1 - unit price,
i is the cost of maintaining stocks (%).

Optimal order quantity (Wilson's formula, EOQ model) is an optimal order size model that determines the optimal order quantity, which minimizes the total variable costs associated with ordering and storing stock.

At the time of the pre-project survey of the network, a formula was incorporated into the model of the optimal order size, which was based on the sales forecast. All orders of the chain were formed in a semi-automatic mode using the 1C 8.2 inventory system using the min-max method, which increased labor costs and reduced the quality of orders, the network had surpluses for some goods and shortages of others. Delivery schedules were maintained by managers in Excel, therefore, when placing orders, managers in manual mode took this information into account. Also, in the accounting system, there was practically no possibility of assessing excess inventory and the reasons for their occurrence.

For effective operation a trading company, which is a client, must fulfill two conditions: on the one hand, to ensure profit, by not selling goods at a discount, by supplying them with a more expensive and faster mode of transport, and on the other hand, to increase sales, for this to keep more inventory, sell with discounts, supply with more expensive and faster means of transport. To satisfy both conditions of the network, it is necessary to determine the optimal batch of the order to ensure the constant availability of the right product in the right place in the right time, while not having commodity surpluses.

To optimize the network and improve financial performance, TOP management decided to implement a specialized management solution commodity stocks.

System selection criteria for determining the optimal order size

To select a program for inventory management and automatically determine the optimal order size, a market analysis was carried out, the company involved external consultant to assess the capabilities of the system and after a detailed study of the main characteristics of the product, the choice was made on a solution from ABM Cloud, the algorithms of which are based on the Theory of Constraints (TOC) methodology.

TOC solution for distribution and retail is based on two installations:

• Supply to ensure availability;
• Establish and maintain a reliable distribution system aimed at ensuring product availability.

Unlike the classical sales forecast replenishment model, TOC uses the concept of a “stock buffer”, which characterizes the required and sufficient level of stock at each storage point for each managed unit, as well as the dynamic change in this stock depending on the area where the remainder is located.

Work algorithms automated system Inventory management ABM Cloud is based on the TOC methodology. The system provides:

• Maintaining the volume of inventories at a predetermined level, which ensures the constant availability of goods with optimal stocks in the system. This is achieved by automatically executing processes:
  1.1. Planning an order
  1.2. Forming an order
  1.3. Calculation of the optimal order size
  1.4. Order optimization
  1.5. Sending an order
  1.6. Periodic adjustment of the required storage level
  1.7. Business case for sustained levels
  1.8. Control over the state of stocks
• Assortment management (by determining the items least demanded by consumers; as well as determining the items of the custom-made assortment that are in constant demand to enter them into a regular assortment matrix)
• Detailed analytics on the state of stocks and their impact on financial indicators business.

In addition to the methodological component, an important argument for making a decision in favor of the system was the possibility of using the program as a service, the SaaS model. The cloud model of the product does not imply the purchase of a system and installation on users' computers; payment is made monthly, upon the use of the system. This allows significant savings: no capital investment is required in the product, there are no additional costs for expensive equipment and maintenance of the system in working order. The company gets access to the system installed on secure servers in the data center, where all calculations and processes of work with stocks and orders take place.

Description of the project

The project took place in 2 stages: connecting external suppliers and connecting a distribution center.

Before the start of the project, the goals were formulated to be achieved:

• Determine the optimal order lot
• Reduce excess inventory and optimize assortment;
• Improve the turnover indicators of the enterprise;
• Automate orders;
• Optimize work time personnel by automating the processes of working with stocks and orders.

In the course of the project, all main categories of goods were connected to the ABM inventory management system, except for the group of goods in the Fresh segment. Currently, there are 332 suppliers under the control of the system, about 108 thousand items of goods.

The system automatically generates from 150 to 200 orders to the central warehouse every day, depending on the agreed schedule of orders, as well as from 500 to 1000 orders to external suppliers, and about a third of these orders (28%) are sent to suppliers without the participation of a manager, the rest of the orders are adjusted less than by 20%.

For each SKU, at each storage point, when connected, its own stock level (buffer) is set, which is calculated based on the consumption from this link and the delivery schedule. After several cycles, the system automatically (or after confirmation by the manager) changes the buffers based on real consumption (not predicted). This mechanism is called Dynamic Buffer Managemen (DBM) and is one of the main tools in TOC inventory management. The optimal order level is shown on the chart.

Buffer Inventory Management

In the process of connecting the inventory management system, managers carried out work on correctly filling in the parameters of goods in the 1C inventory system, drawing planograms (since this information can be automatically taken into account when placing an order). Using these systems, the inconsistencies of the shelf display with sales were identified and corrected. This improved the inventory turnover indicators: the shelf turnover was accelerated from 32 to 20 days, and the data on its turnover was used in negotiations with suppliers to justify marketing payments.

About 30% of the entire assortment is delivered to shelves without storage at the DC, this is implemented in the system using the Cross-Docking functionality. This functionality allows you to more efficiently use the warehouse area, while for the supplier the delivery procedure is not complicated by the delivery of goods to retail outlets- that is, the system is mutually beneficial to both the supplier and the buyer. In addition, the load on the warehouse is reduced, logistics costs are reduced, and the warehouse space is used more optimally.

To focus the attention of specialists, the main indicators of the effectiveness of inventory management - surplus, lost sales and turnover - are presented on the main screen of the system. Lost sales is an indicator that is rather difficult to calculate, although it is easiest to identify visually - since a missed sale is an unfulfilled sale due to the lack of goods on the shelf, and which most of all affects the impression of the store.

It is one of the key functions manager, because only by determining the cause of the problem, you can find the optimal solution. From the main screen, you can go to the list of problematic positions and focus on them.

The company pursues an active marketing policy, which includes promotions and sales in order to attract customers. Also, sales of some products have pronounced seasonal fluctuations. To manage such items, the ABM system provides a surge planning procedure, which is widely used by managers in their daily work.

The optimal order level, delivery schedules and minimum order quantities are entered directly in the system, allowing them to be changed immediately upon receipt. new information from the supplier and immediately place an order according to the updated information.

The ABM system, in addition to its direct function - auto-order, also allows you to control the efficiency of inventory management using a reporting system. The system generates about 30 reports on various processes of inventory management: correction of orders sent by managers, optimal order size, fulfillment of orders by suppliers, goods with excessive inventory levels, lost sales, a list of TOP-goods (providing 80% of the turnover), balances of goods withdrawn from the assortment and etc.

The specialists of the client company use the report on the dynamics of stocks, both throughout the enterprise and in the context of warehouses and suppliers to evaluate the work. The graph contains information about all the main KPIs of inventory management - surplus, lost sales, stock and sales levels, as well as turnover and ROI. By the end of the year, the chain's stocks increased slightly due to the opening of a new store, as well as a preliminary increase in stock by managers on the eve of the New Year.

Weekly dynamics of inventory management indicators.

The daily report on shortages of TOP-goods is actively used, which warns of the risk of a shortage of goods even before it occurs and makes it possible to place an unscheduled order from a supplier.

Using the report on NON-movers (products that generate less than 2% of the company's profit), a decision is made to remove the product from the assortment.

In the negotiation activities, data from the supplier's reliability report are used, where its discipline for fulfilling contractual obligations is calculated.

Optimal order size, reduced lost sales and other project results

During the period from January 2016 to November 2016, the following results were achieved:

• Orders are automated, the ordering process, as well as inventory management in general, has become transparent. The optimal stock order lot is automatically determined.
• By the main indicators of inventory management:
  • The turnover decreased by 1.5 times.
  • Lost sales decreased by 39%.
  • Surplus declined by 21%.
• The assortment of stores has been optimized. Low-turnover goods were identified and removed from the assortment, the assortment was reduced by 6%. As a result, turnover indicators have improved, the level of obsolete stocks has been reduced, and frozen funds have been released.
• Optimized the model of optimal ordering of promotional goods.

We thank the project teams for their professionalism and fruitful work to achieve the set goals. Special thanks to the TOP-management of the company for an active position in implementation issues, as well as for the constant search for opportunities to improve the current indicators of inventory management.

Do you want to implement a system for calculating the optimal stock?

Contact us!

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