Units of production per year need. Wilson formula. Optimal order size: definition, model and calculation example. Tasks for independent work

If your company is a small business, then manually determining the optimal order size will seem like a simple task. However, as your business grows, you should consider investing in to manage 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 simply keeping track of stock levels. The main prerequisites and reasons for investing in an automated inventory management system have recently been confronted by a large retail network eastern region of Ukraine.

About company

A retail company in the East Region with about 20 stores. The company has its own production: confectionery shop, bakery. Has its own distribution center and wholesale base.

• General trading area– more than 6.5 thousand m 2
• The total number of active SKUs is more than 11,000
• The number of system users is more than 30
• Over 500 promotional offers daily

Optimal order size, delivery schedule, inventory levels and other considerations

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

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

Optimal order quantity (Wilson's formula, EOQ-model) is a model of the optimal order size that determines the optimal volume of ordered goods, which allows minimizing the total variable costs associated with ordering and storing inventory.

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 network orders were formed in a semi-automatic mode using the 1C 8.2 commodity accounting system using the “min-max” method, which increased labor costs and reduced the quality of orders, there were surpluses for some goods and shortages for others in the network. Delivery schedules were kept by managers in Excel, so when placing orders, managers manually took into account this information. Also, in the accounting system, there was practically no possibility of assessing excess inventories and the reasons for their occurrence.

For the effective operation of a trading company, which is a client, it is necessary to fulfill two conditions: on the one hand, to ensure profit, by not selling goods at a discount, by supplying a more expensive and faster mode of transport, and on the other hand, to increase sales, to do this, keep more inventory, sell at a discount, deliver more expensive and faster mode of transport. To satisfy both network conditions, 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 right time without having any surplus.

To optimize the operation of the network and improve financial performance, the top management decided to implement a specialized solution for inventory management.

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 engaged an 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 the solution from ABM Cloud, the algorithms of which are based on the Theory of Constraints (TOC) methodology .

The 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 the availability of goods.

Unlike the classic sales forecast replenishment model, TOC uses the concept of "stock buffer", which characterizes the necessary and sufficient stock level at each storage point for each managed unit, as well as the dynamic change of this stock depending on the stock location area.

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

• Maintain inventory levels at a set level that ensures continued availability of goods with optimal inventory in the system. This is achieved by automatically executing processes:
  1.1. Order planning
  1.2. Order formation
  1.3. Calculation of the optimal order size
  1.4. Order optimization
  1.5. Sending an order
  1.6. Periodic adjustment of required storage level
  1.7. Supported Tier Business Case
  1.8. Inventory control
• Assortment management (by identifying the items least in demand by consumers; as well as identifying custom-made assortment items that are in constant demand for entering 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 involve the purchase of a system and installation on users' computers, payment is made monthly, upon use of the system. This allows significant savings: no capital investment in the product is required, no additional costs for expensive equipment and maintenance of the system in working condition. The company gets access to the system installed on secure servers in the data center, where all calculations and processes for working with stocks and orders take place.

Project description

The project took place in 2 stages: connection of external suppliers and connection of the distribution center.

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

• Determine the optimal batch of the order
• Reduce inventory surpluses and optimize assortment;
• Improve the turnover of the enterprise;
• Automate orders;
• Optimize working time personnel by automating the processes of work 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 of the Fresh segment. Currently, the system manages 332 suppliers, about 108 thousand items of goods.

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

For each SKU, at each storage point, upon connection, 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 forecast). This mechanism is called Dynamic Buffer Managemen (DBM, Dynamic Buffer Management) and is one of the main tools in inventory management according to the TOC methodology. The optimal order level is visible on the chart.

Inventory management with a buffer

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 the data of the system, inconsistencies between the shelf layout and sales were identified and corrected. This improved inventory turnover: the shelf turnover itself was accelerated from 32 days to 20 days, and the shelf turnover data was used in negotiations with suppliers to justify marketing payments.

About 30% of the entire assortment is delivered to the shelves without storage at the DC, this is implemented in the system using the Cross-Docking functionality. This functionality allows more efficient use of the warehouse space, while the delivery procedure for the supplier is not complicated by the delivery of goods to retail outlets - that is, the system is mutually beneficial for both the supplier and the buyer. In addition, the load on the warehouse is reduced, logistics costs are reduced, and storage 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 a metric that is quite difficult to calculate, although it is easiest to identify visually - since a lost sale is a lost sale due to the lack of goods on the shelf, and which most affects the experience of the store.

Tracking the dynamics of surpluses and lost sales and the reasons for their occurrence, especially for TOP-mover (products that generate 80% or more of the company's turnover), new products, stock products, is one of key functions manager, because only by determining the cause of the problem, you can find the best solution. From the main screen, it is possible to go to the list of problem positions and focus on them.

The company is actively marketing policy, which includes promotions and sales in order to attract customers. Also, sales of some products have pronounced seasonal fluctuations. To manage such commodity 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 quantity data are specified directly in the system, which allows you to change them immediately upon receipt of new information from the supplier and immediately place an order according to the updated information.

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

The specialists of the client company use the report on the dynamics of stocks, both for the entire enterprise and in the context of warehouses and suppliers, to evaluate the work. The graph contains information about all the main key indicators Inventory management efficiencies – surplus, lost sales, stock and sales levels, as well as turnover and ROI. By the end of the year, the stocks of the network increased slightly, which is associated with the opening of a new store, as well as a preliminary increase in the stock by managers on the eve of the New Year.

Weekly dynamics of inventory management indicators.

The daily report on shortcomings 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 the supplier.

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

In negotiation activities, data from the report on the reliability of the supplier is used, where its discipline in fulfilling contractual obligations is calculated.

Optimal order size, reduction of lost sales and other project results

For 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 optimum stock order lot is automatically determined.
• According to the main indicators of inventory management:
  • Turnover decreased by 1.5 times.
  • Lost sales decreased by 39%.
  • The surplus was reduced by 21%.
• The range of stores has been optimized. Low-turnover goods were identified and withdrawn from the assortment, the assortment was reduced by 6%. As a result, turnover rates have improved, the level of obsolete stock has been reduced, and frozen cash has been released.
• The optimal order model for promotional goods has been optimized.

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 their active position in implementation issues, as well as for the constant search for opportunities to improve the current indicators of inventory management.

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Direction

All publications ABM Cloud Inventory ABM Rinkai TMS Case Study DDMRP Drogerie EDI ERP MRP Replenishment+ Retail TOC WMS Webinar Auto-order Delivery automation Procurement automation Store automation Warehouse automation Inventory management automation bonus program Safety buffer wms implementation wms system implementation Push systems Integrated automation Accounting Loyalty Assortment optimization Delivery processes optimization Warehouse optimization Production planning Loyalty platform Sales forecast Loyalty program Accounting program Surplus allocation Theory of constraints Merchandise surplus Transport logistics Buffer Management Purchasing Management Inventory Management Store Management Supply Management Production Management Management retail Warehouse management Inventory management Transportation management Efficiency of wms implementation

Larin O.N. Candidate of Technical Sciences, Associate Professor of the Department of Economics and Management in Transport, South Ural State University
[email protected]

where Q* - the optimal order size, (units);
l - intensity of consumption of products, (units / per year)
A - the cost of placing an order, (rub / order)
C - the cost of a unit of stock, (rub / unit)
I is the inventory maintenance cost ratio, (cost/year per unit of capital invested in inventory).

The Wilson formula is derived from the condition of the minimum average annual cost of fulfilling orders and keeping them in stock, which are calculated:

, (2)

where Q is the size of the order, (units).

In formula (2), the first term shows the cost of fulfilling orders for a certain period of time, the second - the cost of keeping them in stock for the same period. By optimizing expression (2), the optimal batch size of the ordered goods is determined.

The practice of applying the OCR calculation method, as well as the analysis of a number of works, testify not only to its relative practical value, but also to the existence of differences in approaches to determining the composition and procedure for calculating the corresponding costs.

Some issues of calculating the OCR are touched upon in the work. To develop and supplement the problems raised in this work, we present the following, perhaps not indisputable, remarks.

First of all, I would like to stop here. In a number of works, when describing the method of calculating the OCR, attention is not always properly focused on the fact that the OCR is not determined on the basis of the absolute value of the costs of fulfilling all orders and storing the entire stock, i.e. planned volume of deliveries, but only on the basis of the average cost for a certain period (in expression (1) on average per year). This is important for a correct understanding and application of the RCR calculation methodology and orients the reader to the need to bring costs to the same time interval if consumption intensity (l) and storage costs refer to different periods. It is also necessary to more clearly define the dimensions of the indicators used for the calculation. For example, you can recommend the work.

It seems interesting that in practice, to calculate the cost of storing a stock, it is more convenient to use not the rate of costs of maintaining stocks from the cost of goods in storage (2), but the amount of costs per unit warehouse. A similar approach will be used in this paper when calculating the cost of holding an order.

Consider what constitutes the cost of holding inventory, and what determines the amount of cost of holding a unit of stock.

Inventory costs can be divided into fixed and variable costs.

a) Fixed costs of storing and maintaining a unit of product in stock for a certain period(Z pos, rub) are determined taking into account the costs of maintaining and servicing the premises (taxes, depreciation, heating, lighting, repairs, staff salaries, etc.) for a certain period, which apply to the entire premises as a whole, regardless of the degree its current use.

The value of the fixed costs of storing the order (Q order) is calculated using the value fixed costs for the storage of a unit of stock (I pos).

To calculate the amount of fixed costs for storage and maintenance of a unit of goods in stock for a certain period, fixed costs for this period are attributed to a unit of the total volume of storage capacity (Q skl):

Rub/unit*year, (3)

where Q skl is the total volume (capacity) of the warehouse. The unit of dimension of the warehouse capacity should correspond to the unit of measure of the stored goods - m 2, m 3, tons, pieces, etc.

Then the fixed costs for the storage time of the stock will be determined:

, rub., (4)

where Q order - the amount of stock in the warehouse for the period under review, corresponds to the size of the order - ORZ, units.

Comment. When renting a warehouse, the total amount of rent for the corresponding period can be considered as fixed costs (Z pos), and the prices for renting a unit of storage capacity per year (month, etc.) can be considered as fixed costs (I pos).

b) Variable costs of servicing a unit of production for a certain period(Z lane, rub) are associated with the current costs of servicing stocks (control, accounting, etc.). For determining variable costs the value of variable costs is used, which are determined from the ratio of the variable costs of servicing the stock in a particular period to the volume of this stock.:

Rub/unit*year, (5)

where Q current - the size of the stock, in connection with the maintenance of which variable costs are formed in the period under review, units.

The amount of variable costs per unit of stock is usually constant. The amount of the current stock changes as the stock is used up. Then the variable costs of inventory maintenance for the storage period are determined from the expression:

, rub., (6)

When calculating total storage costs, fixed and variable costs are summed up:

, rub. (7)

The need to divide the total costs into fixed and variable is due to the fact that the amount of variable costs always depends on the current (average) volume of stock in the warehouse, and the amount of fixed costs may vary depending on the conditions of inventory management. For example, consider the following types of storage space use, which we conventionally denote as:

1. "Flexible" stock management.

As the stock decreases, the vacant warehouse space is used for storage of other products. This suggests that the fixed costs of holding inventory will decrease as the inventory is used up, i.e. reducing its volume in the warehouse. Then, on average, these costs will be half of the maximum level calculated for the entire order volume:

, rub., (8)

Taking into account (8), the total storage costs are determined by:

Rub. (9)

2. "Fixed" inventory management.

There is no operational redistribution of vacant warehouse space for storage of other products in the warehouse. This situation can be both when renting a warehouse, and when operating your own. Then the level of fixed costs for storing stocks remains the same regardless of the decrease in their actual volume and will be determined in accordance with (4). The total storage costs will be determined by:

, rub. (ten)

One more case should be singled out, when own warehouse is operated and due to various technological features and (or) specifications warehouse, the latter is not fully occupied, and the free part cannot be used for storage of other goods or leased. Then the fixed costs (Z pos) for storing the stock will be determined as a whole as for the entire warehouse, regardless of how much goods are in stock (Q order = Q skl):

Taking into account (11), the total storage costs will take the form:

, rub. (12)

Since, according to the condition, the calculated OCR cannot exceed the maximum volume of the warehouse or its part used for storage (Q * If the calculated OCR (Q * races) will be greater than the maximum possible volume of the warehouse (Q * races > Qmax), which, when using the entire warehouse, is determined by its total volume (Qmax \u003d Q skl), and in case of partial use - the actual volume occupied (Q ma x \u003d Q), then when planning supplies, the maximum storage volume (Q * pl \u003d Q max) should be taken as the OCR.

Taking into account the components of storage costs discussed above, in formula (2) when calculating the average cost of storing an order, one of the expressions (9), (10), (12) can be used. The choice of a specific one depends on the specific storage conditions of stocks.

The derivation of the OCR formula should be made already for the new composition of average costs.

And the last. We offer a variant of the answer to the question posed in the paper about the possibility of including the costs of its transportation in the cost of fulfilling the order.

The paper expresses the opinion that the composition of the costs associated with the order includes transport and procurement costs, including the costs of transportation, which are constant for each order and are not related to its volume, since even if the vehicle during the transportation of the next the delivery line is not fully loaded, then the payment for the use of this vehicle (wagon, container) is charged in full. Following the logic of this reasoning, only one vehicle is used to transport an order unit. At the same time, the paper does not consider the option when the calculated OCR exceeds the carrying capacity of the vehicle used and several transport units are required to transport the order, or one will need to make several turns. In this case, the amount of transportation costs will increase in proportion to the number of Vehicle or trips, and the number of orders and the cost of their implementation will remain at the same level.

This contradiction related to the inclusion of transportation costs in the cost of fulfilling orders is not the only one.

If the tariff per unit of goods is constant, then the cost of transporting the order is determined by:

, (14)

where З tr - transportation costs, rub.,
Itr - tariff for non-transportation, rub / unit.

This shows that the cost of transportation depends on the size of the transported lot. Therefore, it is hardly reasonable to take into account the costs of transportation in the calculation of the cost of an order, since the costs of an order are assumed to be constant regardless of its size, and the costs of transportation will vary from its size.

In addition, the value of the tariff for the transportation of a unit of goods may depend on the size of the order. The larger the volume ordered, the lower the transportation tariff can be, which is reduced for large consignments due to the use of economical heavy-duty rolling stock. As a result, the amount of transportation costs depends on the volume of the order in direct and inverse proportions at the same time. Which once again proves the groundlessness of including non-transportation costs in the cost of order fulfillment.

In general terms, the interest of researchers in the calculation of OCR taking into account transport costs deserves attention. This corresponds to the modern approach to optimizing the costs of performing logistics functions, in particular, the function of supplying an enterprise with various resources. Taking into account the cost of transportation, the expression for calculating the OCR can be converted into a formula for calculating the optimal size of the supply. In this case, it is advisable to take into account the above remarks. Bibliographic list

1. Headley J., Whiten T. Analysis of inventory control systems. - M.: Nauka, 1969. - 512 p.

2. Logistics: Textbook / Ed. B.A. Anikina: 2nd ed., revised. and add. - M .: INFRA-M, 2000. - 352 p.

3. Workshop on logistics: Proc. allowance / Ed. B.A. Anikina. - M.: INFRA-M, 1999. - 270 p.

4. Lukinskiy V.S., Tsvirinko I.A. Options for solving the logistic problem of determining the optimal order size. // Organization of international and domestic transportation using the principles of logistics: Sat. scientific tr. / Editorial board: V.S. Lukinsky (responsible editor) and others - St. Petersburg: SPbGIEU, 2001. - 228 p.

5. Bely B.N., Derbentsev D.A., Yukhimenko A.I. inventory management models. - Kyiv: KTEI, 1978.

6. Geronimus B.L., Tsarfin L.V. Economic and mathematical methods in planning for road transport: Textbook for students avtotransp. technical schools. - M.: Transport, 1988. - 192 p.

Condition: Within a month, the company needs 3 brands of cars to organize sales. During this period of time, determine:

a) the optimal number of purchased cars;

b) the optimal number of orders;

c) optimal variable costs for inventory storage;

d) the difference between variable costs according to the best option and the case when the purchase of the entire batch is carried out on the first day of the month.

Initial data (options are indicated in brackets):

- the need for cars during the month (pcs.) - 1) 67; 2) 37; 3) 29;

- cost of ordering a consignment of goods (rubles) - 1) 217; 2) 318; 3) 338;

- the cost of storing a unit of goods (rubles) - 1) 49; 2) 67; 3) 91.

Solution.

a) the optimal amount of purchased household appliances within a month, we calculate according to the following formula:

K o \u003d √ 2С s P / I (pcs), (1)

where Сз is the cost of ordering a consignment of goods (rubles);

P - the need for household appliances during the month (pcs.);

And - the cost of storing a unit of goods for a month (rubles).

b) the optimal number of orders for household appliances during the month is calculated by the following formula

H \u003d √ PI / 2C3. (2)

c) we calculate the optimal variable costs for storing inventory during the month using the following formula:

And o \u003d √2PIS 3. (3)

d) the difference between the variable costs for the optimal variant and the case when the purchase of the entire batch is carried out on the first day of the month, we calculate using the following formula:

P \u003d IP / 2 + C 3 - And o. (four)

4. Determination of system parameters with a fixed time interval between orders.

Condition: Annual requirement for materials is 1550 pieces, the number of working days per year is 226, the optimal order quantity is 75 pieces, the delivery time is 10 days, the possible delay in deliveries is 2 days. Determine the parameters of the inventory management system with a fixed time interval between orders.

The time interval between orders is calculated by the formula:

where I– time interval between orders, days;

N- the number of working days in the period;

OPZ– optimal order size, pcs.;

S– need, pcs.

Table 1

Calculation of the parameters of the inventory management system with a fixed time interval between orders

	Index	Meaning
	Need, pcs.
	Time interval between orders, days	see formula 1
	Delivery time, days
	Possible delay in deliveries, days
	Expected daily consumption, pieces/day	:[number of working days]
	Expected consumption during the delivery, pcs.
	Maximum consumption during delivery, pcs.
	Guaranteed stock, pcs.
	Maximum desired stock, pcs.

5. Determining the parameters of the system with a fixed order size.

Condition: The annual requirement for materials is 1550 pieces, the number of working days per year is 226, the optimal order size is 75 pieces, the delivery time is 10 days, the possible delay in deliveries is 2 days. Determine the parameters of the inventory management system with a fixed order size.

The procedure for calculating the parameters of the inventory management system with a fixed order size is presented in Table. 2.

Order Calculation Formula– in FMCG companies, the rule of forming an order for goods based on actual sales outlet for the previous period and the balance of the goods on the day of the order. It has a general look:

Order = Average daily sales in the previous period × Number of days until the next delivery - Remaining goods. At the same time, Average daily sales in the previous period = Sales volume for the previous period / Number of days in the period.

The first part of the formula determines the required order quantity based on the assumption that approximately the same amount of product is sold each day. If this were the case, then this half of the formula would be sufficient for the calculation: Order = Average Daily Sales × Number of days until the next delivery. However, in each outlet there are random and non-random fluctuations in demand, and the smaller the average daily sales volume, the more these fluctuations can be expressed as a percentage. Therefore, the formula adjusts the order quantity by feedback about the situation with the balance of goods at the point of sale: Order = Average daily sales in the previous period × Number of days until the next delivery - Remaining goods.

Thus, each time exactly the amount of goods that is needed before the next delivery is ordered, no more and no less. The client does not “freeze” his funds in excess goods, and at the same time he always has the necessary stock of goods. For example, companies supplying perishable goods work according to this version of the formula: it is simply impossible for them to create an additional stock of goods at retail outlets.

However, the uneven demand for goods can be very pronounced, with a large spread over the days of the week or months of the year. In addition, the supplier companies themselves can periodically carry out promotions to promote goods to end consumers, and this requires the creation of a safety stock of goods in retail outlets. If a company is supplying non-perishable goods, it may adopt an order calculation formula as a standard, which implies the creation of a safety stock, expressed in days or in volume of production, for example:

Order = Average Daily Sales × Number of Days Until Next Delivery + Safety Stock in Days – Stock Remaining.

In particular, in the Coca-Cola company, the standard for working with general trade outlets is to create a safety stock equal to 50% of the order volume for the period.

Companies that adhere to the push marketing strategy (pressure on the retail environment) include adjustment factors in the formula on the principle of "a little more than necessary." The most well-known variant is the so-called "Rule of 1.5", which uses a correction factor of 1.5 in the formula to constantly increase the order:

Order \u003d Average Daily Sales × Number of days until the next delivery × 1.5 - Remaining goods.

Since the balance of goods is subtracted in the formula each time, the real the increase in the volume of the order does not occur by 1.5 times, but by a number of times in the range from 1.0 to 1.5. Thus, there is a slight but constant pressure on the outlet to increase the volume of ordered goods. The increase in stocks forces the retail staff to take measures to increase sales to the end consumer: reduce the margin, increase the visibility of the product, etc. The task is to sell the idea to the client, that is, to argue the need to order just such a quantity of goods, referring to the average sales of the outlet and the "formula".

The main characteristics of current assets are liquidity, volume, structure and profitability. There are fixed and variable parts of working capital. Permanent working capital (the system part of current assets) is the necessary minimum of current assets for the implementation of production activities. Variable working capital (the variable portion of current assets) reflects the additional current assets required during peak periods.

In theory financial management allocate various strategies for financing current assets, depending on the choice of the amount of net working capital. Four models are known.

1. The ideal model assumes that current assets are equal in size to short-term liabilities, i.e. net working capital is zero. From the standpoint of liquidity, this model is the most risky, since under adverse conditions the company may be faced with the need to sell part of fixed assets to cover current debt. The basic balance equation has the form

DP = VA, (4.1)

where DP - long-term liabilities; VA - non-current assets.

2. The aggressive model means that long-term liabilities serve as sources of coverage for non-current assets and the systemic part of current assets. Net working capital is exactly equal to this minimum. The basic balance equation has the form

DP \u003d VA + MF, (4.2)

where MF is the system part of current assets.

3. The conservative model assumes that a varying portion of current assets is also covered by long-term liabilities. Net working capital is equal in size to current assets. Long-term liabilities are set at the following level:

DP \u003d VA + MF + HF, (4.3)

where VC is the varying part of current assets.

4. The compromise model assumes that non-current assets, the system part of current assets and half of the varying part of current assets are covered by long-term liabilities. Net working capital is equal in size to the sum of the system part of current assets and half of their variable part. This strategy assumes the establishment of long-term liabilities at the level given by the following basic balance equation:

Control working capital involves the analysis and decision-making on all items of current assets, including:

Analysis and management of cash (and cash equivalents);

Analysis and management of receivables;

Analysis and management production stocks etc.

aim inventory management is to find a compromise between the low cost of holding stock and the need to increase it. In the theory of inventory management, special models have been developed to determine the volume of a batch of order frequency. One of the simplest models is

(4.5)

where q is the optimal batch size in units (order size);

S is the total need for raw materials for the period in units;

Z is the cost of fulfilling one batch of an order;

H - the cost of storing a unit of raw materials.

Used in inventory management following models:

(4.6)

where RP is the inventory level at which an order is placed;

MU is the maximum daily requirement for raw materials;

MD - the maximum number of days of order fulfillment;

SS - minimum stock level;

AU - average daily need for raw materials;

AD - average number of days of order fulfillment;

MS - maximum stock level;

LU - minimum daily requirement for raw materials;

LD is the minimum number of days to complete an order.

To money optimization models developed in inventory management theory can be applied. For the purpose of cash management, their total volume is determined; the share that should be kept in the current account (in the form of securities), as well as the policy for the transformation of cash and marketable assets. In Western practice, the Baumol model and the Miller-Orr model are most widely used.

Baumol model is based on the assumption that the enterprise starts operating with the maximum level Money and then constantly consumes them. All incoming funds are invested in short-term securities. As soon as the cash reserve is depleted (reaches a given level of security), the company sells part of the securities and the cash reserve is replenished to its original value.

The amount of replenishment of funds (Q) is calculated by the formula

(4.9)

where V is the need for cash in the period;

c - expenses for converting cash into securities;

r - acceptable interest income on short-term financial investments, for example, in government securities.

The average stock of cash is Q/2, and the total number of transactions for the conversion of securities into cash (K) is equal to

Total Costs (OR) of Cash Management

The first term is direct costs, the second is the lost profit from keeping funds in the current account.

Model developed by Miller– Orrom, is based on the assumption that the balance of the account changes randomly until it reaches the upper (lower) limit. As soon as this happens, the company begins to buy (sell) enough securities in order to return the stock of funds to a normal level (point of return).

The implementation of the model is carried out in several stages:

1. The minimum amount of funds (He) is established, which it is advisable to constantly have on the current account.

2. The variation of the daily receipt of funds (v) is determined.

3. Expenses (P x) for keeping funds on a current account (usually correlated with the rate of daily income on short-term securities) and expenses (P t) for the mutual transformation of cash and securities are determined.

4. Determine the range of variation of the balance of funds (S) according to the formula

(4.12)

5. Calculate the upper limit of cash on the current account (O c), above which it is necessary to convert part of the cash into short-term securities

(4.13)

6. Determine the return point (T in) - the amount of the balance on the current account, to which it is necessary to return if the actual balance of funds goes beyond the interval (O n, O in):

(4.14)

An important element of working capital management is their substantiated rationing, through which the total need for own working capital Oh.

Working capital ratio- this is a relative value corresponding to the minimum volume of stocks of inventory items, set in days. Working capital ratio- this is the minimum required amount of funds, determined taking into account the need (the product of the amount of one-day consumption or output and the norm for the corresponding types of working capital). Consider the following standards:

1. Standard for funds in inventories calculated on the basis of their average daily consumption and the average stock rate in days

, (4.15)

where n pz is the rate of inventories, in days;

r pz - one-day consumption of inventories.

2. The standard of funds in work in progress

, (4.16)

where n np is the rate of work in progress, in days;

r np - one-day consumption of stocks for production (output at cost);

C - the cost of production;

Q is the annual volume of output;

t is the time of the production cycle, in days;

k is the cost increase factor;

T is the number of days in a year.

According to the nature of the increase in costs in the production process, all costs are divided into one-time (costs that are made at the beginning of the production cycle) and accruing. The increase in costs can occur evenly and unevenly. With an even increase in costs

where C 0 - one-time costs; C 1 - increasing costs.

With an uneven increase in costs by days of the cycle

where P is the cost of the product in work in progress;

C is the production cost.

The general formula for calculating the cost escalation factor is:

, (4.19)

where C 1 ... C n - costs by days of the production cycle;

C 0 - uniform costs;

t is the duration of the production cycle;

t 1 ... t n - time from the moment of one-time costs to the end of the production cycle;

FROM- production cost of products .

3. Working capital ratio for balances finished products is determined by the formula

, (4.20)

where S is output at production cost;

T is the number of days in the period;

n gp - the rate of working capital for finished products.

4. Working capital ratio for inventory:

, (4.21)

where TR is the turnover (revenue) for the period under review;

n tz - the rate of working capital for inventory.

Aggregate standard for the enterprise is equal to the sum of the standards for all elements of working capital and determines the total need for working capital. The required increase in working capital is determined as the difference between the total need for working capital (total standard) and working capital at the beginning of the period.

4.2. Guidelines

Task 1. Calculate the increase in working capital for the quarter, the need for working capital for work in progress, finished products, inventory. Output of products at cost - 27,000 rubles, the norm of working capital for finished products - 2 days, the norm of work in progress - 3 days. The turnover of goods at purchase prices is 9,000 rubles, the norm of commodity stocks is 2 days. Working capital at the beginning of the quarter - 1,546 rubles.

Solution.

1. Based on the data on the output of products at cost (VP) for 90 days, we determine the one-day output (rubles):

2. Determine the need for working capital for work in progress (rubles) using the formula (4.16):

3. The need for funds for finished products (rubles):

4. The need for funds for inventory (rubles):

5. Total need for funds at the end of the quarter (rubles):

6. The increase in the need for working capital of the PR (rubles) is determined as the difference between the total standard and the amount of working capital at the beginning of the period (OS beginning):

Task 2. The cost of fulfilling a batch of an order is 20 rubles, the annual need for raw materials at the enterprise is 2,000 units. Storage costs are 10% of the purchase price. Calculate the optimal order size and the required number of orders per year.

Solution.

1. Determine the cost of storing a unit of raw materials (rubles):

H = 0.1 × 20 = 2.

2. The optimal order size (unit) is found by the formula (4.9):

3. Number of orders per year (K), based on the annual need for raw materials (S) and the optimal lot size:

K \u003d S / Q \u003d 2,000 / 200 \u003d 10.

4.3. Tasks for independent work

Task 1. The non-current assets of the company amount to 60 thousand rubles, and the minimum need for sources of funds is 68 thousand rubles. Calculate various options for a working capital financing strategy, taking into account the following data (thousand rubles):

Indicators

Months

Current assets

seasonal need

Task 2. Determine the standard of working capital in work in progress, the turnover of current assets with an annual release of 10,000 units, the cost of production - 80,000 rubles. The price of the product is 25% higher than its cost, the average annual balance of working capital is 50,000 rubles, the duration of the production cycle is 5 days, the cost increase factor in work in progress is 0.5.

Task 3. The company works with 2 clients: Mr. Ivanov offers to pay for products within 1 month after purchase. Mr. Petrov receives a 10% discount thanks to the advance payment. Which option is preferable from the position of the seller, if the cost of production is 8 rubles, the price of products without a discount is 10 rubles, to produce 30,000 units, it is necessary to maintain 450,000 rubles in production.

Task 4. Determine the volume of the company's cash release in the planned year, if the amount of working capital is 100 thousand rubles. with a sales volume of 400 thousand rubles. It is planned to increase the volume of sales by 25% and reduce the duration of the turnover of funds by 10 days.

Task 5. Determine the coefficient of increase in costs if the production costs on the first day amounted to 400 thousand rubles, and in the subsequent - 234 thousand rubles.

Task 6. Production cost amounted to 200 thousand rubles. with a production cycle of 6 days. Production costs amounted to: on the first day - 54 thousand rubles, on the second day - 50 thousand rubles, and on the rest - 96 thousand rubles. daily. Determine the cost escalation factor.

Task 7. Analyze the turnover of funds through the amount of release (involvement) of funds as a result of acceleration (deceleration) of turnover for the quarter.

Indicators, thousand rubles	Period
	2006	2007
Average working capital balance

Task 8. In the first quarter, the company sold products worth 250 million rubles, the average quarterly balances of working capital amounted to 25 million rubles. In the second quarter, the volume of sales of products will increase by 10%, and the time of one turnover of working capital will be reduced by 1 day. Define:

The turnover ratio of working capital and the time of one turnover in the first quarter;

The turnover ratio of working capital and their absolute value in the second quarter;

The release of working capital as a result of a reduction in the duration of turnover.

Task 9. Determine the stock level at which to order, as well as the maximum and minimum stock levels, given an optimal order of 500 units.

Task 10. The company places an order for raw materials. Need per week: average - 75 units, maximum - 120 units. At what level of stocks it is necessary to place an order (order lead time 14 days).

Task 11. The company buys steel for production.

The cost of fulfilling an order is 5,000 rubles, the cost of storing one kilogram of steel is 2 rubles. There are 310 working days in a year. Calculate: optimal order level, stock level at which to place an order, minimum and maximum stock levels.

Task 12. The annual requirement for raw materials is 2,500 units. The price per unit of raw materials is 4 rubles. Select the inventory management option: a) lot size - 200 units, order fulfillment cost - 25 rubles, b) lot size 490 units, free delivery of the order.

Task 13. Determine the optimal order and the number of orders per year, if the annual need for raw materials is 2,000 units, the cost of storage is 5 rubles / unit, the cost of order fulfillment is 60 rubles. If the supplier refuses to supply raw materials more than 8 times a year, what amount can be paid in addition to remove these restrictions (maximum batch - 230 units)?

Task 14. The annual need for raw materials is 3 thousand units. Storage costs 6 rubles. per unit, and the cost of placing the party is 70 rubles. Determine which batch is more profitable: 100 or 300 units. Determine the optimal lot size.

Task 15. Cash expenses of the company during the year - 1.5 million rubles. The interest rate on securities is 8%, and the costs associated with their sale are 25 rubles. Determine the average amount of cash and the number of transactions for the transformation of securities into cash per year.

Task 16. The minimum cash reserve is 10 thousand rubles; expenses for the conversion of securities - 25 rubles; interest rate 11.6% per year; standard deviation per day - 2,000 rubles. Define a policy for managing funds.

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