Let's look at some of these models.

1. Model of economically justified demand for reserves (EOQ). The EOQ mathematical model determines the optimal amount of inventory based on the goal of minimizing the cost of acquiring and storing them while meeting the predicted demand for these goods. These costs vary depending on the quantity ordered, as shown in Figure 3.

Fig.3. Cost variation

Other characteristics of the model are as follows:

The demand for goods per unit of time is definitely known;

Stocks are depleted at a linear rate.

Procurement and loading costs material assets warehouses remain constant, and there are no discounts for purchases in large volumes;

Terms of realization of the order are known in advance and equal to zero;

Deficiencies are unacceptable;

Replenishment of stocks is carried out instantly.

With these parameters, the optimal order lot, based on the criterion of minimizing total costs, is determined by the equation:

D - annual demand for the product for which stocks are formed (tn);

C 0 - the cost of placing an order (rubles); with more complex interpretations of the model, this also includes the preparation of materials for production, tooling, quality control;

C h is the total annual cost of storing a unit of goods for the period (rubles). These costs include transportation and warehousing costs, insurance, losses from theft and damage, opportunity costs from investment in inventory;

Q opt - the optimal lot of the order (tn).

2. Material requirements planning (MRP) model - is a computer information system, designed to process orders and schedule the formation of stocks, depending on the demand for the company's products. MRP is designed to answer three questions: what, how much, and when. The main components of the model are, firstly, the inventory invoice, which specifies what will be required to produce the final product. The waybill is generated from a computer simulation of each product that describes its material structure, inventory status, and manufacturing process. Secondly, this is the main schedule, which shows how much the company will need to deliver end products and when. Thirdly, it is a database (in paper form - an accounting file) of inventory items, which records how much inventory is available and how much is ordered.

All this information is processed using various computer programs to determine the material requirements for each planning period. As a result of computer processing, a planned schedule for order fulfillment, dispatch of orders, necessary corrections in orders, a report on the execution of deliveries, a planned report and a report on deviations from the order fulfillment plan are obtained.

The calculation of the need for components obtained using computer simulation is used to determine the schedule for loading equipment in production shops. These schedules are compared with the capacity of each of the workshops in order to determine the ability to meet the main schedule. If there are bottlenecks, then the main schedule is revised. When this is done, purchase orders are placed and shop floor operations are scheduled.

3. Just-in-time (JIT) system. Each system seeks to build up enough inventory to meet projected demand. And at the same time, it should function at the lowest cost. Japanese companies, primarily automotive companies, have been the most successful in practical implementation of this task by creating a “just in time” inventory management system, which is known as “Kanban”. In a JIT system, the authorization for the production of a part to be produced at each work station is generated by the requirement for the part coming from the next work station on the production line. As parts are consumed on the final assembly line, parts requisition cards are sent to determine the need and authorize the production of replacement parts. The process is repeated at all previous workstations, moving parts through the production system as they become needed and, accordingly, determining the volume of purchases of raw materials and purchased parts from suppliers. This approach is called demand pull. Through this system, WIP is reduced, and bids are authorized for exactly those parts that are "just in time" to be used, resulting in "zero stock" or "out of stock production." The components in this system go directly to the assembly shop, bypassing the warehouse.

4. ABC method - classifies groups of goods in stocks depending on their importance. Most Attention is given to the goods of group "A", the most expensive, less goods less expensive (group "B"). The cheapest goods from group "C" are given the least attention.

The classification of stocks by groups of inventory items is carried out using step by step procedure. The first step is to break down the entire annual inventory into separate units: finished goods by type (for example, cars by brand), raw materials by groups (glass, bodies), etc. In the second step, by multiplying the unit cost by the expected annual use the annual use of each type of inventory is calculated in monetary units. The third step ranks each group of reserves from the largest in terms of annual use in monetary terms to the smallest. The fourth classifies stocks. This is done, for example, as follows: group A includes the first 20% of inventory items, group B - the next 30%, and finally group C - the last 50%. In this case, in monetary terms, group A will be, for example, 70% of the cost of reserves, group B - 20%, group C - 10%. The numbers may vary, of course, depending on the goals of the company, whether different types of controls are planned for each group, and what resources are available for inventory management.

Fig.4. Fixed stock model

5. The fixed inventory model works like this: the warehouse has the maximum desired stock of products, the demand for this product reduces the quantity in the warehouse, and as soon as the quantity reaches the threshold level, a new order is placed.

The optimal order size is chosen so that the amount of products in stock again equals the maximum desired stock. Since products are not delivered instantly, the expected consumption at the time of delivery must be taken into account. Therefore, it is necessary to take into account the reserve stock, which serves to prevent shortages.

6. The model with a fixed time interval between orders works as follows: an order is placed at a given frequency, the size of which should replenish the stock level to the maximum desired stock.

Fig.5. Model with a fixed time interval between orders

7. The model with the established periodicity of replenishment of stocks to the established level works as follows: orders are made periodically (as before), but at the same time the level of stocks is checked. If the inventory level reaches the threshold, then an additional order is made.

8. The model "Minimum - Maximum" works as follows: control over the level of stocks is done periodically, and if during the check it turned out that the level of stocks is less than or equal to the threshold level, then an order is made.

It should be noted that other models of inventory management are also used in practice, and the choice of a particular model depends on the specifics of the business and other influencing factors.

test questions

1. Ways to determine the need for current stocks.

2. Inventory management systems with fixed and variable order sizes.

3. Pros and cons of FIFO and LIFO methods.

4. Characteristics of the stock management model with a fixed order period.

5. Characteristics of the stock management model with a fixed stock level.

6. Comparative characteristics of various models of inventory management

The cost of customer frustration is usually an imputed value that can be estimated and imputed into costs to more fully account for economic profit.

Inventory management is an important area management activities in many enterprises of various industries, both for the production of goods and for the provision of services.

In a market economy, the issues of rational and effective organization management processes and control over the movement of material and financial flows at the enterprise in order to increase the efficiency of the material and technical supply of the enterprise itself and the sale of its products finished products. This is necessary to optimize the level of reserves and their efficient use, reduce their level, as well as minimize working capital invested in these stocks.

The lack of inventories at the enterprise leads to a violation of the rhythm of its production, a decrease in labor productivity, overspending of material resources due to forced irrational replacements and an increase in the cost of products. The lack of marketing stocks does not allow for an uninterrupted process of shipment of finished products, respectively, this reduces the volume of its sale, reduces the amount of profit received and the loss of potential customers of consumers of products manufactured by the enterprise. At the same time, the presence of unused stocks slows down the turnover of working capital, diverts material resources from circulation and reduces the rate of reproduction and leads to high costs for maintaining the stocks themselves.

The functioning of the enterprise with a relatively high level of its stocks will be completely inefficient. In this case, the enterprise has stocks for certain groups of inventory items that are greater than their actually required values ​​- excess stocks (“lying”). In this regard, it must additionally invest significant working capital in them, which leads, respectively, to a lack of free financial resources - a decrease in the solvency of the enterprise, the inability to timely acquire the material resources and equipment necessary for production, pay off the budget and off-budget funds for taxes and wages. personnel, etc.

Besides, high level excess stocks leads to an increase in the costs of the enterprise for the maintenance of the stocks themselves: the need to have large storage areas, you need to have increased staff (storekeepers, loaders, accountants) for processing and accounting for materials in the warehouse, these are additional communal payments and property taxes. All this leads to increased costs for: depreciation due to the created additional storage facilities for the storage of excess stocks, the cost of the salary of increased accounting and warehouse staff (storekeepers, loaders processing these stocks), increased utility bills - for lighting, heating additional storage facilities, etc. Additional costs increase the cost of finished products manufactured industrial enterprise, and reduce its competitiveness in the market of goods.

Literature

1. Richard Thomas. Quantitative methods for analyzing economic activity / Per. from English. - M .: Publishing house "Delo and Service", 1999. – 432 p.
2. Taha Hamdi. Introduction to operations research. M.: Mir, 1985.
Description

site site

Company

First system. Trade Automation Center

federal state budgetary educational institution higher vocational education

Volgograd State Technical University

Department of Economics and Management

Faculty of Engineering Personnel Training

Inventory management models

Volgograd 2014

Introduction

1. The main provisions of the theory of inventory management

2. Types of inventory management models

3. Generalized inventory management model and its elements

4. Wilson model

Conclusion

Bibliography

Introduction

Widely used at present, logistics systems use stocks. Therefore, an important task for the enterprise is the development; optimal inventory management strategy. Inventories can be considered as raw materials, semi-finished products, components and finished products. The task of inventory management is directly related to the organization of the procurement process, that is, the supply of the enterprise, as well as the sale of finished products.

There is a need to have reserves if at least one of these factors exists:

fluctuations in demand for goods;

fluctuations in the timing of delivery of goods from the enterprise;

certain conditions requiring the purchase of products in batches;

the presence of some costs associated with a shortage (lack of stock) or a delay in delivery.

In most trading situations, there is a combination of these factors. It is obvious that only in exceptionally rare cases will an enterprise be able to operate without stocks.

1. The main provisions of the theory of inventory management

Inventory management theory is one of the youngest branches of operations research.

Fundamentals of the modern theory of inventory management - problem statement, analysis of factors influencing the solution, a way to account for uncertainty in demand. In the created theory, for example, such tasks as:

management of stocks of a homogeneous product in an isolated warehouse with a fixed delay in deliveries;

Inventory management in case of an accidental delay in deliveries;

management of multi-item stocks, etc.

Maximum Desired Headroomdetermines the level of inventory that is economically feasible in a given inventory management system. This level may be exceeded. In various management systems, the maximum desired stock is used as a guide when calculating the order quantity.

threshold levelstock is used to determine the point in time of issuing the next order.

current stockcorresponds to the inventory level at any point in time. It can be the same as a maximum desired level, a threshold level, or a safety margin.

Warranty(or insurance) stockdesigned for continuous supply of consumers in case of unforeseen circumstances.

The inventory management model consists of three blocks:

Sales forecasting block - forecasting weekly/daily sales of goods;

Inventory management block - optimization planning of guaranteed stock, current stock, etc. taking into account the chosen inventory management model for each product category;

Supply management block - optimization planning of deliveries within the company's logistics network, taking into account planned sales, supplies from the manufacturer, availability of residues, transport capacities, various restrictions and business rules.

Stock types

The concept of inventory

Reasons for creating inventories

The concept of material stock.Inventories are raw materials, materials, components, finished products and other material assets awaiting entry into the process of production or personal consumption.

The main part of the stocks at the enterprise is the items of production included in the material flow at various stages of its technological processing.

The reasons for the creation of inventories.Stocks at the enterprise are formed for two main reasons:

inconsistency of supply volumes with volumes of one-time consumption;

the gap in time between the moment of receipt of the material and its consumption.

The supply of raw materials is carried out in most cases periodically, and their consumption occurs, as a rule, continuously and does not coincide in time with receipt. Therefore, to ensure uninterrupted operation, each enterprise creates certain stocks of the types of raw materials, materials, semi-finished products, fuel and other resources it needs. There are some other reasons leading to stockpiling. These are seasonal price fluctuations; violation of the established delivery schedule (unpredictable decrease in the intensity of the input material flow); the possibility of fluctuations in demand (unpredictable increase in the intensity of the output flow), etc.

Types of inventories.On the way to the transformation of raw materials into the final product and the subsequent movement of this product to the final consumer, two main types of stocks are created: production and commodity stocks.

Industrial stocks are formed in consumer organizations and are designed to ensure continuity production process.

Commodity stocks are stocks of finished products from manufacturers, as well as stocks along the route of the goods from the supplier to the consumer, i.e. at wholesalers and retail, in procurement organizations and stocks in transit. They are necessary for the uninterrupted provision of consumers with material resources.

Production and commodity stocks are divided into current, preparatory, insurance and seasonal:

Current stocks are necessary for the enterprise to ensure uninterrupted operation in the interval between two deliveries and to ensure the possibility of producing products in batches of the optimal size. This part of the stock is formed in conditions of uniform and regular supply due to the mismatch between the volumes of supply and one-time consumption, as well as delays associated with the movement of materials.

Preparatory stocks are allocated from production to ensure uninterrupted operation during the period necessary to prepare materials for use and deliver them to workplaces.

Guaranteed (insurance) stocks are necessary to ensure the operation of the enterprise in case of possible interruptions in the supply process or fluctuations in production volume. With the help of these stocks, deviations of actual demand from the forecast, deviations of the actual volume of output from the planned one, and deviations of the actual terms of execution of various operations from the planned ones are compensated.

Seasonal stocks are due to seasonal fluctuations in production or consumption. This stock is intended to meet the projected (seasonal) increase in demand, as well as some unloading of the enterprise for the holiday period.

2. Types of inventory management models

Despite the fact that any inventory management model is designed to answer two basic questions (when and how much), there are a significant number of models that use a variety of mathematical tools to build.

This situation is explained by the difference in the initial conditions. The main basis for the classification of inventory management models is the nature of the demand for stored products.

Depending on the nature of demand, inventory management models can be

deterministic;

probabilistic.

In turn, deterministic demand can be static, when the intensity of consumption does not change over time, or dynamic, when reliable demand can change over time.

Probabilistic demand can be stationary, when the probability density of demand does not change over time, and non-stationary, where the probability density function changes with time.

The simplest is the case of a deterministic static demand for products.

However, this type of consumption is quite rare in practice. The most complex models are models of non-stationary type.

In addition to the nature of demand for products, when building inventory management models, many other factors must be taken into account, for example:

· Terms of execution of orders. The duration of the procurement period can be constant or be a random variable;

Replenishment process. Can be instantaneous or distributed over time;

· the presence of restrictions on working capital, storage space, etc.

3. Generalized inventory management model and its elements

Providing the needs of economic, social and military facilities in various material means includes three phases: planning, production and distribution. As a rule, by the time the supply is realized, the data underlying the application are outdated and the scope of the supply no longer corresponds to the actual need. In order to prevent a stop in production in case of insufficient supply, stocks are created at consumers and in the supply chain. The following factors lead to the need to create reserves:

Discretion of deliveries

Random fluctuations

in demand for the interval between deliveries;

in the scope of deliveries;

in the duration of the intervals between deliveries.

Expected market changes:

seasonality of demand;

seasonality of production;

inflation expectations;

expected price increase.

These factors create a tendency to increase stocks.

There are, however, a number of considerations in favor of minimizing inventories:

Fee for physical storage of stocks;

Losses in stock quantity (evaporation, shrinkage, theft);

Qualitative changes (deterioration of consumer properties due to irreversible processes in the stored product);

Obsolescence.

Inventory management consists in establishing the moments and volumes of the order for replenishing them and distributing the newly arrived batch to the lower levels of the supply system. The set of rules by which these decisions are made is called the inventory management strategy. Finding the optimal strategy is the subject of inventory management optimization theory.

When comparing strategies, only the variable components of the cost function, which depend on the choice of strategies, are taken into account. in many models of inventory management, it is possible to ignore most of the costs of maintaining the administrative apparatus (except for the costs of processing deliveries), as well as the cost of production of material assets proportional to the volume of the lot, which for a sufficiently long period of time is determined by the total demand and does not depend on the organization of supply.

The mathematical formulation of the problem of finding the optimal strategy depends on the situation under study. However, the commonality of the factors taken into account allows us to speak of a single model of inventory management. Let's bring her qualitative description, limiting for simplicity to one warehouse, which receives a random flow of qualitatively homogeneous requirements - requests from consumers. Applications are immediately satisfied until their total volume (since the beginning of the planning period) does not exceed the initial stock. All subsequent requests cannot be served immediately, as a result of which the consumer is idle and incurs a loss. This loss is attributed to the supply system - it pays a fine. From time to time, the stock of stored property is replenished from the warehouse of a higher association, a central base or from industry, and with each such replenishment certain additional expenses. Finally, the warehouse bears the cost of storing the property located in it. It is required to choose the moment and volume of the replenishment order in such a way that the total costs of storage, fines and deliveries are minimal. Some restrictions may apply to warehouse operation. In these cases, a conditional minimum cost is sought.

Thus, the elements of the inventory management task are:

Supply system;

Demand for supplies;

Possibility of stock replenishment;

cost function;

Restrictions;

Inventory management strategy.

The supply system is understood as a set of sources of applications and warehouses, between which, in the course of supply operations, the stored property is transported. There are three options for building a supply system:

Decentralized. All warehouses directly serve consumers, and the shortage in one or more warehouses, at the decision of the supply management authority, can be covered by excess stocks in other warehouses.

· Linear. The production chain is considered and the distribution of buffer stocks according to the degree of product readiness is calculated.

· Echeloned. Each shortfall is covered by the final stocks of the higher level warehouse.

Storage costs:

Proportional to the average level of positive stocks for the period and time of existence of a positive stock;

proportional to the positive balance at the end of the period;

proportional to the maximum stock;

non-linear functions of one of the above quantities.

Inventory Management.

Types of expenses

Practical implementation management concepts material flows associated with the optimization of total reserves. The inventory optimization criterion is the total cost of order fulfillment and storage of materials.

In the system of procurement and storage of materials, expenses are divided into the following groups:

costs for the execution of the order;

direct costs determined by the purchase price;

inventory holding costs;

"deficit costs".

Order Fulfillment Costs associated with the placement and delivery of an order. These include such items of expenditure as the cost of developing the terms of delivery and preparing them for approval; expenses for the acquisition of advertising catalogs; costs associated with the control of the execution of the order and the reduction of the period of their implementation; transportation costs, if the cost of transportation is not included in the cost of the goods received; warehousing and ordering costs.

Some of them are fixed in the order and do not depend on the volume, others, such as transport and storage costs, are directly dependent on the size of the order. In general, the cost of fulfilling an order includes any type of expense, the amount of which depends on the number of orders fulfilled. Direct costs are determined by the price of purchased materials and vary depending on the wholesale discount to the price, which is set when the order lot size is increased. Inventory maintenance costs are determined by the cost of storing materials and the very fact of having stocks. This group of expenses includes such cost items as possible interest on capital invested in stocks; costs of warehouse operations and fees for the use or rent of the warehouse; operating costs for the maintenance of warehouses belonging to the production unit; costs associated with the risk of damage and obsolescence of materials, as well as insurance and tax costs. Decrease in inventories leads to a decrease in storage costs and operating costs for the maintenance of storage facilities. "Scarcity costs" are the costs incurred due to the limited in some period of certain material resources. This group of costs includes three types of losses:

stock management model loss in production associated with the suspension of the production process due to lack of necessary materials, as well as replacing the material with another one for more high price;

the cost of lost sales in case of non-fulfillment of the order if the customer turns to another manufacturer (in such a situation, the cost of shortage is defined as loss of profit);

additional costs arising in case of waiting for the execution of the order.

Warehouse costs. Storage costs are generally calculated according to the general norm, which takes into account the ratio of the fixed and variable parts of the costs. The rate of storage costs is

where H is the rate of storage costs; And - the interest rate on the capital enclosed in stocks; B - the rate of expenses for storing materials in a warehouse;

where G - the cost of storing materials in a warehouse for a certain period; D is the average cost of inventory.

4. Wilson model

Mathematical models Inventory management (IC) allows you to find the optimal level of stocks of a certain product, minimizing the total cost of purchasing, placing and delivering an order, storing goods, as well as losses from its shortage. The Wilson model is the simplest KM model and describes the situation of purchasing products from an external supplier, which is characterized by the following assumptions:

· consumption intensity is a priori known and constant value;

· the order is delivered from the warehouse where the previously produced goods are stored;

· the delivery time of the order is a known and constant value;

· each order is shipped as one batch;

· the cost of the order does not depend on the size of the order;

· the cost of holding the stock is proportional to its size;

· lack of stock (shortage) is unacceptable.

Input parameters of the Wilson model

) u- intensity (speed) of stock consumption, [unit. comrade / unit t];

) s - the cost of storing the stock, [rub./item.* unit. t];

) K - costs for the implementation of the order, including the execution and delivery of the order, [rub.];

) t d - order delivery time, [un.t].

Output parameters of the Wilson model

) Q - order size, [unit. comrade];

) L - total costs for inventory management per unit of time, [rub/unit t];

) t is the delivery period, i.e. time between orders or deliveries, [un.t];

) h 0- reorder point, i.e. amount of stock in the warehouse, at which it is necessary to place an order for the delivery of the next batch, [un. comrade].

The stock level cycles in the Wilson model are graphically presented in fig. 1. The maximum number of products that are in stock is the same as order quantity Q.

Fig.1 Chart of inventory change cycles in the Wilson model

Wilson Model Formulas

(11.1)

where Q w - optimal size order in the Wilson model;

The cost schedule for ultrasound in the Wilson model is shown in Fig. 2

Rice. Fig. 2. Graph of costs for KM in the Wilson model

Conclusion

Until recently, it was believed that the more inventory an enterprise has, the better. This is true when the enterprise has problems with logistics, in conditions where it is necessary to create significant safety stocks. However, in modern conditions scarcity is much less acute, enterprises can make a wide variety of investments. The owner of the enterprise is forced to create stocks, since otherwise costs will increase or profits will decrease.

consumer demand stock management model

Bibliography

1. Blank I.A. Financial management: Training course. - 2nd ed., - K .: Elga, Nika-Center, 2008.

Nerush Yu.M. Logistics: Textbook for universities. - 2nd ed. - M.: UNITI-DANA, 2007.

Financial management: theory and practice: Textbook. / Ed. Stoyanova E.S. - 2nd ed., revised. and additional - M.: Perspektiva Publishing House, 2000.

Afanasenko I.D. Workshop on supply logistics: questions and tests / Afanasenko I.D., Borisova V.V. - St. Petersburg. : Publishing House of St. Petersburg State University of Economics, 2011. - S. 131-134 (188 p.)

Http://ru. wikipedia.org-< свободная энциклопедия>

logistclub.com.ua< Типы моделей управления запасами>

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Types of Inventory Management Models

Despite the fact that any inventory management model is designed to answer two basic questions (when and how much), there are a significant number of models that use a variety of mathematical tools to build.

This situation is explained by the difference in the initial conditions. The main basis for the classification of inventory management models is the nature of the demand for stored products.

Depending on the nature of demand, inventory management models can be

deterministic;

probabilistic.

In turn, deterministic demand can be static, when the intensity of consumption does not change over time, or dynamic, when reliable demand can change over time.

Probabilistic demand can be stationary, when the probability density of demand does not change over time, and non-stationary, where the probability density function changes with time.

The simplest is the case of a deterministic static demand for products.

However, this type of consumption is quite rare in practice. The most complex models are models of non-stationary type.

In addition to the nature of demand for products, when building inventory management models, many other factors must be taken into account, for example:

· Terms of execution of orders. The duration of the procurement period can be constant or be a random variable;

Replenishment process. Can be instantaneous or distributed over time;

· the presence of restrictions on working capital, storage space, etc.

Generalized inventory management model and its elements

Providing the needs of economic, social and military facilities in various material means includes three phases: planning, production and distribution. As a rule, by the time the supply is realized, the data underlying the application are outdated and the scope of the supply no longer corresponds to the actual need. In order to prevent a stop in production in case of insufficient supply, stocks are created at consumers and in the supply chain. The following factors lead to the need to create reserves:

1. Discretion of deliveries

2. Random fluctuations

in demand for the interval between deliveries;

in the scope of deliveries;

in the duration of the intervals between deliveries.

3. Expected changes in the market situation:

seasonality of demand;

seasonality of production;

inflation expectations;

expected price increase.

These factors create a tendency to increase stocks.

There are, however, a number of considerations in favor of minimizing inventories:

1. payment for the physical storage of stocks;

2. losses in stock quantity (evaporation, shrinkage, theft);

3. qualitative changes (deterioration of consumer properties due to irreversible processes in the stored product);

4. obsolescence.

Inventory management consists in establishing the moments and volumes of the order for replenishing them and distributing the newly arrived batch to the lower levels of the supply system. The set of rules by which these decisions are made is called the inventory management strategy. Finding the optimal strategy is the subject of inventory management optimization theory.

When comparing strategies, only the variable components of the cost function, which depend on the choice of strategies, are taken into account. in many models of inventory management, it is possible to ignore most of the costs of maintaining the administrative apparatus (except for the costs of processing deliveries), as well as the cost of production of material assets proportional to the volume of the lot, which for a sufficiently long period of time is determined by the total demand and does not depend on the organization of supply.

The mathematical formulation of the problem of finding the optimal strategy depends on the situation under study. However, the commonality of the factors taken into account allows us to speak of a single model of inventory management. Let us give its qualitative description, limiting for simplicity to one warehouse, which receives a random flow of qualitatively homogeneous requirements - requests from consumers. Applications are immediately satisfied until their total volume (since the beginning of the planning period) does not exceed the initial stock. All subsequent requests cannot be served immediately, as a result of which the consumer is idle and incurs a loss. This loss is attributed to the supply system - it pays a fine. From time to time, the stock of stored property is replenished from the warehouse of a higher association, a central base or from industry, and with each such replenishment certain additional costs are associated. Finally, the warehouse bears the cost of storing the property located in it. It is required to choose the moment and volume of the replenishment order in such a way that the total costs of storage, fines and deliveries are minimal. Some restrictions may apply to warehouse operation. In these cases, a conditional minimum cost is sought.

Thus, the elements of the inventory management task are:

1. supply system;

2. demand for supplies;

3. the ability to replenish stocks;

4. cost function;

5. restrictions;

6. inventory management strategy.

The supply system is understood as a set of sources of applications and warehouses, between which, in the course of supply operations, the stored property is transported. There are three options for building a supply system:

Decentralized. All warehouses directly serve consumers, and the shortage in one or more warehouses, at the decision of the supply management authority, can be covered by excess stocks in other warehouses.

· Linear. The production chain is considered and the distribution of buffer stocks according to the degree of product readiness is calculated.

· Echeloned. Each shortfall is covered by the final stocks of the higher level warehouse.

Storage costs:

Proportional to the average level of positive stocks for the period and time of existence of a positive stock;

proportional to the positive balance at the end of the period;

proportional to the maximum stock;

non-linear functions of one of the above quantities.

Inventory Management.

1. Types of expenses

The practical implementation of the concept of material flow management is associated with the optimization of total reserves. The inventory optimization criterion is the total cost of order fulfillment and storage of materials.

In the system of procurement and storage of materials, expenses are divided into the following groups:

costs for the execution of the order;

direct costs determined by the purchase price;

inventory holding costs;

"deficit costs".

Order Fulfillment Costs associated with the placement and delivery of an order. These include such items of expenditure as the cost of developing the terms of delivery and preparing them for approval; expenses for the acquisition of advertising catalogs; costs associated with the control of the execution of the order and the reduction of the period of their implementation; transportation costs, if the cost of transportation is not included in the cost of the goods received; warehousing and ordering costs.

Some of them are fixed in the order and do not depend on the volume, others, such as transport and storage costs, are directly dependent on the size of the order. In general, the cost of fulfilling an order includes any type of expense, the amount of which depends on the number of orders fulfilled. Direct costs are determined by the price of purchased materials and vary depending on the wholesale discount to the price, which is set when the order lot size is increased. Inventory maintenance costs are determined by the cost of storing materials and the very fact of having stocks. This group of expenses includes such cost items as possible interest on capital invested in stocks; costs of warehouse operations and fees for the use or rent of the warehouse; operating costs for the maintenance of warehouses belonging to the production unit; costs associated with the risk of damage and obsolescence of materials, as well as insurance and tax costs. Decrease in inventories leads to a decrease in storage costs and operating costs for the maintenance of storage facilities. "Scarcity costs" are the costs incurred due to the limited in some period of certain material resources. This group of costs includes three types of losses:

management stock model losses in production associated with the suspension of the production process due to the lack of necessary materials, as well as the replacement of the material with another one at a higher price;

the cost of lost sales in case of non-fulfillment of the order if the customer turns to another manufacturer (in such a situation, the cost of shortage is defined as loss of profit);

additional costs arising in case of waiting for the execution of the order.

2. Norms of warehouse expenses. Storage costs are generally calculated according to the general norm, which takes into account the ratio of the fixed and variable parts of the costs. The rate of storage costs is

where H is the rate of storage costs; And - the interest rate on the capital enclosed in stocks; B - the rate of expenses for storing materials in a warehouse;

where G - the cost of storing materials in a warehouse for a certain period; D is the average cost of inventory.

The inventory management system is a set of measures for the creation and replenishment of stocks, the organization of continuous monitoring and operational planning of supplies.

The main mechanism of the inventory management system, which must be implemented in the work of all elements, is to implement the feedback principle. The essence of this principle lies in the fact that if the leading link of the system has a control effect on its working element, then the system must have " Feedback”, which provides data on the new state of the entire system and evaluates the effectiveness of its functioning. The system will be controlled if, after the impact on it, it is possible to determine its new state, evaluate it, and, taking into account the new data about the system, take the next corrective action on it.

At the first level of the system, modules of the warehouse program and databases are placed, in which information is accumulated on the movement of goods and work with buyers for the shipment of goods.

The second level of the system consists of various inventory management models that use the necessary mathematical apparatus to assess the current state of inventory and develop recommendations for their effective management.

At the third level, there is a financial management model and rules that allow you to control financial condition stocks. Here is estimated economic efficiency adopted rules for the formation of reserves are determined financial sources for their acquisition and general financial strategy inventory management.

Thus, the basis of the inventory management system is the technology for analyzing the state of reserves and the environment, as well as the rules for making decisions on the formation of reserves. The rules themselves can be implemented in the form of specialized software modules and instructions for personnel.

Within the framework of many theoretical studies and vast practical experience in solving the problem of inventory management, a number of firms use one of the following systems, which have their own advantages and disadvantages.

In the process of inventory regulation, various quantitative levels of reserves are distinguished:

The maximum reserve equal to the sum of guaranteed, preparatory and maximum current reserves. Its size is set to control excess resources,

Average, or rolling stock, equal to the sum of the guaranteed, preparatory and half of the current stocks. The value of this indicator corresponds to the standard size of the stock;

The minimum stock equal to the sum of guaranteed and preparatory. Reduction of stocks to this level is a signal for their emergency replenishment.

In the process of inventory management, it is important to establish the moment, or point of order, and its required size.

The reorder point is the established maximum stock level, upon reaching which an order is placed for the delivery of the next batch of material assets.

The order quantity is the quantity of materials that must be ordered to replenish their stock. If the minimum stock is reached when a new batch is received, then it reaches the maximum level.

You can adjust the size of the order by changing the volume of lots, the interval between deliveries, or changing the volume and delivery interval. Depending on this, the following systems are used in the practice of inventory management:

1. The system of control over the state of stocks with a fixed frequency of the order. According to this system, inventory control is carried out at regular intervals (a week, a decade, a month) through an inventory of residues. For example, every Tuesday the manager of the firm reviews the stock of goods and places an order for the supply of a new batch of goods. Thus, the time interval between orders remains constant, and the size of the order varies depending on the intensity of consumption, i.e. is a variable.

T - fixed time interval between deliveries of goods

The size of the ordered consignment of goods is determined by the difference between the maximum commodity stock provided by the norm and the actual stock. Since the execution of the order requires a certain period of time, the size of the ordered batch is increased by the amount of the expected expense for this period (safety stock). The size of the ordered batch (P) is determined by the following formula:

P \u003d s max - s fact + s str,

where З max - maximum margin, statutory; Z fact - actual stock at the time of verification: Z str - safety stock.

The intensity of demand in this model is the magnitude of the variable. And since the order is carried out at regular intervals, the size of the ordered batch in different periods will be different. Therefore, this system can be applied when it is possible to order lots of different sizes. For example, in the case of container or wagon delivery of goods, this system is unacceptable. In addition, the system is not used if shipping or placing an order is expensive. For example, if the demand for the past period was insignificant, then the order will also be insignificant, which is permissible only if the costs associated with the execution of the order are insignificant. Another feature of the system is that it allows for scarcity. If demand rises sharply, stock will run out before the order deadline. This means that the system is applicable when the possible losses from the deficit for the enterprise are imperceptible.

Thus, the inventory control system with a fixed order frequency is used in the following cases:

Terms of delivery allow you to receive orders in batches of various sizes;

Ordering and shipping costs are relatively low;

Losses from a possible shortage are insignificant.

The advantage of the considered system is its simplicity, since the regulation is carried out once during the entire interval between deliveries. Among the disadvantages of the system can be attributed the risk of depletion of stocks in case of their unforeseen intensive consumption before the next moment of the order.

2. The system of control over the state of stocks with a fixed order size. In this system, the restocking order quantity is a constant value. The time intervals through which an order is placed may be different in this case. The quantity of ordered products is determined by agreement between the supplier and the buyer. It is definite and fixed, and the time of the order is taken as a variable. An order for the supply of the next batch is given when the size of the stock in the warehouse decreases to the established threshold level - the order point. The intervals between deliveries of successive batches to the warehouse depend on the intensity of consumption (consumption) of material resources. After placing the next order, the stock continues to decrease, since the order is not executed immediately, but after a certain period of time (T). The stock level corresponding to the order point is equal to the expected demand during the lead time of the delivery from the order plus the safety stock:

where Z ta is the stock of the order point; P - average daily consumption of material; T - order fulfillment period; Z str - safety stock.

The stock value at the reorder point is chosen such that in normal working situation during the time T the stock did not fall below the insurance. If demand unexpectedly increases or the delivery time is violated, then the safety stock will start working. The commercial service of the enterprise in this case must take measures to ensure additional supply. As can be seen, this control system provides for the protection of the enterprise from the formation of a deficit.

In this case, it is conditionally assumed that the time interval between the submission of the purchase order and the receipt of the batch at the warehouse (T) is constant

In practice, a stock control system with a fixed order quantity is mainly used in the following cases:

Large losses due to lack of stock;

High inventory holding costs;

The high cost of the ordered goods;

High degree of demand uncertainty;

Availability of discounts from the price depending on the quantity ordered.

The advantage of this system lies in the fact that the receipt of material in the same lots leads to a reduction in the cost of delivery and maintenance of stocks. The disadvantage of the system is the need for constant labor-intensive control over the availability of stocks and, as a result, an increase in the costs associated with their regulation.

3. A system for managing the state of the stock of a material resource with a marginal (or production) level of stock and random demand. The movement of stocks (receipt, consumption) in the considered control system is carried out at random times.

A system with a marginal stock level and random demand must have the ability to adjust the size of the demand for resource consumption, otherwise situations with an absolute shortage may be created. In this regard, one should consider various situations that characterize the inventory management system with their marginal level and random demand.

The system, in principle, is organized by one parameter - the marginal level of stock. The threshold level is only a guideline when determining when to place an order. Since the demand in the system is random by the condition, then, therefore, at any time the consumption of the resource can be different in value, including being equal to the entire balance of the resource, which forms an absolute shortage of the resource until the next supply.

Such a system is organized in those fairly frequent cases when the demand for a resource in production or trade is highly uneven, and this unevenness is a function of the size of the order, the time of the order, and the number of consumers.

High demand for a resource often ends in a sharp decline. This circumstance makes it necessary to form a resource stock based on two possible states: 1) production stock and 2) marginal stock, i.e. ensure the consumption of the resource in the intervals between deliveries (manufacturing stock) or at the time of completion of one turnover of working capital (marginal stock). If the demand for the resource is high, then you should focus on the marginal stock; if the demand for a resource falls, then the reference point for the required stock may be its production option.

4. The "Minimum-Maximum" inventory management system has a fundamental difference from other systems due to the fact that it is focused on a situation with significant costs for maintaining stocks and replenishing them. In this system, the costs associated with inventory management can be commensurate with the losses from inventory shortages, while orders are filled provided that stocks in the warehouse at a certain point in time turned out to be equal to or less than the established minimum level. The order size is calculated so that the supply replenishes stocks to the maximum level. Thus, inventory management in the system under consideration is carried out according to their two levels: minimum and maximum, which led to its name.

If at the time of placing an order, the balance turned out to be less than the minimum level provided, then a situation with a shortage of a resource may arise. This circumstance must be taken into account at the time of debiting a part of the resource on the basis of a demand or a limit-fence card. In other words, at the time of writing off the resource, the balance of the stock should not be less than what is provided for by the program.

Necessary inventory management parameters in the "Min-Max" system:

The need for a material resource and the average daily consumption are determined;

Established: minimum and maximum reserves; the lead time of the order and possible delay in delivery;

The guaranteed reserve is represented by the sum of the preparatory and insurance reserves;

The minimum stock level is the difference between the maximum and guaranteed stocks.

The minimum-maximum system is preferred when it is necessary to quickly respond to changes in sales.

When designing a logistics inventory management system, a number of factors must be considered:

1) production capacity;

2) the volume of products produced for a certain period of time (day, week, month);

3) the current level of stocks;

4) the required size of the guarantee (insurance) stock;

5) frequency of delivery.

The main inventory management systems are a system with a fixed order size, a system with a fixed time interval between orders, MRP-1, MRP-2, etc.

Fixed order system is a model of inventory management in which the main determining factor is the determination of the optimal order size, the size of which subsequently does not change. The optimal order size (ORS) is determined by minimizing the total cost of holding and repeating the order. It is calculated according to the formula Wilson:

ORZ— optimal order size, pcs.;

BUT- the cost of supplying a unit of the ordered product, rub.;

S

x is the cost of storing a unit of the ordered product, rub./pc.

System with a fixed time interval between orders is a stock management model in which the main determining factor is the determination of the time interval between orders, taking into account the optimal order size. The optimal order size allows you to minimize the total cost of holding inventory and repeating the order.

The time interval between orders is defined as follows:

D- the number of working days in a year, days;

S- the need for the ordered product, pcs.;

ORZ— optimal order size, pcs.

The material requirements planning system (MRP-1 and MRP-2) is an inventory management model in which production, and therefore inventory, is planned based on the demand for end products. These systems are referred to as pushing systems for the advancement of material flows. The pushing system is a system for supplying materials (components) from the previous technological operation to the next, regardless of the needs. In such a system, the formation of orders is carried out in accordance with the forecast of sales volume. The MRP-1 and MRP-2 systems use a large number of different computer programs that provide coordination, operational regulation of supply, production and marketing functions across the company in real time. Determining the need for materials involves solving a number of tasks on demand forecasting, inventory management, procurement management, etc.

In the MRP-1 system processing and adjustment of information on the arrival, movement and consumption of materials (raw materials, components), inventory accounting at the place of their storage, selection of strategies for replenishment and control of inventory levels for each item of the nomenclature of raw materials and materials, control of inventory turnover rate, etc. . To solve procurement management tasks, an order file is used, into which information about orders and their fulfillment is entered.

MRP-2 system is an advanced material requirements planning system and differs from the MRP-1 system primarily in the range of functions performed. It combines production, financial planning and logistics operations.

Inventory management is a solution to problems related to accounting, systematization, analysis and optimization of inventory levels. Inventory management is based on the study of the patterns of formation and consumption of reserves. The stock consists of usable but unused resources. The reserve problem arises when the amount of resources can be regulated. The purpose of solving the problem— minimization of actual or expected costs.

One of the main tasks in inventory management is to achieve optimal balance between production volumes and stocks.

Controlled Variables in the Inventory Problem

1. The incoming volume of resources, those. how much needs to be purchased, released, etc.

2. The frequency or timing of the receipt of resources, those. frequency and times. These variables can be adjusted separately or together.

3. The degree of product readiness, held in stock. The higher the degree of readiness of stocked products, the less the delay in meeting demand, but the higher the cost of creating a stock.

Uncontrolled variables are divided into cost and other

1 . Inventory holding costs increase in direct proportion to the increase in stock volume and storage time. Cost components:

1) the cost of warehouse operations (labor, the cost of loading and unloading mechanisms, etc.);

2) cost of storage, incl. room fee;

3) insurance premiums and taxes;

4) depreciation deductions, losses from damage to products, losses from obsolescence (fashion goods, food products).

2. Deficit losses and fines.

3. Costs due to changes in pace production. For example, an increase in the pace - staff training, a decrease in the pace - dismissal.

4. Purchase price or direct costs production. The cost of purchases depends on the wholesale.

5. Demand- the volume of production required for a certain period of time. For example, should a new batch of products be put into production?

6. Lead time- the time interval between the moment of placing an order and the moment of replenishment of the stock.

7. The volume of supplied products.

Inventory management tasks arise everywhere, incl. and when accounting for labor reserves (for example, in security agencies, the question arises of how many employees are needed. If you train less, you may need to pay overtime.

At the firm level, inventories are among the objects that require large capital investments, because it is a factor that determines the policy of the enterprise and affects the level of logistics services.

Since demand is a random quantity, graphically it is a stepped line. But for the analytical description, it is replaced by a straight line or a curve.

When replenishing stocks, two cases are possible.

1. Time interval from the conclusion of the contract for delivery to receipt is 0.

2. Product replenishment is delayed.

AT In the first case, two methods of control are distinguished.

1. Periodic S - var, T - const.

The disadvantage of this control is the possibility of running out of stock, which entails more expensive control.

2. Relaxation- the number of products S - const, T - var. T and S are not equal, but depend on the law of stock change.

There is no risk, management is cheaper. In the second case, the value corresponding to the moment of receipt is known, constant, the moment itself is not fixed.

Logistics concepts in inventory management

Stocks as an economic category play an important role in the production and circulation of products. Inventory management is an essential condition for the successful functioning of any company. Currently, there are a large number of inventory management systems, each of which is associated with logistics costs. The following can be used as optimization criteria: minimum logistics costs associated with inventory management; minimum order lead time; maximum supply reliability, etc.

The most widely used logistics concept in the world is the concept of "Just-in-time" (Just-in-time, JIT). The original slogan of this concept was the potential exclusion of stocks of materials, components and semi-finished products in the production process of assembling cars and their main units.

The initial statement was that if the production schedule is set, then it is possible to organize the movement of material flows in such a way that all materials, components and semi-finished products will arrive in the required quantity, at the right place and exactly at the appointed time for the production or assembly of finished products. With such a formulation, insurance reserves, which froze the company's cash, turned out to be unnecessary.

The concept of "Just-in-time" eliminates the requirement for a minimum inventory - resources must come as the needs of production.

The concept of "Just-in-time" is a modern concept of building a logistics system in production, supply and distribution, based on the synchronization of the delivery of material resources and finished products in the required quantities by the time the links of the logistics system need them, in order to minimize costs associated with stockpiling.

The work of the logistics system, built on the principles of the Just-in-time concept, can be represented as a two-bunker inventory management system. One silo is used to satisfy demand in production or distribution, and the other is replenished as the first one is used up. Management of material flows in this case is carried out by "pulling" the order (Fig.).

Rice. Pulling material flow control system. MP - material resources, NP - work in progress, GP - finished products

The concept of "Just-in-time" is characterized by the following main features:

1) minimum (zero) stocks of material resources, work in progress, finished products;

2) short production (logistics) cycles;

3) small volumes of production of finished products and replenishment of orders (supplies);

4) relationships for the purchase of material resources with a small number of reliable suppliers and carriers;

5) effective information support,

6) high quality finished products and logistics services.

The concept of "Just-in-time" allows you to: minimize the level of stocks; improve the quality of finished products and services; change the corporate style of management.

Information Support operational management of material flows on the principle of "Just-in-time" is implemented by the KANBAN micrologistics system, developed and implemented by Japanese automotive companies. The KANBAN micrologistics system is a system for organizing a continuous production flow, capable of rapid restructuring and requiring almost no safety stocks.

The means of transferring information in the system is a special kanban card in a plastic envelope. Two types of cards are common: selection and production order.

The selection card indicates the number of parts (components, semi-finished products) that should be taken at the previous processing (assembly) section, the order card indicates the number of parts that should be manufactured (assembled) at the previous production area. These cards circulate both within the enterprise and throughout external environment-between the corporation and the companies cooperating with it, as well as at the enterprises of branches.

An analysis of the world experience in the use of the KANBAN micrologistics system shows that it makes it possible to reduce production stocks by 50%, commodity stocks by 8%, with a significant acceleration in the turnover of working capital and an increase in the quality of finished products.

The concept of "requirements/resource planning" is often contrasted with the concept of "just in time", meaning that "push-type" logistics systems are based on it.

A push (push) system is a production organization system in which parts, components and semi-finished products are fed from the previous technological operation to the next in accordance with a pre-formed rigid production schedule (Fig.).

Rice. 12. Push-out material flow control system. MP - material resources, IP - work in progress, GP - finished products.

Material resources and semi-finished products are "pushed" from one link of the production logistics system to another. A common drawback of the "push" system is insufficient tracking of demand with the mandatory creation of safety stocks. As a result of inventory storage, the turnover of working capital of the enterprise slows down, which increases the cost of production of finished products.

Proponents of this concept note greater resilience in the face of sharp fluctuations in demand and the unreliability of resource suppliers compared to the just-in-time concept.

The basic micrologistics systems of this concept are the production resource planning (MRP) system and the product distribution planning (DRP) system.

The usual practice of using MRP systems in business is related to the planning and control of procedures for ordering and supplying (purchases) of material resources, as a rule, a wide range for industrial enterprises manufacturing engineering products.

The objectives of the MRP implementation are:

Improving the efficiency and quality of planning for resource requirements;

Planning the production process, delivery schedule, purchases;

Reducing the level of stocks of material resources, work in progress and finished products;

Improving inventory control procedures;

Reducing the costs associated with these logistics functions.

The implementation of logistics goals in the MRP system can be expressed in the form of a diagram (Fig.).

Rice. Implementation of logistics goals in the MRP system

MRP systems are predominantly effective in cases of:

When the demand for initial material resources is highly dependent on consumer demand for final products;

When a firm has sufficiently long production cycles in the face of uncertain demand.

The DRP system is the extension of the logistics of building MRP systems to distribution channels for finished products. They are determined by the production schedule, which is regulated and controlled by the manufacturer of the finished product.

The functioning of DRP systems is based on consumer demand, which is not controlled by the manufacturer. Therefore, MRP systems are generally more stable than DRP systems.

The logistics tool in DRP systems is the schedule (schedule), which coordinates the entire process of supply and replenishment of stocks of finished products in distribution network. This schedule is generated for each dedicated storage unit and each link in the logistics system (manufacturer's own warehouses or wholesalers' warehouses).

The DRP system allows you to solve the following tasks:

Planning and coordination of logistics and marketing functions;

Forecasting market conditions;

Planning the size and location of deliveries and stock levels in the central and regional warehouses of the manufacturer;

Optimization of logistics costs of storage and stock management of finished products;

Reducing the time of delivery of finished products;

Planning transportation and etc.