Seasonal factors and their impact on activities. Topic: The influence of seasonality on the efficiency of inventory management in an enterprise

Management of business entities with a seasonal nature of activity pursues the goal of reducing the level of seasonal fluctuations. To achieve these goals, it is necessary to redistribute labor resources, reload production capacities, advertise, and reduce prices, which is impossible without forecasting.

In modern conditions of complex interweaving of economic relations between industries, seasonal fluctuations that arise in one industry are transmitted to others, causing corresponding fluctuations in subsequent stages of the production cycle. Seasonality in agriculture causes fluctuations in the production process in the manufacturing industry, then seasonal waves are formed in trade and consumption.

Since the industrial sphere and its environment (the market for resources, goods and services, households, the financial market, the state) are directly connected, fluctuations are observed here that can be attributed to seasonality. Seasonal changes in socio-economic processes and phenomena will be determined not only by climatic factors, but also by social, economic, and legal ones. For example, an increase in the level of unemployment in winter, an increase in average wages and per capita income at the end of the year, periodic cash flows of tax payments, contributions to various funds, and payments for services.

It seems necessary to assess the dynamics of seasonality using the example of the industry that is most susceptible to seasonal fluctuations - sugar production.

When considering the dynamics of seasonality in sugar production, it is necessary to take into account that beet sugar is mainly produced in September - November, raw sugar in March - July. This seasonal nature is associated with periods of beet ripening and purchases of imported raw sugar.

The seasonal fluctuation in sugar prices is confirmed by the graph below.

Rice. 1. Wholesale and retail prices for sugar in Russia

(January 2006 - April 2009)

The graph shows that the increase in wholesale prices occurs at the end of January - February, which is associated with the processing of beet stocks from producers and the transition of production to raw beets. So in 2006, the price increase in February, compared to the beginning of January, was 350 rubles per ton (16,848 rubles per ton), and in February 2008, compared to January, 300 rubles per ton (14,022 rubles per ton). Thus, every year there is a seasonal decrease in selling prices for sugar at the end of the year and their increase at the beginning of the year.

Rice. 2. Wholesale prices for sugar in Russia

2008 is characterized by the lowest exchange rate of the ruble against the US dollar, which led to a significant drop in wholesale prices for sugar in September - December last year, despite the fact that the cost of beet sugar from the 2008 harvest is 16.8 rubles. per kg (including VAT). Prices on the domestic market were under pressure from raw sugar inventories and traditional competition from agricultural producers in the autumn. Taken together, these factors led to lower sugar prices during this period.

Sugar reserves on the Russian market, including raw sugar, at the end of 2008 amounted to a record 2.91 million tons, compared to 2.78 million tons at the end of 2007. This is the result of record production of beet sugar in 2008/09 - 3.55 million tons (from August to February), in 2007/08 - 3.12 million tons. Even raw sugar reserves at sugar factories, according to Soyuzrossakhar, as of February 9, 2009, are 1.5 times higher and amount to 301 thousand tons compared to 197 thousand tons a year earlier.

Rice. 3. Sugar reserves in the Russian Federation at the end of the month, thousand tons.

According to Soyuzrossakhar, in the context of a shortage and rising cost of credit resources in the 3rd and 4th quarters of 2008, sugar factories were not able to attract credit resources and only provided services for toll processing of sugar beets, which, unlike the previous year, led to a change in the ownership structure of commodity sugar reserves towards their increase on the balance sheets of agricultural producers. The lack of sufficient storage capacity to store such quantities of sugar led to its massive sales.

Sugar production in Russia is becoming more seasonal every year: October beet peaks are growing, production of raw sugar is decreasing (due to difficult to predict profitability), and imports of finished sugar, primarily from Belarus, are not decreasing. In addition, sharp changes in import duties and fluctuations in the world market leave their mark. The problem of developing infrastructure around sugar factories and accelerating the increase in factory sugar storage capacity, primarily at relatively promising sugar factories with an actual capacity of more than 3,800 tons per day (there are about 31 such factories in the Russian Federation) and the development of instruments for seasonal business financing is becoming increasingly urgent.

The development of agricultural production in Russia in 2008 was carried out under the influence of a number of negative factors, in particular the rapid rise in prices for material resources used in agricultural production and construction, as well as the complicated situation with lending to agricultural producers. During the period of seasonal work, the increase in prices for mineral fertilizers amounted to 70%, electricity - 13.2%, natural gas - 11.3%, the rise in price of diesel fuel (by December 2007) - 45%, which led to significant additional costs. At the same time, prices for agricultural products in January-November 2008 increased by only 3.4%.

The situation with seasonality is somewhat different in the metallurgical industry. At the beginning of 2009, a fairly serious surge in demand for rolled metal products was recorded from consumers in the Asia-Pacific region. The increase in demand was selective and associated solely with the need of manufacturing enterprises to replenish stocks. But, nevertheless, in conditions of uncertainty, even this was enough to give the market a short-term boost of optimism and players began to raise forecasts for the industry’s prospects and put into operation production facilities frozen in the 4th quarter of 2008.

For Russian metallurgists, an additional factor that significantly affected their business was the rather sharp devaluation of the ruble. The weakening of the national currency made the products of Russian metallurgists more competitive and allowed them to partially replace the decline in domestic demand with export supplies. According to the results of the 1st quarter of 2009, the share of exports in the structure of supplies of Russian metallurgists increased to 70-80% from 40-50% at the end of 2008.

In addition, the devaluation of the ruble allowed metallurgists to increase prices on the domestic market, bringing them into line with world levels. As a result, Russia became one of the few countries where, based on the results of the first three months of 2009, an increase in steel production compared to the level of December 2008 was recorded, albeit insignificantly.

Despite the fact that the 1st quarter of 2009 was eventful and confirmed most of the new trends in metallurgy, which we wrote about in the annual strategy, it did not provide a complete understanding of the situation, and the influence of the seasonality factor traditional for metallurgy in 2009 can be characterized as quite moderate.

The factors that shape seasonality differ both in their nature and character, and in the degree of impact. They can be combined into the following groups:

1. Natural and climatic. They influence the formation of seasonal fluctuations in production, trade, and consumption.

2. Economic factors. This is primarily the volume of production, retail trade turnover, prices and, accordingly, the income of the population.

3. Social factors. These include the social structure of society, the level of culture of the population, national traditions and holidays. They have a major influence on the formation of seasonal fluctuations in demand and consumption.

4. Demographic factors: family composition and size, age, gender, population migration. Mainly influence demand and consumption.

5. Legal factors - legally established all kinds of payments to various funds, for example, tax payments, pension and insurance payments, fees for communication services.

Seasonal fluctuations that arise in the manufacturing sector are transmitted to the financial sector, where they change, as natural and climatic factors are intertwined with the actions of socio-economic and legal factors.

For example, for economic entities that produce their products unevenly, the demand for money increases in certain periods. In the spring, the need for borrowed funds from agricultural enterprises increases sharply, and in the fall the need for additional funds from processing enterprises increases, seeking to provide themselves with raw materials for the future after harvesting. Credit institutions, taking into account the economic and financial conditions in the local market, must anticipate this changing demand and satisfy it at each specific point in time. Many industry banks have been created, focused on lending to enterprises in the relevant industry.

The foreign exchange market is influenced by export-oriented industries and companies, many of which are influenced by seasonal fluctuations in their activities (automotive industry, oil and gas production, metallurgy), which in turn affects the state of the country’s balance of payments.

Contributions to many funds are also transferred periodically (pension funds, compulsory health insurance funds, State Employment Fund and others). In calculating specific amounts of tax revenues to budgets of different levels, forecasting the growth and decline of production and trade turnover, including due to seasonal factors, is of great importance. These data are important for the next formation of budgets at all levels, since they can more reliably reflect the regions’ needs for federal resources in the form of subsidies, subsidies and transfer financing. It should be taken into account that there are regions that have an agricultural or other raw materials focus. Therefore, the study of seasonality in financial processes is of great interest.

Analysis and forecasting of various socio-economic indicators are also important for the development of social and economic policy of the state.

Extensive information is used on the state and development trends of all sectors of the economy. Most of the predicted processes are, to one degree or another, influenced by seasonality (for example, monetary aggregates, bank loans to the economy, average wages, income and expenses of the population, balances of household deposits in banks, dynamics of the number of unemployed, consumer price indices and industrial wholesale prices) . Therefore, when analyzing them, it is necessary to take into account not only monotonic trends, but also periodic (seasonal) ones.

The stock markets also experience oscillatory processes with pronounced cycles: monthly, quarterly and 21-week, weekly. As the reasons causing such cycles, the authors indicate the periods and volumes of securities placement, the issuer's need for funds, the issuer's regulation of the term structure of the debt, and others. The listed cycles are caused by temporary, subjective factors and they must be taken into account when considering specific, particular tasks. Since fluctuations in the financial market are close to periodic in nature and end within a year, they are classified as seasonal fluctuations.

The aggravation of the economic situation associated with the financial crisis is forcing industrial enterprises to more actively identify and realize savings reserves in all their assets. In this regard, the analysis of the state of corporate inventories deserves close attention. Current assets in inventories at enterprises are quite significant. According to Rosstat, the share of all types of reserves in the composition of property at manufacturing enterprises is about 20%, and at machine-building enterprises - about 30%. Inventories of goods and materials as part of working capital occupy approximately 15% at manufacturing enterprises, and in mechanical engineering - about 20%. Unfortunately, in recent years, the turnover of working capital, including the turnover of inventories, has not received any significant acceleration.

The transition to a market economy eliminated the problem of shortages in supplying enterprises with material resources; enterprises were able to abandon large inventories and bulky warehouses for them. But at the same time, new problems arose related to unstable and constantly rising prices, lack of working capital and loans for them, violations of contractual obligations by partners when supplying goods and materials, unstable sales of finished products, etc. Uncertainty in the demand for manufactured products causes uncertainty in forecasting the required material resources. In this regard, accumulated inventories become a factor in coordinating real supply and demand, as well as reducing production costs.

The results of a monthly survey of managers of industrial enterprises, conducted by order of “Business Russia” on the panel of the IET market survey laboratory in April 2009, on the relative current state of enterprises, are presented in Fig. 2.4-2.6.

Rice. 4. Average prices for products of respondent enterprises in October 2008 - April 2009.

Rice. 5. Changes in inventory volumes at responding enterprises in October 2008 - April 2009.

Rice. 6. Dynamics of growth in the balances of the components of the Current State Index in October 2008 - April 2009 compared to the same period last year.

In Fig. 2.7 shows the increases in the balances of the monthly components of the Index of the current state of expectations in comparison with the same period last year, calculated to eliminate seasonality. The values ​​of component balances for April 2009 were included in the Current State Index of the Business Russia Barometer, presented in Fig. 2.8.

One of the main directions for achieving savings in the field of logistics is to reduce costs associated with inventories through the development of an inventory management policy, which is a structure of rules for determining the moment and volume of purchases. As part of the inventory management policy, supply plans are formed that establish at what points in time and for what volumes inventory should be replenished.

In 1 sq. In 2009, for the first time during the crisis, the balance of the actual number of employed people, correlated with expected demand, became sharply negative. In January 2009, only 7% of enterprises assessed their personnel as “insufficient” (in October 2008 it was 26%), and as “excessive” - 33% (from 12%). The inertia of a long period of rapid production growth, when personnel was often in short supply, is passing. The situation on the labor market is becoming quite acute, and this can have not only economic, but also social consequences.

In 1 sq. In 2009, the current state index, calculated on the basis of the increase in balances for the year, amounted to -40.9 (in the 4th quarter of 2008 it was -32.0). We have to note a rather sharp deterioration in the current situation compared to Q1. 2008. Surely it will find expression in a noticeable drop in industrial production and real GDP. A comparison with past dynamics leads to the unambiguous conclusion that such a sharp change in the situation for the worse has not occurred since 1996, that is, from the very first moment for which the quarterly index of the current state can be calculated.

On the other hand, an analysis of the monthly dynamics of individual components of the current state index shows that no further acceleration of the decline has yet been observed. This is evidenced by the relative stabilization of the balances of several components of the current state index: a) production volumes after the “collapse” in November-December 2008; b) prices for finished products after the “collapse” in December 2008 – January 2009; c) inventories of finished goods after the “collapse” in January-February 2009. Undoubtedly, the general economic decline in Russia continues (no signs of recovery are yet visible, all components of the index remain negative), but the pace of this decline is most likely not accelerating yet.

The problem of inventory management is particularly acute, due to the following reasons. Firstly, there is an exceptional variety of species of consumed goods and materials, which is associated with the complexity and multicomponent material structure of products and the presence of auxiliary industries. Secondly, the composition of consumed goods and materials often changes due to the renewal of manufactured products. Thirdly, material flows between production links are often not synchronized, which leads to a lot of intermediate inventories in production and logistics chains.

Inventory management at domestic enterprises during the years of the planned economy was based mainly on a normative approach. In this case, inventory norms were determined empirically either as a percentage of the annual volume of consumption, or as the normalized duration of one turnover by type of inventory. The regulatory approach did not produce reliable, cost-effective results and inventories were routinely overestimated.

Inventories created at various enterprises serve primarily to equalize the different intensities of interacting material flows, as well as to reduce the impact on the enterprise of random factors leading to supply disruptions. The presence of reserves implies certain costs for their formation and maintenance. For definiteness, the costs of storing inventories, as well as administrative costs for fulfilling supply orders, will be called inventory management costs, and the costs associated with the acquisition of material resources (the product of the price by the purchased volume) will be called procurement costs.

Currently, many industrial enterprises are faced with the problem of ineffective working capital management. This is especially acute in enterprises with a long production cycle, where working capital averages 80% of annual revenue. The presence of significant volumes of unclaimed inventory and overdue accounts receivable adversely affects the financial condition of enterprises and does not allow them to remain competitive. The existence of this problem is due to a number of factors.

Firstly, with the formation of a market economy in Russia, the conditions in which enterprises operate have undergone fundamental changes. Previously, there was a system of centralized planning, in which plans for the production and sale of products for enterprises were set externally on the basis of the formed balance of the national economy, and enterprises could produce products “for storage”, realizing that they would be sold. Currently, uncertainty in the relationship of an enterprise with the external environment has increased significantly: enterprises need to independently carry out planning based on predicted customer demand, which has become of paramount and determining importance, the starting point when planning production and sales. In addition, the development of competition encourages enterprises to constantly improve the efficiency of internal business processes in order to satisfy the needs of their consumers as efficiently as possible and maintain their position in the market. Thus, the approach to enterprise management is fundamentally changing, therefore, there is a need to improve the working capital management system. The tools used for this in a planned economy can no longer be used in their pure form; they must be adapted to modern conditions for the functioning of enterprises.

Secondly, the negative results of the experiments carried out in Russia in the 90s of the 20th century. reforms, expressed in a sharp drop in industrial production, significant inflation, lack of investment in fixed assets for a long time, a payment crisis and other consequences, inevitably caused a decrease in the efficiency of all main business processes of industrial enterprises. The presence of unproductive processes or their individual parts increases the duration of the enterprise’s operating cycle, as a result of which the turnover rate of funds invested in working capital decreases, the profitability of the enterprise’s assets and its liquidity decreases, and the debt position increases, i.e. all the main economic indicators of the enterprise deteriorate.

It should be recognized that by the standards of developed countries, the level of inventory management in Russia is quite low. The question of how to effectively manage inventory today, when the marginal income from the activities of enterprises is declining, access to borrowed funds is deteriorating, and competition is growing, is of paramount importance.

Traditional analytical models are based on three pillars:

– firstly, for ABC analysis,

– secondly, on the optimal order formula EOQ (economic order quantity),

– thirdly, on the assumption that all random processes can be described by a normal distribution (Gaussian distribution).

Significant progress in inventory management has been made in the last century using these models. Considering that a hundred years ago there were no modern computers and complex calculations required a lot of time, and the models considered are very simple, they are rightfully considered classic. Today, these models are suitable only for use as educational material, but in practice they are practically not used. In addition, it is quite obvious that these models do not take into account the seasonality factor at all, and therefore are not applicable for the purposes of this study.

Modern computer technology makes it possible to solve the problem of inventory management correctly and at a fundamentally higher level than before. The era of fast desktop computing has opened up new possibilities for inventory management that are still poorly understood. The objective reason for this is the immaturity of the Russian market, and the subjective reason is the insufficient mathematical literacy of the personnel of commercial enterprises.

In our opinion, it is currently impossible to develop inventory management methods without good mathematical training. In addition, experience in the warehouse and retail business is required.

The main goal of almost all modern computer inventory management systems currently in use is to automate the purchasing process based on a clearly formulated goal and on the basis of a financial and economic optimization model. Another goal of introducing a modern inventory management system is to ensure the possibility of objective control over the purchasing situation.

The basis for optimization is the financial and economic model. For each assortment item, it is necessary to obtain a number of coefficients characterizing its financial efficiency (profitability per piece, cost of storing a piece per day, cost of replenishing a piece). The main goal of the system is to optimize the profit of the enterprise. For each unit of inventory, there are control parameters that determine when (at what balance) and in what quantity an order should be placed. In other words, for each position control parameters are determined within the framework of a flexible threshold strategy.

Effective inventory management is about economic optimization, and the measure of efficiency is profit. As a rule, the efficiency of inventory management means maximizing the net profit of the enterprise to the extent that this profit depends on inventory management. In this regard, one of the components of the work to increase the efficiency of inventory management is the correct financial model of the enterprise. All current business processes in an enterprise need to be considered from the point of view of costs associated with inventory management. This includes the cost of storing inventory, the cost of replenishing it, and the costs of shortages in the form of lost profits (including additional penalties for refusal of service).

All processes in the supply chain: transport, rental of buildings and equipment, personnel costs, purchasing activities, sales organization, interest on loans, accounts payable, accounts receivable, taxes, etc. - must be adequately reflected in the financial model. A correct model should show absolutely accurately, in rubles, how much costs decrease with an increase in inventory, how much storage costs increase, costs from shortages decrease, etc.

The presented approach to solving inventory management problems is not fundamentally new. In the 60s of the twentieth century, Yu.I. Ryzhikov wrote classic works on inventory management. Attempts to put theory into practice were clearly ahead of their time. The lack of convenient and fast computing machines, as well as, more importantly, the lack of natural business motivations in a society of total scarcity, did not allow theoretical developments to be put into practice. Nowadays, there are a huge number of tools available both in price and in terms of user skill level. Applied mathematics has developed very powerful algorithms, and modern computer technology allows calculations to be carried out very quickly. All of the above is directly related to inventory management.

There is a belief that a complex problem such as optimal inventory management under seasonal conditions cannot have an adequate mathematical implementation. However, in our opinion, this is fundamentally wrong. With the advent of modern computer technology and increased market competition, the topic of inventory management has gained a “second wind.” New opportunities have emerged that make it possible to solve problems of resource efficiency at a level that until recently was considered unattainable, including in relation to taking into account the seasonal factor.

The optimal inventory management policy can be found using mathematical modeling methods. The classic single-product inventory management model (Wilson model) was developed back in 1934. The problem of inventory management in the Wilson model is reduced to determining the order volume for a planned period of time in such a way as to minimize inventory management costs. The model itself is a description of the processes of changing inventory and associated costs under certain assumptions that limit its practical application. Therefore, a number of modifications of this model are being considered, related to the possibility of shortages and taking into account the costs caused by them; with a system of discounts depending on the size of the purchase batch; with a finite speed of delivery to the warehouse, etc.

Our research to study the feasibility of practical application of inventory management models is based on data from the functional divisions of providing material resources to a group of companies in the mining industry. The main features of the industry are the wide range of purchased material resources and the instability of their consumption. This is due to the fact that most material resources are provided not by a streamlined technological process with proven standards, but by capital construction and equipment of mines. The instability of consumption is associated with the staged nature of such processes, and the stochastic nature of consumption is caused by the fact that the progress of capital construction is influenced by external organizational and natural factors.

The range of supplied material resources includes hundreds of product groups, so the task arises of classifying the supplied material resources in order to identify groups in relation to which uniform approaches to the formation of inventory management policies can be applied. In table 2.8 shows the main directions and goals of a possible classification of material resources.

Table 2.8.

Directions and purposes of classification of purchased material resources.

The study of the range of supplied material resources according to the first three classification criteria involves an analysis of the strategic importance of the product; as well as a detailed study of specific delivery conditions, such as the minimum size of the purchased lot, the deadline for fulfilling orders, the need to carry out labor-intensive operations at the stage of receiving products into the warehouse, storage conditions, etc. This is necessary to select one or another modification of the Wilson model and clarify its parameters.

The classification according to the stability of consumption and the amount of storage costs is interesting from the point of view of determining the possibility of using the Wilson model, the stability of the results obtained on its basis and the requirements for the accuracy of these results. In table Figure 2.9 presents the corresponding matrix for classifying material resources according to the stability of consumption and the amount of storage costs.

Table 2.9.

Procurement Policy Selection Matrix

The idea of ​​this classification is that as the stability of consumption (Z-Y-X group) increases, the stability of the results of applying the Wilson model increases. And as the share of commodity items in turnover and storage costs increases, interest in more accurately determining the size of the delivery lot increases, since high accuracy allows for tangible savings.

The group of material resources in cell “AX” is the most interesting from the point of view of applying the Wilson model, since it occupies a high share in turnover, is associated with high storage costs and is characterized by stable consumption. The group of material resources in the “AY” cell requires a preliminary analysis of the demand function, since it is characterized by low consumption stability. Group “Z” includes rarely purchased, usually unique, material resources. Such items are purchased on the basis of requests from the relevant divisions of the enterprise, as a rule, are not subject to storage, and the Wilson formula is not used for them. Application of the inventory management model for group “C” does not require high accuracy in determining the optimal order size. To manage the reserves of this group, approximate forecasts of annual demand are sufficient. However, constant monitoring of consumption dynamics and stock levels is necessary to reduce unmarketable inventories.

The result of the classification of material resources consumed by a group of companies is presented in Figure 2.1.

Rice. 2.1. Results of classification of product groups of material resources

Let's consider examples of using inventory management models for supplied material resources of some matrix cells. So, for example, the group of material resources of the “AH” cell includes the commodity item “Sheet Steel”, characterized by high volumes and stability of consumption.

The calculated value of the optimal delivery lot size for the item in question assumes frequent shipments. However, upon detailed study of the delivery conditions, it turned out that this was not feasible due to the technical limitations of the supplier. In this regard, the actual size of the order batch was three times higher than the optimal one, which resulted in an increase in storage costs (Fig. 2.2).

Rice. 2.2. Dependence of storage costs and ordering
from the volume of the purchase batch

In relation to the case under consideration, the use of an inventory management model along with a detailed study of delivery conditions makes it possible to discover reserves for increasing the efficiency of logistics. Thus, concluding a supply agreement with another supplier of rolled metal products will allow the company to deliver in optimal quantities and reduce costs.

In the case of unstable consumption for expensive items (cell matrix “AU”), it is advisable to study the consumption function, for example, using one of the methods of time series analysis. As an example, consider the product item “Machine oil”.

In Fig. Figure 2.3 illustrates the construction of an additive model for a time series of engine oil consumption based on annual data. For the position under consideration, it is possible to quite accurately select an additive model due to the pronounced severity of the seasonal component. Based on time series analysis, it is possible to make forecasts of consumption intensity and, in accordance with this, calculate the size of order batches.

Rice. 2.3. Analysis of the demand function for motor oil

Demand forecasting using an additive time series analysis model allows you to reduce storage costs by 2 times, compared to calculating an order batch based on the assumption of uniform consumption of material resources (as assumed by the Wilson model). The main difference between inventory management using demand function analysis and inventory management based on the classical Wilson model is that in the first case the size of the purchased batch depends on the volume of consumption, and therefore on time, and in the second it is constant. In this regard, forecasting the distribution of annual consumption over time allows us to formulate a supply plan that is close to intense. A tight supply plan is one in which, at the time of receipt of the next delivery batch, the stock in the warehouse is zero. It has been proven that only a tight plan can be an optimal supply plan.

It should be noted that when determining the optimal order quantity using the classical Wilson model, the main reason for high storage costs is the presence of a significant trend (high growth rates of consumption volumes), and not fluctuations caused by seasonality of demand. This is illustrated in Figure 2.4, which shows the results of calculating the costs of storing machine oil using various methods for determining the order quantity.

Rice. 2.4. Cumulative costs for storing machine oil for various methods for determining order batches

Analysis of the dependence of demand on time using the least squares method (OLS) makes it possible to establish a trend in consumption dynamics. Calculation of order lots based on the least squares method allows you to create a supply plan in which storage costs do not differ significantly from the supply plan formed with the analysis of seasonal fluctuations in demand.

This example shows that for expensive product items of groups “A” and “B”, an important issue is determining the annual demand and forecasting the dynamics of consumption throughout the year. In the case of inventory management for group “C” product items, the degree of forecast accuracy is not so important. This is due to the fact that even quite significant deviations of the actual annual consumption volume from the planned one lead to insignificant deviations in inventory management costs. Based on the stability analysis of the results of the Wilson model, it can be shown that a significant deviation in the annual volume of consumption leads to an insignificant deviation in storage and ordering costs. So, for example, for the commodity item “Electric lamps for general purpose”, located in the “CX” cell, a deviation from the annual consumption volume by 50% will lead to a change in inventory management costs by 16%, which is no more than 1% of similar costs for commodity item of group “A” “Sheet steel”. Thus, to manage inventories for group “C” product items, it is enough to have approximate estimates of annual consumption volumes, which can be obtained based on the experience of supply service specialists managing these items.

Another important area of ​​achieving economic efficiency in the field of inventory management of a group of companies is the unification of the needs for material resources, which allows the formation of consolidated purchasing plans that are characterized by lower costs. The main sources of benefits from consolidating needs are:

Savings on administrative costs for placing orders;

Reducing inventory storage costs;

Obtaining discounts by increasing the volume of purchases.

Assessment of cost savings due to centralized decision-making on the volumes of purchased batches and the frequency of purchases can be carried out on the basis of mathematical models of inventory management.

Within the framework of the Wilson model, it can be shown that if consumption volumes increase by a certain number of times α, the optimal order quantity, storage costs and order fulfillment costs will increase by a factor. Those. By combining the inventory management of several companies, it is possible to reduce the overall costs associated with ordering by reducing the number of supply transactions and thus reducing the administrative costs of fulfilling orders, as well as by reducing overall inventories and reducing storage costs.

In the case of centralized supply of a group of enterprises that consume a similar range of material resources, it is possible to achieve savings through the formation of a common consolidated inventory management policy. In this case, the reduction in inventory management costs can be assessed as follows. Let's consider the consolidation of purchases for one type of material resource for a group of n companies. Let Qi - annual volume of consumption of a certain type of product i- th company belonging to the group. Then the total annual demand for goods of a group of companies is determined as:

The share of the i-th company in total consumption is

According to the Wilson model, the costs of inventory management for the i-th company are the sum of the costs of fulfilling orders and storing inventory:

Where g– order fulfillment costs;

s– costs of storing a unit of stock;

qi- optimal order batch size for the i-th company, calculated using Wilson’s formula:

Using expressions (2.2) and (2.4) we obtain:

q total- optimal order batch size when consolidating the needs of group companies

Substituting the resulting expression for qi In equality (2.3) we determine the relationship between the costs of managing inventory of the i-th company and the amount of cost of managing inventory in the case of centralized supply:

Then the ratio of inventory management costs in the case of independent inventory management to costs in the case of centralized inventory management will be:

Let us illustrate the effect of cost savings using the example of calculating inventory management costs for cases of centralized and decentralized inventory management for the product item “Hardware” (Table 2.10).

Table 2.10.

Calculation of cost savings on inventory management when centralizing supply using the example of the commodity item “Hardware”

From the presented calculations (Table 2.10) it is clear that for the group of companies under consideration, the costs of inventory management with decentralized supply are almost twice as high as the same costs with centralized supply. Please note that the cost values ​​in columns (7) and (8) are close. This is not accidental and is explained by the fact that the optimal order size, at which the minimum cost is achieved, is the point of intersection of two curves characterizing the costs of storing and fulfilling orders (Figure 2.2). In this regard, the amount of savings in the costs of storing and fulfilling orders are close between themselves.

The presented model for estimating savings in inventory management costs when centralizing supply is based on the Wilson model, and therefore includes all the limitations of the classical inventory management model, and also assumes that the costs of storing a unit of inventory and order fulfillment are the same for all companies in the group. The last limitation should be given great attention if the group companies are located in different regions, differing in different levels of wages, prices for renting office space, etc.

Despite these limitations, the presented model illustrates the possibility of achieving savings by centralizing supply and suggests an approach to assessing them.

The assessment of economic benefits from centralization of supplies received from discounts for increased volumes of purchases deserves special consideration. To assess cost savings on purchased material resources, it is necessary to examine supplier proposals for each item in the product range. It is most advisable to search for profitable offers on those product items that occupy large shares in the total purchase amount. For the group of companies under study, these are material resources located in groups “A” and “B” (Fig. 2.1). This is due to the fact that, with certain volumes of annual consumption, a group of companies can become a strategic partner of a supplier who is a manufacturer of products, and not an intermediary. The condition for entering into such a partnership is, as a rule, compliance with the supplier’s requirements for minimum annual consumption volumes. The benefits of such cooperation are significant discounts and stability of supplies.

Let us illustrate the effect of obtaining economic benefits by centralizing supply using the example of calculating savings in purchasing costs for the product item “Hardware” (Table 2.11).

Table 2.11.

Calculation of procurement cost savings when centralizing supply using the example of the commodity item “Hardware”

The above calculation shows that centralization of supply, consisting of consolidating the needs of group companies for common items of purchased items and combining inventory management processes, allows obtaining economic benefits by reducing costs for inventory management and procurement.

Thus, the use of inventory management models allows you to:

– identify reserves for increasing the efficiency of activities in the field of logistics;

– achieve savings in logistics costs by optimizing the delivery batch of purchased material resources;

– along with a detailed study of the range of supplied material resources, increase the efficiency of the enterprise by reducing storage costs by releasing assets from non-liquid inventories;

– reduce costs for inventory management and procurement by centralizing the supply of the group of companies.

The conceptual model for optimizing inventories is presented in Fig. 2.5.

Rice. 2.5. Stages of inventory optimization.

1st stage. At this stage, the problem of identifying and systematizing a set of factors that can affect the required level of inventory and lead to a shortage or excess of materials is solved.

Factors affecting the level of available inventories of materials can be divided into three groups.

The 1st group of factors characterizes the influence of suppliers. This group includes: violation by the supplier of the materials delivery schedule, non-compliance of the quality of materials with the contract, non-compliance of the quantity of materials with the contract, non-compliance of the supplied materials with the nomenclature.

The 2nd group of factors characterizes the influence of buyers of the enterprise's products, expressed in changes in the amount of demand.

The 3rd group of factors characterizes the influence of the production and economic situation at the enterprise. This group includes factors such as high turnover and low training of personnel, imperfection of the resource-saving motivation system, and errors in planning the need for material resources.

The influence of the first group of factors leads to deviations in the actual delivery period from the planned one Q(Δ tP). The influence of the other two groups is expressed in a change in the need for materials compared to the planned (standard) value Q(Δ consumption(tP) ) in the period of time between two next deliveries.

2nd stage. At this stage, the problem of assessing the nature and degree of influence of factors on the level of production inventory is solved. An analysis of possible situations causing the formation of a shortage or excess of materials is carried out. A quantitative assessment of the magnitude of a possible shortage or excess of stock is carried out.

The greatest contribution to the study of deficit theory was made by Janos Kornai. In a work entitled “Scarcity,” he defines the concept of “scarcity” as follows: “the absence of the necessary resources to realize any intention” [link].

In his theory, he proceeds from the fact that a planned economy, in principle, cannot objectively reflect the needs of enterprises for various resources. The reasons for the shortage are constant errors in calculating the need for certain resources, which, according to Kornai, inevitably lead to a shortage of goods in some industries. In a market economy, the causes of shortages are not “resource restrictions”, but “restrictions caused by demand” for the enterprise’s products, as well as the mode of supply of necessary material resources and their consumption in the production process of products.

Thus, in a market economy, the concept of “deficit” has undergone a transformation, caused by changing economic conditions.

In the inventory management process, the difference between the actual amount of materials stock at the beginning of the planning period Qthem(tn) and the amount provided for by the plan ( Qnormal) may change. Difference Qthem(tn) - Qnormal < 0 characterizes the amount of material shortage δ :

δ = Qthem(tn) - Qnormal. (2.8)

There are several approaches to adapt manufacturing enterprises to conditions of shortage of material resources:

1. Reducing production volumes to a level that allows the existing level of stock of materials to be realized. In this case The volume of products produced and supplied to the market is reduced, which ultimately leads to a decrease in profits. The company suffers losses that negatively affect its financial stability.

2. Change in the cost structure (forced replacement of one type of material resource with another). If there is a shortage of one resource, the enterprise purchases another, more expensive one if the replacement resource is of better quality, or a cheaper one, but of lower quality. This inevitably entails a decrease in the quality of products.

3. Change in the structure of products.

Practice shows that determining losses due to a shortage of material resources is associated with certain difficulties, the cause of which is not only the seasonality factor, but also the randomness and unpredictability of the consequences of the influence of various factors of the external and internal environment of the enterprise on the level of inventories. However, having statistical data for past periods of time, it is possible to predict deviations from planned indicators that arise in such areas of production and economic activity of an enterprise as supply, production and sale of finished products.

Amount of expected losses WITH(δ ) due to a shortage of material resources, it is equal to:

WITH(δ ) = М[∆Т(f i)] , (2.9)

Where - average price of products sold on the market, rub.;

QG - annual volume of products produced by the enterprise, pcs.;

365 - number of days in a year;

M[∆T(f i)] - mathematical expectation of the deviation of the parameters for the supply of materials caused by the action of the factor f i (i = 1, 2, 3, 4).

To create a deficit δ In addition to the factors listed above, the influence is exerted by:

1. A high percentage of defects in the manufacture of products due to low technological discipline, outdated equipment, and low qualifications of workers.

2. Unforeseen increase in demand for the company's products.

3. Inaccurate forecast of demand for the enterprise's products.

4. Financial instability of the enterprise, which does not allow timely conclusion of contracts with suppliers for the supply of materials of the required range and quantity.

The process of loss formation due to a shortage of material resources arising under the influence of the listed factors is presented in Fig. 2.6.

Rice. 2.6. The process of generating losses associated with shortages of materials

Emergence of shortage δ entails the following negative consequences:

· downtime of production facilities;

· replacement of materials missing from stock;

· speeding up the production of products after eliminating downtime.

Each of these consequences causes losses for the enterprise. In case of production downtime and subsequent acceleration of the production process, damage is determined as the sum of the basic and additional wages of workers with deductions; when replacing raw materials, materials, components, damage is determined as the difference between the cost of actually used resources and the cost of replaced resources. The amount of damage is taken into account when determining the total losses caused by the shortage.

The influence of factors in the external and internal environment of an enterprise can lead to the formation of excess stocks of materials. In such a situation, the actual amount of materials stock is Qthem(tn) at the beginning of the planning period will be greater than the value Qnormal provided for by the plan. Difference Qthem(tn) - Qnormal > 0 characterizes the amount of excess material stock s:

s = Qthem(tn) - Qnormal. (2.10)

Occurring in conditions of excess s losses WITH(s) due to the presence of excess reserves, they are characterized as freezing of working capital in inventories.

Expected losses due to the presence of excess reserves are determined by:

WITH(s) = M[s] * r, (2.11)

Where - average price of a unit of material resource, rub.;

- average daily consumption of material resources, t/day;

M[s] – mathematical expectation of the amount of excess stock of materials;

r- interest on bank deposits, %.

When developing a short-term production plan for the next period, it is assumed that the standard level is known Qnormal stock and actual available level Qthem(tTo) stock of materials at the enterprise at the end (beginning of the next) planning period. Below the normative level Qnormal stock is understood as the planned balance of the stock of materials for the next planning period.

As a result of the influence of the above factors, the existing level Qthem(tTo) materials stock and standard level Qnormal stocks can be in one of the following relationships with each other - either Qthem(tTo)= Qnormal, or Qthem(tTo)> Qnormal, or Qthem(tTo)< Qnormal. Events ( Qthem(tTo)= Qnormal), (Qthem(tTo)> Qnormal), (Qthem(tTo)< Qnormal) are random, each of which occurs with probability P( Qthem(tTo)= Qnormal), R( Qthem(tTo)> Qnormal), R( Qthem(tTo)< Qnormal). These events form a complete group of pairwise incompatible events, and the probability of their occurrence is equal to one:

R(Qthem(tTo) = Qnormal) + P(Qthem(tTo) > Qnormal) + P(Qthem(tTo) < Qnormal) = 1. (2.12)

Possible ratios of the values ​​of the available stock level at the end of the planning period Qthem(tTo) and standard stock Qnormal are reflected in a tree-like model of the formation of possible situations of the formation of a shortage of material reserves (Fig. 2.7), and on its basis a tabular form was built to represent the variety of possible losses caused by a shortage or excess of reserves δ And s.

Events S 1 , S 2 , S 3 , S 4 , S 5 , S 6 , S 7 , S 8 , S 9 form a complete group of pairwise incompatible random events, so the equality holds P 1 + P 2 + P 3 + P 4 + P 5 + P 6 + P 7 + P 8 + P 9 =1.

Model of the formation of losses caused by fluctuations in factors of the external and internal environment of the enterprise.

Formulas for calculating the amount of shortage or excess of material resources for all nine situations are presented in table. 2.12, where ν , ν - coefficients of variation in the volume of production consumption and the supply interval exceeding the planned values; ν , ν - coefficients of variation in the volume of production consumption and the supply interval, the values ​​of which are lower than planned.

Rice. 2.7. Tree of formation of logically possible situations of shortage and excess of materials

in inventory management

Table 2.12.

Formulas for determining deficiency or excess of material

Knowing the magnitude of the shortage or excess of materials in each of nine possible situations, as well as the probability of the situation occurring, we can determine the mathematical expectation M shortage or excess of materials:

If the value M0, then there is an excess supply of materials s.

Knowing the amount of losses due to shortage or excess of materials in each of nine possible situations S 1 , S 2 , …, S 9 , as well as the likelihood of their occurrence P 1,R 2, …,R 9, we can determine the mathematical expectation of losses M[S].

Emergence of shortage δ entails the need to create a safety stock in order to minimize losses caused by a lack of material resources. The occurrence of excess s indicates the need to reduce the level of stock of materials, entailing a “freezing” of working capital invested in stocks of material resources.

Thus, the amount of the stock of material resources Qnormal at the beginning of the planning period, ensuring the continuity of the production process, will be equal to:

Qnormal = Qtech + Qpreg + Qfear, (2.13)

Where Qfear = M[δ ].

3rd stage. Optimizing the level of stock of material resources comes down to minimizing the mathematical expectation of losses caused by the influence of random factors. The optimal stock level will be the one at which the mathematical expectation of losses reaches a minimum.

4th stage. Identification of bottlenecks, the complete or partial elimination of which will reduce the size of the required reserves of material resources.

The results of the analysis of the influence of factors on the level of stock of materials make it possible to determine a set of necessary logistics transformations in the activities of various structures to improve the results of these activities.

5th stage. At this stage, the task of developing organizational measures is solved, the implementation of which will reduce the necessary reserves of material resources. The main directions for eliminating bottlenecks are presented in Table. 2.13.

The main efforts to minimize losses caused by shortages or excesses of material resources in the field of supply logistics should be aimed at solving the problem of ensuring consistency of actions between the supplier and the recipient enterprise of materials in order to comply with planned delivery conditions. At the same time, production logistics should strive to ensure the minimization of production losses, and distribution logistics should strive to increase the accuracy of forecasting demand for the enterprise’s products.

The theory of optimizing the level of stock of material resources, developing since the beginning of the 20th century, had the goal of reducing the size of the stock to a level that ensures the minimum cost of its creation and maintenance. In this case, losses due to a lack or excess of materials were not considered.

Table 2.13.

List of measures aimed at minimizing inventories of material resources

Thus, the proposed approach to inventory management is based on a methodology for optimizing inventory levels according to the criterion of minimum losses caused by a shortage or excess of materials due to seasonal fluctuations.

The economic effect of using the proposed methodology for determining the level of inventories of material resources, minimizing losses due to their shortage, is as follows:

1. Calculated on the basis of the proposed methodology, the optimal level of foundry iron stock for 2009 is significantly lower than the standard value in force at the VEMZ OJSC enterprise (Table 2.14).

Table 2.14

Comparative assessment of the level of cast iron stock for 2009

Developed methodology

VEMZ

in tons

in thousand rubles

in % of the monthly material requirement

in tons

in thousand rubles

in % of the monthly material requirement

1st quarter

2nd quarter

3rd quarter

4th quarter

Average

190,0

242,4

The standard for working capital invested in foundry iron reserves for the 1st quarter of 2009 is 33% of the monthly requirement for this type of material resource. In the 1st quarter of 2009, the standard iron stock in force at JSC VEMZ was 50% of the monthly requirement, which is significantly more than the amount of stock required to ensure the production process.

2. Formation of a stock of cast iron in the amount determined on the basis of the proposed methodology allows us to reduce the level of material balances at the beginning of the planning period by 242.4 tons -190.0 tons = 52.4 tons. Consequently, the turnover of the cast iron stock increases by 27.5%. The value of the Δ indicator TOabout equals: Δ TOabout= 242,4/190=1,275.

Since the value Δ TOabout> 1, then there is a situation where the use of the proposed methodology makes it possible to reduce the amount of working capital advanced for the formation of a stock of material resources.

3. The required amount of financial resources advanced for the formation of a stock of cast iron in accordance with the current stock standard for 2009 is 1260 thousand rubles. monthly or 15120 thousand rubles. for 2004

Savings of working capital invested in foundry cast iron reserves, the optimal value of which was determined on the basis of the developed methodology, amounts to 3264 thousand rubles. for 2009 (Table 2.15).

Table 2.15

Calculation of savings from the release of working capital,

invested in cast iron reserves in 2009

4. The level of supply of cast iron production on average for 2009 will be at least 95%. For comparison, the actually approved standards for the stock of cast iron (for 2009) significantly exceeded the required level of stock of materials. The level of production supply with cast iron in 2004 ranged from 107% to 152%, amounting to 137% at the end of the year.

Material reserves in economic systems are formed for a number of reasons. The main reasons for the formation of material reserves are the following: discrepancy between the volumes of supply and demand for material resources (intermediate and final products) in time and space; possible disruptions in the normal course of production, distribution and transportation of material resources, as well as sudden changes (fluctuations) in the amount of demand; seasonal fluctuations in production (supply), consumption (demand), as well as those determined by the conditions of transportation of material resources; speculative intentions and inflation expectations; economic factors based on savings: transportation costs, due to discounts on prices for the size of the purchased lot; costs for placing an order; as a result, minimizing production downtime, with immediate service to customers (clients), etc.

One of the reasons for stockpiling is the possibility of seasonal fluctuations in demand. The demand for a stocked product can be deterministic (in the simplest case, constant over time) or random. Demand randomness is described by either a random moment of demand or a random amount of demand at deterministic or random times. We study inventory management (IM) models with random demand volumes. Usually, if you do not have a sufficient supply of goods or raw materials for its production in the case of a company working “to order,” a situation cannot be ruled out when effective demand will not be satisfied.

In modern economic conditions in Russia, one of the main problems of a company’s financial and economic activities is the problem of rising prices. A significant increase in the cost of material resources necessary for the production process adversely affects the functioning of the enterprise, leading to supply interruptions, even stopping the production process. Thus, investing available funds in inventories is one of the possible ways to avoid a fall in the purchasing power of money.

On the other hand, a system that has managed to foresee inflationary processes in the economy creates a reserve in order to make a profit by increasing the market price.

When studying any inventory management problem, it is necessary to determine the quantity of products ordered and the timing of their placement. Demand can be satisfied by creating a one-time stock for the entire time period under consideration or by creating a stock for each time unit of this period.

Thus, decisions regarding the relative size of the order are determined from the conditions for minimizing the total costs of the inventory management system, which are expressed in the form of Figure 2.8.

Rice. 2.8. Inventory management system

Static models (tasks) of inventory management are understood as such models, all parameters of which remain unchanged throughout the entire management period or their changes can be neglected. There is a definition by other authors, for example: “If all the parameters of the model do not change over time, then it is called static, and otherwise - dynamic” .

In static inventory management problems, the planned management period is a time period in which a decision regarding the inventory level is made only once, at the beginning of this period, taking into account all previous history and does not depend on time.

The study of static models is of interest when it is necessary to establish the initial inventory level of new products, which is the starting point for solving dynamic inventory management problems. Unlike static ones, dynamic inventory management models arise in situations where the value of model parameters changes over time.

Let's assume that all the products being stocked are aggregated into one product. Some of these reserves can be used in the production process, and some of them can be used for consumption. The study of these models is of independent interest and is the source material for the study of multi-product inventory models.

The single-product KM problem consists of choosing a solution, which consists in finding such a volume of product inventory x, which minimizes the total costs, consisting of the cost of the inventory, as well as the expected storage costs and losses from shortages of stocked products, i.e.

under restrictions

xÎ X= {x: 0 ≤ x ≤ x ≤}. (2.15)

Here is the cost function f(X,ω) is given as follows:

Where cx– costs of creating a reserve; a – specific storage costs, measured in monetary units; b - unit costs due to shortages, measured in monetary units; z- selling price of a unit of goods; x – vector of guaranteed demand; - the upper level of stocked products for the period under review; φ (ω) dω- the probability that demand ω for the period under consideration is in the interval (ω, ω + dω).

Task (2.14) and (2.15) is a special case of the stochastic optimization problem.

For comparison with the algorithms proposed in the work, we present the usual - classical (or traditional) - approach to solving problem (2.14), (2.15) without restrictions. Then it is a necessary condition that x* is the optimal stock level, will

Here – derivative of the objective function F(x) V point x*,– derivative of the cost (integral) function f(x, w) at the optimal stock level x* and demand w.

According to (2.16)

Fx(x)= With+ a R(w ≤ x)- (b+z)(1- P(w ≤ x}) =

= With+ (a + b+z) P(w ≤ x) – (b+z) = 0,

because - distribution function w, then

Therefore, the optimal stock level, which corresponds to the minimum of the objective function F(x), is determined using the inverse of function (2.17), i.e. .

If we take into account the constraint (2.15), then the solution is usually found as follows: if, then we accept; if, accept; if, then X* is the true solution to the optimal inventory level.

Thus, we determined the volume of investment I into material and technical reserves according to the formula:

I = P c · X*, (2.18)

Where P c– market value of a unit of stocked products, X*- optimal stock level.

When solving problems (2.14) and (2.15) using the classical method, a number of difficulties usually arise, consisting of the following: it is not always possible to determine the functions (law) of demand distribution, i.e. solving equation (2.16) becomes difficult.

These features limit the use of the classical approach, therefore it is necessary to create special methods focused on solving KM problems of the form (2.14) and (2.15), which are solved using available information about observations (realizations) of demand values ​​w and the value of the cost function f(x,w) for fixed demand w and stock level X.

Algorithm 1. Let the approximation be obtained at the sth iteration x s , s= 0, 1, ..., to the optimal stock level X*(x 0 – the initial approximation can be chosen arbitrarily equal to 0). Then:

1. In accordance with the initial data on specific demand values, we obtain observation w s over the implementation of the random variable w at the sth iteration. Note that a demand simulation model can be used for this.

2. Construct the vector of the stochastic gradient of the function Fx(x), defined by (2.14):

where is the stochastic gradient of the function f(x, w) by X at the point (xs, w s), is defined as follows:

Here x 0 = 0; ρ s is the step size in the direction of gradient descent at the sth iteration.

These conditions are necessary for the convergence of the sequence ( xs), obtained according to (2.20) to solve the problem X* probability 1.

The algorithms do not change with changes in the demand distribution law w; explicit knowledge of these laws is not required. The latter means that the algorithm is applicable to solving more complex problems in which demand is specified using a simulation model. This algorithm can be easily implemented on a computer.

Unlike single-product tasks, the company organizes inventory m types of products. The task is to find such a volume of stock x= (x 1 , ..., x m), which minimizes expected costs, i.e.

under restrictions

Here is the cost function f i (x i ,ω i), related to the stock volume x i and demand ω i, can be represented in the following form:

Where with i – costs associated with creating a stock of a unit of goods i-th type (including costs of order fulfillment); α – unit costs associated with storing excess inventory i th products per unit of time; β i– unit costs associated with losses from shortages i th products per unit of time; z i – selling price i-th type of product; And - respectively, lower and upper limit volumes of stocked products i-th type.

In particular, when F(x) has continuous derivatives, its minimum without taking into account restrictions (2.22) is made by a classical method similar to (2.17), the required solution is x i *, i= 1,...,m is found from the equation, i= 1,2 …, m, where Ф i(x i) = P{ω i < x i} - distribution function ωi.

If the distribution function is known, then.

In the case when the function Ф is unknown i(Xi), the application of the stochastic gradient method is reduced to analytical algorithm 2.14.

Algorithm 2. Let the approximation be obtained at the sth iteration , s= 0, 1, ..., to the optimal stock level ( – the initial approximation can be chosen arbitrarily, for example, equal to 0). Then:

1. In accordance with the initial data on demand values, we obtain an observation of the implementation of the random variable w at the sth iteration. Note that a demand simulation model can be used for this.

2. Let's construct a stochastic gradient vector, where is the stochastic gradient of the function f i (x i , w i) at a point - is defined as follows:

3. We determine the new approximation according to the recurrent rule:

For the sequence () to converge to the solution of the problem, similar conditions given in Algorithm 1 are sufficient.

The solution to the KM problem with adjustment decisions is that the initially made (based on available statistical data on demand) decision on the volume of stocked products in conditions of inaccurate information and demand is subsequently clarified and adjusted as more and more accurate information about them is received. The general scheme for solving the management problem with correction is as follows: decision (accepting the initial stock level) - observation (implementation of demand) - decision (determining the optimal correction of the stock level). Here, the main goal of inventory management problems with correction is to select a stock level that minimizes the expected costs of its implementation and correction. KM problems with adjustment decisions have adaptive properties when making an optimal decision regarding inventory levels.

Adjusting the inventory level is not a consequence of shortcomings in the company's functioning; it is organically inherent in inventory management in probabilistic conditions.

In the problem of inventory management, taking into account possible transportation, taking into account the correction in which it is necessary to minimize the expected costs of surplus, transportation of products and expected losses from shortages, i.e.

At x i≥ 0, i= 1, ... , m. (2.26)

Here f(x, w) is a random variable, the optimal value of the objective function of a stochastic transport problem is determined as follows: the minimum of the function:

To variables y ij , r i, And h i the following are subject to restrictions

; ; y ij ≥0 , h j ≥ 0, i=1, … , m; . j=1, … , n. (2.28)

Problem (2.26) – (2.27) is a US problem with correction, where (2.26) is correctional; (2.28) - correctional.

In the indicated tasks, there are respectively two stages of decision-making: the first is making a decision on the initial stock level; the second is the redistribution of inventories between markets after the magnitude of demand becomes known.

To solve the problem (2.26) - (2.28), algorithm 2.16 is proposed.

When considering and analyzing the practical application of the KM problem with correction, a conclusion is drawn about which variables will be in the task of determining the initial inventory level, and which are in the correction task.

Dynamic KM problems arise when the values ​​of model parameters change during the control interval. Such changes can occur continuously, at every moment in time, and then a dynamic model with continuous time is considered, or at the moments of transition from one subinterval (period) of control to another - then a dynamic model with discrete time is considered.

It should be noted that for a number of reasons (lower information complexity, simpler mathematical modeling apparatus, discrete nature of obtaining information and changing control actions, etc.), dynamic models with discrete time are most often found. To solve these problems, methods based on the ideas of dynamic programming and queuing theory were proposed. The success of applying these methods to inventory management problems is ineffective, since these methods impose very stringent requirements on the dimension of problems and on the laws of distribution of random variables.

Dynamic KM models, in which the management period is subject to fragmentation, and the product remaining at the end of the previous time period can be used to satisfy demand in the next time period, i.e. control actions are functions of time.

Changes in model parameters over time cannot always be neglected. This can be done, for example, in the case of a relatively short control interval or in the case of a stationary control process.

Deterministic and stochastic problems of dynamic inventory management were considered in the works of domestic and foreign scientists. To solve these problems, methods based on the ideas of dynamic programming and queuing theory were proposed. The success of applying these methods to inventory management problems is ineffective, since these methods impose very stringent requirements on the dimension of problems and on the laws of distribution of random variables.

Let's consider t interval, which is divided into N period. During these periods the company must meet random demand w t for some homogeneous product x t V t-th period. The demand distribution function or its implementation is considered known. Demand w t is satisfied in full or in part - to the extent that the available stock allows this to be done. If demand w t is not fully satisfied, then the amount of unsatisfied demand y t determined by the formula

Let us assume that the amount of previously unsatisfied demand att not taken into account in ( t+ 1)th period. In this case, the company suffers losses directly proportional to the amount of unsatisfied demand ω t. The inventory management strategy is to check whether the stock level has reached the lower control (critical) level, i.e. whether the condition is met x t≤ . If this is the case, and the previously sent application to increase the volume of stock is satisfied, then a new application is submitted to increase the volume of stocked products. The volume of simultaneous increase in stock is fixed and equal to the upper control level , > . In this case, the volume of stocked products is checked only at discrete points in time at regular intervals, for example, coinciding with the beginning of each period. The delivery time for a new batch of products ordered is l, l< N .

The mathematical formulation of the problem is to find such optimal parameters , , which minimize the company's expected costs F(, ) = Mf(, , w) provided 0≤ ≤ .

Here f(, , w) – cost function, expresses the total costs associated with the operation of the company, and is determined as follows:

Here: ; ; respectively, are the costs of creation, the costs of storing excess and losses from shortages of stocked products.

Figure 2.9 shows a block diagram of the functioning of the simulation model of the inventory management problem under consideration.

Rice. 2.9. Flowchart for calculating expected total costs

As a result of (playing) the experiment, at the output we obtain the numerical value of the function (2.30). The corresponding simulation cycle is outlined behind the dashed rectangle.

The algorithm for solving the problem is not fundamentally different from the previous ones.

Consideration of the conceptual formulation of another practical KM task is as follows. Planning of united air squads in the hierarchical MTS systems is carried out annually for a certain period before the end of the current year. Based on the balance of this material expected at the end of the year, an annual request is made (resource requirement) P:

P = PP + (NC + NW – ABOUT), (2.31)

where PP is the production reserve to meet the demand of the assigned aircraft and helicopter fleet; ABOUT - remainder; NZ- minimum reserve intended to meet the demand of scheduled aircraft of other state airline administrations (GUAP); NW- safety stock designed to compensate for supply disruptions.

Since deliveries are provided quarterly, the inventory level is determined for each quarter (except NW, which is carryover) and the annual application is obtained by summing quarterly inventories taking into account balances according to formula (2.31), which is insufficient.

In fact, the levels of reserves of each type, and accordingly the need for resources, are determined by the demand for property for the planned period (year). The complexity and responsibility of planning in a hierarchical multi-element supply system with random demand is aggravated by the need to take into account large losses from downtime of the aircraft and helicopter fleet in the event of a shortage of aviation equipment and significant costs for storing and maintaining surplus stock in normal condition in the event of an excess of aviation equipment.

For it, in addition to the introduced notations, the following notations are introduced: x i, - initial stock level for i-th warehouse; wj, - random variables characterizing the demand for spare parts j th aviation technical base (ATB); y ij- volume of supplies of spare parts from i th warehouse at j th base; c ij- unit costs for transportation of spare parts from i th warehouse at j th base; α i- unit costs for storing spare parts i-th warehouse; β j- specific losses caused by shortage of spare parts at j th base. It is assumed that β j ≥ max c ij, where the maximum is calculated for those storage points i, transportation from which to the point of consumption j are acceptable.

The objective is to select an initial inventory level that minimizes the expected total costs associated with storing, stocking out, and transporting spare parts.

The main characteristics of the commodity flow as an object of trade logistics is its quantity, which is determined by: the volume and mode of consumption of the user and the capacity of the manufacturer; reseller bandwidth; the nature of the production process of the supplier-manufacturer; efficiency of transport and communications; financial capabilities of trading entities, their ability to supply products in a timely and complete manner.

The object of the development is a trading company (or a trading investment company) that sells building materials. The company has a conglomerate - a chain of stores. These stores sell building materials. There is a general warehouse where materials are supplied for temporary storage, and stores where they are sold at retail. At the same time, goods are sold wholesale from the warehouse.

When solving problem (2.14), (2.15), calculations were carried out for the following values ​​of its parameters: the cost of 1 m 3 of sawn timber at the time of delivery to the warehouse (including order fulfillment costs) is With= 153 USD; storage costs for 1 m 3 of boards α = 3 USD per year; losses from a shortage of 1 m 3 of boards β = 44 USD; demand ω – uniformly distributed over the interval, i.e. according to the classical approach, the optimal stock level will be x*= 3226.2 m 3. At the same time, the volume of investment is

I = 153 ·3226.2 = 493608.6 c.u.

The calculations performed show that the size of the optimal delivery lot for the purpose of creating inventories significantly depends on the costs of storage costs and the realized price. So, if the organization of supply and storage of one car of timber material, according to our calculations, amounts to 9180 USD, then the cost of storing 60 m 3 of timber for a year is determined in the amount of 60 m 3 x 3 USD. = 180 USD

The result using Algorithm 1 is shown in Table 2 and Figure 6.

As can be seen from the third row of Table 2, the value of expected costs coincides with its value found by the classical method, and the stock level x*= 3229,137m 3 does not match. This picture naturally arises due to the inaccuracy of a priori information regarding random demand. When carrying out calculations, there is no need to obtain high accuracy solutions.

Calculations were carried out for the following values ​​of model parameters: ω i– random variables uniformly distributed over the interval [ l i, qi], i= 1,...,5. Vectors l = (l l, ..., l 5), q= (q 1 , ..., q 5), a= (α 1, ..., α 5); β = (β 1, ..., β 5), given in the form l= (9700, 9500, 7000, 6600, 4850), q= (10000, 10000, 7500, 6800, 5000),

Table 2.

Calculation of the optimal level of lumber stock when storage costs change and the selling price remains unchanged

(z = 244 cu)

α = (5, 5, 5, 5, 5),

β = (50, 45, 45, 30, 39),

с=(210, 200, 190, 185, 157),

z=(260, 245, 235, 215, 196).

Rice. 2.10. Graph of the inventory level optimization process every 10 iterations

Demand ω – uniformly distributed over the interval [ l i, qi].

x* = (9780,7972; 9644,3672; 7168,0885; 6655,7884; 4880,9800),

F(X*) = 8949085,51.

As a result of the study of Algorithm 2, the optimal stock level was obtained.

Based on the conducted scientific research, the following conclusions and proposals can be made:

1. A comprehensive study of theoretical, methodological and practical problems of the formation and use of inventory, optimization of their size in modern conditions showed that, in general, the introduction of stochastic models and methods of inventory management has a certain economic effect, their widespread use in wholesale trade will reveal hidden internal company reserves and increase the level of efficiency of their activities.

2. As a result of the study, it was established that companies receive profits that are clearly insufficient for normal functioning in market economic conditions, there is a low turnover of funds invested in inventory and a high level of distribution costs. The reason for this is partly that decisions regarding the regulation of inventory in trading and investment companies are mainly made intuitively, without taking into account special economic calculations. As a result, even minor mistakes become big mistakes that cost the company dearly. Therefore, the use of mathematical methods in inventory management creates the prerequisites for making scientifically based decisions.

3. Based on the developed complex economic and mathematical models of inventory management, it was revealed that the size of the optimal delivery lot for the purpose of creating inventories depends on the costs of formation, maintenance, price of goods, income levels, seasonality and competitiveness factors.

4. A systematic analysis of the prerequisites for the practical use of a system of inventory management models was carried out, the proposed methods of which may well be used in practice, in particular, in wholesale trade companies. In market conditions, the latter have the opportunity to independently make decisions regarding the timing and size of the order of goods, independently establish economic relations with suppliers,, if necessary, attract additional working capital, and also independently set the selling price of goods.

5. The level of the main economic indicators of the activities of higher levels of management of the company is determined by a system of generalized indicators. However, the analysis methods used in practice do not fully meet modern requirements. In this regard, stochastic optimization methods are promising, in particular, the two-stage stochastic programming problem of a special structure.

6. The results of the scientific research were the development of a methodology for constructing a set of economic and mathematical models for optimizing inventory management, aimed at increasing the level of efficient use of material and labor resources. The introduction of this method through the implementation of optimization models allows you to increase profits and improve the economic efficiency of the enterprise.

“The list of seasonal industries, work in whose organizations during the full season when calculating the insurance period is taken into account in such a way that its duration in the corresponding calendar year is a full year,” approved. Decree of the Government of the Russian Federation on July 4, 2002 No. 498.

Sudakevich S. A., Features of planning and accounting at enterprises of the canning industry in new working conditions, M., 1970.

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Seasonal analysis has long been a closed area of ​​professional traders, but over the past decade it has become widespread among individual traders and investors. Good information about seasonal trading is still difficult to come by, which in itself is not bad, since there is still a niche that can be effectively exploited.

Determination of seasonality

Seasonality refers to patterns that depend on the time of year. The seasonal factor, as such, manifests itself in many areas of business. For example, sales of Christmas cards quite logically peak before Christmas. Accounting services reach their peak at the end of the financial year. The peak sales of red roses occur on the eve of February 14th. Many businesses, products and statistics are subject to seasonal changes. For a prepared trader, this could mean a good trading opportunity.

What drives seasonal patterns

The answer to this question is the same as for price - supply and demand. Consider the demand for beef. In any economy, demand is greatest when the weather is coolest. This is quite logical, since people eat more hot dishes in winter than in summer. While demand for beef is high during barbecue season, it tends to be less than demand for a good home-cooked meal.

On the supply side, in turn, the weight gain of live cattle during the winter is quite low. Thus, during winter, demand is high and supply remains tight. This leads to seasonal price variations. If you choose the right time to enter the market, you can make good money from this.

Another example of seasonality in a commodity market is coffee. Coffee consumption is much higher in the northern than in the southern hemisphere, and more active in winter than in summer. Thus, after March, consumption begins to decline. Additionally, harvest in the southern hemisphere usually begins in June. Accordingly, producers tend to liquidate inventories by this time, making delivery on May futures (beginning April 20) less desirable. This creates a good opportunity to trade short.

Fundamental or technical basis of seasonal trading

For many traders, it is important to know whether they are following technical or fundamental factors. Let's take a look at the definition of each factor group and how it relates to seasonal trading:

Technical analysis- study of price trends and patterns. Often this refers to graphical analysis, although to be precise, graphical analysis is a subfield of technical analysis.

Fundamental Analysis associated with the analysis of the dynamics of supply and demand, rather than price charts.

So, what is seasonal analysis? There are two ways to look at it. On one hand, you can say that seasonal analysis is fundamental in nature because it evaluates the change in supply and demand at any time of the year. In the examples given, we looked at seasonality from the point of view of fundamental factors. The examples looked at crop and production cycles, weather and consumer demand - these are, of course, fundamental factors that analyze supply and demand.

You can also look at seasonal trading from a technical perspective because it is an analysis of price patterns in the market. These price patterns can be repeated and represent trading opportunities accordingly. Identifying repeating patterns is the basis of technical analysis, so we can consider seasonal analysis as a type of technical analysis.

Keep in mind that there is no right or wrong approach to this matter. All traders have their own preferences and may have their own individual understanding of hay trading. However, there are some pretty important things to consider.

Find a good information source. Unless you are a quantitative analyst, you need to get seasonal data from somewhere. Do not use seasonal data to trade futures directly. Consider trading spreads, where signals tend to be more reliable. Find a good broker who will give you the ability to place spread orders efficiently. Do not use seasonal data in isolation. This is what fails many traders. Seasonal data is only part of the overall market equation. Take a systematic approach. Having the right information and following a plan is the best course of action. Don't chase seasonal deals at all costs. It is much more important to get the right information and place trades accordingly.

Even if you don't trade commodities, given the close interconnectedness of financial markets, incorporating seasonality analysis can be very helpful in finding profitable trading opportunities in other markets as well.

A special place among the factors influencing the development of tourism is occupied by seasonality, which acts as the most important specific problem.

Seasonality is the property of tourist flows to concentrate in certain places over a short period of time. From an economic point of view, it represents repeated fluctuations in demand with alternating peaks and troughs. In countries of the Northern Hemisphere with a temperate climate, the main (“high”) seasons are summer (July-August) and winter (January-March). In addition, there are off-season (April-June, September) and “low season” (October-December), during which tourist flows die out and demand is reduced to a minimum.

Features of the seasonality of demand in tourism are as follows: it varies significantly by type of tourism. Thus, educational tourism is characterized by less significant seasonal fluctuations than recreational tourism. Lower seasonal unevenness of demand is also typical for medical and business tourism; Different tourist regions have specific forms of seasonal unevenness in demand. Therefore, we can talk about the specifics of tourist demand in a certain locality, region, country, and on a global scale.

Thus, according to statistics, in Europe the two summer months account for up to half of all tourist trips. In countries where annual fluctuations in temperature and other climate elements are insignificant, the seasonality of tourism is less pronounced (for example, Morocco has a year-round tourist season); Seasonality in tourism is determined mainly by factors such as climatic, social and psychological influences.

The seasonality of demand is also influenced by psychological factors (traditions, imitation, fashion). The peaks and valleys of tourist activity can largely be explained by the conservatism of the majority of tourists, i.e. the deep-rooted opinion that summer is the most favorable time for vacations.

Seasonal fluctuations in tourist demand have a negative impact on the national economy. They lead to forced downtime of the material and technical base and give rise to social problems. The fact that most enterprises in the tourism industry and its personnel are used only for a few months a year is the reason for the increase in the share of semi-fixed costs in the cost of tourism services. This reduces the possibility of implementing a flexible pricing policy, complicates the actions of tourism enterprises in the market and reduces their competitiveness.

The negative consequences of seasonal unevenness in demand require studying this phenomenon and taking organizational, economic and social measures to smooth out seasonal peaks and recessions in tourism. For this purpose, tourism organizations and enterprises practice seasonal price differentiation (increased prices in the high season, moderate prices in the off-season and lower prices in the “low season”; the difference in hotel rates depending on the season can reach 50 percent), incentives development of types of tourism that are not subject to seasonal fluctuations (for example, business, congress, etc.).

Smoothing out seasonality in tourism has a great economic effect, allowing you to increase the service life of the material and technical base, increase the degree of use of personnel throughout the year, and increase tourism receipts.

Accommodation and catering establishments occupy a special place in the tourism industry. The attractiveness of the region for tourists largely depends on the level of hotel and restaurant service. But the tourism industry, especially accommodation and catering enterprises, is subject to fluctuations in demand for tourist services throughout the year (seasonality), which leads to an increase in the costs of maintaining accommodation and catering enterprises and an increase in the cost of their services.

tourism natural geographical economic

A special place among the factors influencing the development of an organization’s activities in the service sector is occupied by the seasonality factor. Depending on the season, the volume of services may vary greatly. Organizations and institutions are taking a number of measures aimed at reducing seasonal downturns, for example, introducing seasonal price differentiation (the difference in tariffs can reach 50%).

Seasonality refers to changes in time series that have an intra-annual cyclicity, depending on the calendar period of the year, natural phenomena, holidays, etc. For example, sales of fur factory products will increase in October, reach a maximum in November, decrease by March, and then remain at a very low level until September - October. As an example, it is interesting to compare seasonal changes in the price level in Russia and Western European countries. In Russia, the price level on holidays (for example, Christmas, New Year, May 9, September 1, etc.) increases noticeably. Whereas in Western Europe, as a rule, sales are held on pre-holiday days, i.e. For the most part, prices are falling.

Phenomena subject to seasonal changes must be examined for the presence of an underlying development trend. To do this, it is necessary to distribute the volume of change in the phenomenon between the seasonal component and the main trend.

The study and measurement of seasonality is carried out using a special indicator - the seasonality index.

Seasonality indices show how many times the actual level of a series at a moment or time interval t is greater than the average level, or the level calculated by the trend equation f(t). When analyzing seasonality, time series levels show the development of a phenomenon over months (quarters) of one or several years. For each month (quarter), a generalized seasonality index is obtained as the arithmetic mean of the indexes of the same name for each year.

Methods for determining seasonality indices depend on the presence or absence of an underlying trend.

Studying seasonality allows you to:

determine the degree of influence of natural and climatic conditions on the formation of demand for services;

set the duration of seasonal fluctuations;

reveal the factors that determine seasonality;

determine the economic consequences of seasonality at the regional level;

develop a set of measures to reduce seasonal unevenness in service.

Seasonality in the service sector is determined by a number of factors:

natural-climatic - quantity and quality of specific benefits;

economic - the structure of consumption of goods and services, the formation of the solvency of demand through supply;

social – availability of free time;

demographic – differentiated demand by gender, age and other characteristics;

psychological – traditions, fashion, imitation;

logistical;

technological – an integrated approach to providing quality services.

On the one hand, the seasonality factor gives rise to an uneven distribution of working time (overtime during periods of growing demand for services and insufficient workload of workers in the off-season) and, as a consequence, a significant proportion of underemployed workers and staff turnover.

On the other hand, seasonality stimulates the multidisciplinary nature of jobs, when the same worker performs different functions depending on seasonal conditions.

In addition, seasonal work is beneficial for many categories of the population as a source of additional income.

In the process of analyzing and planning the volume of sold services to an organization subject to seasonality, it is necessary to take into account the pattern of deviations of individual month indicators from the annual average.

These calculations are made on the basis of seasonality coefficients, which are calculated as a percentage of average monthly levels for a number of years to the average monthly volume of services sold for the entire billing period using the formula:

Where: - seasonality coefficient, %;

- average level of volume of services sold for a particular month, rub.;

- average monthly volume of services sold for the billing period, rub. .

Activities related to the production and (or) sale of goods, works or services of a seasonal nature are in themselves entrepreneurial in nature and have all the features that characterize entrepreneurial activity:

1. A special type of economic activity. A constant desire for innovation, the search for unconventional solutions and opportunities, expanding the scale and scope of activity and a constant willingness to take risks and find ways to overcome them. All this can be fully attributed to enterprises with a seasonal nature of activity, which is due to the peculiarities of their functioning.

An entrepreneur who has chosen this field of activity is, to a certain extent, prepared for the risk of losing part of the profit during the off-season, and, which is quite natural, is constantly trying to find ways to reduce it. At the same time, increased competition during the seasonal boom forces it to find new, different from existing, solutions that will allow it to capture a large part of effective demand.

2. Independence. As in any other case, the owners of an enterprise with a seasonal nature of activity make their own decisions, as well as the means for their implementation, relying on existing resources. Management decision-making may be limited by legal frameworks or natural processes.

3. Subjects of relations. The presence of all subjects of market relations (the entrepreneur himself, consumers, competitors, the state and other market counterparties) in this field of activity is not subject to any doubt. However, depending on various circumstances, the entrepreneur’s special attention, unlike other areas of activity, may be paid to the state, as a market entity interested in maintaining the enterprise during an unfavorable period of time caused by seasonality.

4. Optimal use of resources. The desire for optimal use of existing resources is typical for any enterprise, since this allows one to gain additional competitive advantages and, as a result, improve the financial and economic position of the enterprise.

For businesses with a seasonal nature of activity, this is especially true due to the seasonal decline in sales. Optimal use of resources (mainly cost reduction) allows the enterprise to more easily survive the seasonal downturn. In this regard, the entrepreneur is constantly looking for ways to better use capital and other resources, which is typical for entrepreneurial activity.

5. Responsibility for performance results. The efficiency of business structures with seasonal sales depends on their ability to respond quickly enough and with the minimum necessary costs to the influence of external factors, i.e. be flexible in a competitive environment.

Analysis of the external environment, the main factor of which is seasonality, assessment of internal resources and capabilities of business structures is the basis for the flexibility of their behavior.

The ineffectiveness of the system for responding to the influence of seasonal factors leads to a decrease in the level of profitability, reliability and the threshold of commercial safety of business structures.

The functioning of the tourism market and related tourism industry enterprises is subject to sharp seasonal fluctuations in demand for the tourism product.

Seasonality is understood as a stable pattern of intra-annual dynamics of a particular phenomenon, which manifests itself in intra-annual increases or decreases in the levels of a particular indicator over a number of years.

The production and service process of tourism has a pronounced dependence on seasonal fluctuations.

Studying seasonality in tourism allows you to:

determine the degree of influence of natural and climatic conditions on the formation of tourist flows;

set the duration of the tourist season;

reveal the factors that determine seasonality in tourism;

determine the economic consequences of seasonality at the level of the region and the tourism company;

develop a set of measures to reduce seasonal unevenness in serving tourists.

Seasonality in tourism is characterized by the following features:

the period of maximum intensity of tourist flow is called the main tourist season;

a tourist region, a travel company, depending on the development of the type of tourism, may have one or several tourist seasons;

tourism-developed countries, regions, centers, and companies have a longer main tourist season, and the intensity of the tourist flow does not have pronounced seasonal unevenness, that is, significant seasonal fluctuations are characteristic of a low level of development of the tourist offer;

Seasonal fluctuations in tourism are different for individual types of tourism over time.

All of the above factors of seasonal fluctuations can be divided into primary and secondary. Primary factors include factors formed under the influence of natural and climatic conditions; to secondary - all the rest.

Consequently, there is a real possibility of influencing the seasonal unevenness of demand in tourism. The seasonality of tourism leads to the seasonal nature of employment of tourism industry workers. This has its positive and negative sides.