The use of economic and mathematical modeling in logistics systems. Application of mathematical models in logistics

Date: 29.09.2019

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Faculty of Logistics

Discipline program

"Economic and Mathematical Methods and Models in Logistics"

In the direction of 080500.62 "Management", special profile
disciplines "Logistics and Supply Chains Management"

_____________________________ ________________________________

"_____" __________________ 2012 «____" _____________________ 2012

Approved by the settlement of the faculty

Scientific Secretary

_________________________________

"____" ___________________2012

Moscow, 2012.

Student Requirements:

For the successful development of the course, students studying this discipline must pre-master the following basic mathematical courses:

mathematical analysis;
linear algebra;
linear programming;
integer programming;
basics of discrete mathematics;
the theory of binary relationships;
probability theory;
Basics of mathematical statistics.

Annotation:

the learning program of the discipline "Economic and Mathematical Methods and Models in Logistics" of the federal component of the DS Cycle is drawn up in accordance with the State Educational Standard of Higher Professional Education of the second generation in the specialty "Logistics" on the basis of a model program of this discipline recommended by UMO on Logistics Education.

The teaching of the discipline "Economic and Mathematical Methods and Models in Logistics Studies" is based on the required level of basic training of bachelor logs for a complete set of necessary research to solve three mandatory problems:

analysis of the current organizational and functional structure of the logistics system;
synthesis of the new organizational and functional structure of the logistics system;
optimization of logistics functions and logistics activities of production and business organizations.

Such problems should be resolved on the basis of the mandatory use of the following methods:

System analysis;

Econometrics;

Theory of research of operations;

Decision-making theory in uncertainty conditions;

Mathematical modeling;

Mathematical programming;

Game theory;

Theory of multicriterial optimization;

Artificial intelligence theory;

Forecasting.

The goal of the course is to study the substantive and formal layout of the main organizational and economic problems of logistics from the above methods, on the basis of which in future bachelors, the formation of solid theoretical knowledge and practical skills on the use of modern economic and mathematical methods and models in analyzing Calculation and prediction of indicators and parameters for logistics operations.

In turn, the present course "Economic and Mathematical Methods in Logistics Studies" is the methodological basis of the following special disciplines:

"Theoretical Fundamentals of Logistics and Supply Chains Management"
"Transportation in supply chains";
"Inventory management in logistics systems";
"Logistics of production";
"Risk management in supply chains."

The discipline program provides for seminars. The topics of such classes are given in the appropriate thematic plan. They are being developed for the skills of the practical use of economic and mathematical methods for modeling logistics systems; The knowledge of the appropriate theoretical material is fixed; Selective express surveys are held. The program provides for the conduct of two test work (one for each pair of modules in the format of this discipline), assessments on which will be reflected in the current and intermediate certification. The program also provides for the execution of a student (also for every two modules) of home settlement and abstract, the subject of which is provided in its corresponding section. In addition to the fulfillment of these tasks, the student's independent work includes: the assimilation of the "current" theoretical material at the level, as sufficient for understanding the seminar sections, and to participate in the work of seminars; Preparation for seminary classes, which implies the fulfillment of appropriate tasks that will help consolidate the skills of owning economic and mathematical methods in logistics research.

^ The educational task of discipline:

The tasks of studying discipline are the implementation of the requirements established in the State Educational Standard of Higher Professional Education, to the preparation of bachelors on issues of solving logistics problems in the management of economic processes.

As a result of studying discipline, the student must:

know the main economic and mathematical methods and models used in the analysis of logistics systems;
freely navigate in applied mathematical works related to their industry;
be able to use suitable economic and mathematical methods and models in their activities;
have an idea of \u200b\u200bapproaches to assess the adequacy of mathematical models; establish the boundaries of their applicability, correctly interpret the conclusions from them in terms of their own specialty;
possess the skills to formulate the problems of economic analysis of logistics systems in the language of mathematics; Learn independent scientific and educational and methodological literature on mathematical modeling of logistics processes.

^ Themed Plan Educational discipline:

№	Topic Title	Just hours on discipline	Audit hours		Independent work
№	Topic Title	Just hours on discipline	Lectures	Sem And the strap. classes	Independent work
Modules 3 and 4 (3 course)
1	^ Section 1. Introduction
1.1	Mathematical models logistic systems: classification, modeling methodology	4	2	-	2
2	^
2.1	General scheme method	14	4	4	6
2.2	Basic procedures of the method in the format of logistics problems	14	4	4	6
3	^ Section 3. Method of permutation of arguments when optimizing costs in supply chains
3.1	Minimization of costs when executing the order portfolio: Penalty Function Accounting Models	8	2	2	4
3.2	Minimizing costs when executing a portfolio of orders: contract price and inflation	8	2	2	4
	^ Section 4. Index Methods of Optimization
4.1	Hits index apparatus: maximization of performance indicators	12	2	2	8
	Annexes of index methods for restructuring costs in logistics	12	2	2	8
5	^ Section 5. Mathematical Inventory Management Models
5.1	Basic model management models and modifications	12	4	2	6
5.2	Multiproduct stock management strategies	10	2	2	6
5.3	The effect of the time value of money for stock management models	14	4	4	6
	Total modules 3 and 4 (3 course)	108	28	24	56
Modules 1 and 2 (4 course)
6	^ Section 6. Application of discrete mathematics in logistics
6.1	Fundamentals of the theory of graphs	6	2	2	2
6.2	Applying optimization methods of graph theory for solving Tasks Logistics	12	2	2	8
7	^ Section 7. Application of streaming theory methods in networks for solving logistics problems
7.1	Extreme tasks for network models	10	4	2	4
7.2	Models of transport tasks as linear programming tasks	18	2	4	12
7.3	The task of appointments	6	2	2	2
8	^ Section 8. Project Management
8.1	Network project graphics: analysis of the critical path	10	4	2	4
8.2	Methods for planning temporary and resource indicators	8	2	2	4
9	^ Section 9. Methods of forecasting in research Logistics
9.1	Prediction costs by methods of random events	16	2	2	10
9.2	Prediction of temporary loss structure during discrete intervention case	8	2	2	4
	^ Section 10 Elements of Mass Maintenance Theory
10.1	Modeling Markov Service Systems	14	2	4	8
	Total for modules 1 and 2 (4 course)	108	24	24	60
	Total on all discipline:	216	52	48	116

^ Basic textbook:

Brodetsy G.L. Economic and mathematical methods and models in logistics studies. Event flows and service systems. - M.: Academy, 2009. - 272 p.

Brodetsy G.L. Inventory management: studies. allowance // - M.: Eksmo, 2008. - 352 p.

Brodetsky G.L., Gusev D.A. Economic and mathematical methods and models in logistics studies. Optimization procedures. - M.: Academy, 2012. - 288 p.

Control forms:

current control is carried out on the basis of estimates in a 10-point scale based on results - 1) express surveys, express tests during seminars; 2) checks of homework (selectively); 3) test work (80 min.); Home Writing (80 min)
Interim control is carried out on the basis of estimates in a 10-point scale according to the results of the test, test work, and current progress; At the same time, the resultant estimate of the intermediate control is a weighted average assessment based on the results of testing, test work, domestic written work and current performance with the same weights as when issuing a summary assessment (see below);

Final monitoring form - Exam;

Summary assessment of PO academic discipline consists of the following elements

(Weights can be clarified by decision of the department / logistics separation):

Work in practical classes (solving problems laboratory works in computer classes) - weight 0.15;

Two written audit test works (80 min.) - Weight. 0.1 each;

Home Writing (80 min) - weight 0.05;

Written exam (80 min.) - Weight 0.6.

Course sections

introduction;
methods of imitation modeling;
the method of rearranging arguments when optimizing the costs of logistics
index optimization methods;
mathematical model management models;
application of discrete mathematics in logistics;
models of transport logistics;
project management;
forecasting methods in logistics studies;
elements of mass maintenance theory.

Topics I. summary

^ Section 1. Introduction

Topic 1.1. Mathematical models of logistics systems: classification, modeling methodology

Logistics system as an object of mathematical modeling. The wording of the organizational and economic formulation of logistics problems. Requirements for the mathematical formulations of the main tasks of logistics. Requirements for the development of algorithms for solving logistics problems. Choosing software tools for implementing algorithms for solving logistics problems. Discrete nature of organizational and economic tasks.

Methodology for modeling logistics systems. Mathematical modeling: Methods and apparatus of the theory of random processes, mathematical theory of reliability, methods of stochastic optimization, theory of mass service and stock management, methods of network planning and management, theory of graphs, methods of the theory of economic decisions, etc. Imitation modeling: features and capabilities of the method. Models for assessing the effectiveness of logistic operations.

^ Main literature

Corporate logistics. 300 answers to professionals / ed. Sergeeva V.I. - M.: Infra-M, 2004

additional literature

Sergeev V.I. Management in Business Logistics. - M.: Filin, 1997.
Workshop on logistics. Tutorial / Ed. prof. Anikina B.A. - 2nd ed. - M.: Infra-M, 2001, - 280 s.
Novikov O.A. and others. Logistics. SPB: SPI, 1996.

^ Section 2. Method of simulation modeling

Topic 2.1. General method of method

Tasks solved by imitation modeling. Features and features of the method. Features of applications to modeling logistics systems. General diagram of the Monte Carlo method. Constructing procedures for the required random variable and upper estimate for its dispersion. Evaluation of the accuracy of the results obtained within the simulation model. Required mathematical apparatus for designing the simulation model and its implementation. Random and pseudo-random numbers. Modeling the base random variable is evenly distributed on (0; 1). Modeling a complete group of random events.

^ Topic 2.2. Main procedures method

Modeling discrete distributions probability. The main model of modeling continuous random variables and the corresponding modeling formulas. Special modeling formulas. Neumanna method for playing continuous random variables. Procedures for building imitation models for basic logistics subsystems. Procedures for estimating the parameters of the effectiveness of their work based on the simulation model. Annexes to the analysis of service systems, stock management systems and other logistics subsystems.

Main literature

Brodetsky G.L., Gusev D.A. Economic and mathematical methods and models in logistics. Optimization procedures - M.: Publishing Center "Academy", 2011.
Sable I.M. Method Monte Carlo. - M.: Science, 1980.

additional literature

1. Study of operations in the economy / ed. prof. N. Sh. Kremer. - M.: Uniti, 1997.

2. Mathematics reference for economists / ed. prof. V. I. Ermakova. - M.: Higher School, 1997

3. Thomas R. Quantitative analysis methods economic activity. - M.: Case and Service, 1999.

4. Gmurman V. E. Guide to solving problems on probability theory and mathematical statistics. - M.: Higher School, 1997.

^ Section 3. Method of rearrangement of arguments when optimizing expenses in logistics

Copyright OJSC TsKB "Bibcom" & LLC "Agent KNIGA-SERVIS" Ministry of Education and Science of the Russian Federation Yaroslavl State University. P. G. Demidov Department of Management and Entrepreneurship Yu. A. Abakumova Mathematical models in logistic solutions Methodical instructions Recommended by the University of Scientific and Methodological Council for students studying in the specialties Management of the Organization, Finance and Credit and under the Magistracy Program Management of Yaroslavl 2011 Copyright JSC " CKB "Bib's" & LLC "Agent KNIGA-SERVIS" UDC 33 + 51 BBK in 9 (2) 40Y73 A 13 recommended by the editorial and publishing board of the university as an educational publication. Plan of the 2010/2011 academic year Reviewer Department of Management and Entrepreneurship of the Yaroslavl State University. P. G. Demidova Abakumova, Yu. A. Mathematical models in logistics solutions: Methodical instructions A 13 / Yu. A. Abakumova; Yarosl. State University. P. G. Demidova. - Yaroslavl: Yargu, 2011. - 60 s. Methodical instructions are recommended for use in practical classes. Students are invited to perform tasks on the complex themes of the discipline to seminars. Designed for students studying by specialties 080507.65 Management of organization, 080105.65 Finance and credit and under the program of preparation of magistracy 080500.68 Management (Logistics discipline, "Mathematical models in logistics solutions", blocks of EN, SD), full-time, part-time and correspondence forms learning. UDC 33 + 51 BBK at 9 (2) 40Y73  Yaroslavl State University. P. G. Demidova, 2011 2 Copyright OJSC TsKB BIBKOM & Agent LLC KNIGA-SERVIS Introduction The integral nature of logistics managers and their broad erudition, the ability to make optimization decisions in order to save material and financial resources to coordinate work both inside the company and with its counterparties in the business allow high-qualification logists to successfully advance in career growth. In many companies, high-ranking logistics managers become presidents, vice-presidents and executive directors. The widespread use of mathematical methods is a prerequisite for the effective scientific and practical activities of the modern specialist. These methods acquire all more important When making management decisions, when to substantiate them is required to find rational and logical arguments. Thus, at the present stage of the economic development of the economy, the activities of any enterprise cannot be submitted without the use of logistics elements, and special attention should be paid to the main mathematical methods in the logistics. When studying the discipline "Economic and Mathematical Methods in Logistics" it is important to master not only the methods of quantitative (mathematical) modeling in the decision-making process, but also, taking into account the continued application of spreadsheets in the management practice, the implementation of the decisions made by Excel, and also to pay attention to the formation of systemic thinking in students associated with mathematical methods and models in logistics tasks, including the formation of a target comprehensive approach to the selection and use of models of optimization and optimal management of logistics systems on macro and micro levels; development of models and decision-making methods for the combination of criteria both in conditions of complete certainty and taking into account the stochastic nature of the external environmental parameters; Acquisition by students of specific skills to carry out the necessary settlements of both manual method and using a computer3 Copyright OJSC TsKB Bibkom & Agent LLC KNIG-SERVIS tera; Fixing practical interest in information about the current state of improving and developing mathematical models and methods used in logistics, in particular, in the field of artificial intelligence on the basis of the use of heuristic approaches. Considerable attention in the course is given to the information support of common and specific logistics models, interpretation, interpretation and convenient to perceive the presentation of results. Due to the diversity of tasks arising in the logistics (transport task, the task of the appointment, the problem of the shortest path, the communication network of minimum length, the maximum flow, the task of the commiveser, the task of a single average, the task of coverage, the basic concepts of the theory of graphs, the task of placement of production, the placement of service facilities , analysis of the placement of the plant and warehouses, factors of production and costs, decision-making, decision-making, temporary series, exponential smoothing, controlled forecast, network planning and management, assembly lines balancing, statistical quality control, stock management, imitation modeling, stock assessment, preventive Equipment maintenance, materials planning, short-term charts, system "Exactly on time", ABC analysis, mass service systems), Discipline "Economic and Mathematical Methods in Logistics" contains information from various sections and directions of modern mathematics, such as Total T Eoria Systems I. dynamic systems as the basis of mathematical models of logistics problems; Compressed and deployed mathematical models in logistics; operations research; Multi-criteria optimization; Theory of Probability and Mathematical Statistics; random functions and processes; Theory of decision making; game theory; methods of approximate calculations; imitation and statistical modeling; Models of artificial intelligence. 4 Copyright OJSC TsKB BIBCOM & Agency "Agent KNIGA-SERVIS" 1. Evaluation of economic costs of logistics services management costs for organizing the promotion of material flow from the enterprise - source of raw materials to the end user is the main one, if not the main thing, the task of logistics. However, control the logistics costs at any stage of their occurrence can only if they are accurately measured. The task of the logistics manager is to analyze the cost of each logistics chain, their differentiation, searching for improving the efficiency of activity. To develop a cost management system, it is necessary to classify logistics costs on various features and determine their role in the specified system. The distribution to constant and variables is very important in the cost management process, depending on the volume of enterprise activities, the logistics chain link. To constant costs (FC, English Fixed Cost) of production include costs, the value of which does not change with the change in production. They must be paid, even if the enterprise does not produce products (deductions for depreciation, rent, property tax, administrative and managerial expenses, etc.). Under the variables (VC, English. Variable Cost) means costs, the total value of which is in direct dependence on the volume of production and implementation, as well as on their structure in the production of several types of products. In the amount, constant and variable costs are general, or gross, production costs (TC, English Total Cost): TC \u003d FC + VC. (1) if permanent costs Unchanging, and variables grow as the production volume increases, it is obviously gross costs will also grow. The averages are the costs of 5 Copyright OJSC TsKB "Bibcom" & LLC "KNIGA-SERVIS" LLC, a unit of material strength. The average costs (AU, English. Average Cost) are calculated by dividing the cost of material flow (q, eng. Quantity) in a natural dimension. In this way, you can calculate the average permanent (AFC, English Average Fixed Cost), medium variables (AVC, English. Average Variable Cost): AFC \u003d FC / Q. (2) AVC \u003d VC / Q. (3) Average gross costs ( PBX, English. Average Total Cost) can be calculated in two ways: first, by dividing gross costs for the volume of material strength; Secondly, summing up the average constant and average variable costs. ATC \u003d AFC + AVC. (4) To effectively control the process of forming the cost of production, it is very important to properly determine the amount of constant and variable costs. There are three basic method of differentiation of costs: 1) the maximum and minimum point method; 2) graphic (statistical) method; 3) Method of least squares. 1. Method method and minimum point The calculation sequence is reduced to the following steps. 1. From the entire totality of the data, two periods are selected with the largest and smallest volume of material flow. 2. The value of variable costs is determined - this is average variable costs at the cost of the material strength: AVC  TC MAX TC Min, Q Max Q Min (5) where TSmax is the maximum gross costs, rubles; TSMIN - minimum gross costs, rub.; Qmax - Maximum 6 Copyright OJSC TsKB Bib's & Agent-Cervice Agent LLC Volumetrial Flow, Pieces; Qmin - minimum volume of material flow, pcs. 3. The total amount of constant costs is determined: FC \u003d TCMAX - AVC * QMAX. (6) 4. Since the dependence of the gross costs from the volume of the material flow is the linear equation of the first degree, the equation is recorded: Tc \u003d Fc + AVC * Q. (7) Consider the cost distribution mechanism in the following example. Example 1. When processing the material flow in the warehouse of the finished products of an industrial enterprise, stationary loading and unloading machines operating from the central power grid are used, storage space covers it. Data on the work of the warehouse for the year are presented in Table. 1. From the total amount of electricity costs, it is necessary to allocate constant and variable costs using the maximum and minimum point method. Table 1 Data on the work of the warehouse of finished products Month January February March April May June July August September The value of the consumption of material flow, electricity, thousand tons. Y. e. 16.5 5022.2 13.2 4867.8 16.5 5022.2 21.5 5253.9 18.2 5099.4 19.8 5176.6 14,9,4945.0 11.6 4790 , 5 12.4 4829.2 7 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" October November December Total average for a month 13.2 16.5 19.8 16,16 4867.8,5022.2 5176.6 5006.1 solution. 1. On the source data of the task, we will choose two periods with the largest and smallest volume of material flow (Table 2) - this is April and August. In April, the amount of variable costs will be maximum, and permanent is minimal. In August - on the contrary. 2. Determine the variable rate by formula (5): AVC  5253.9  4790.5 21.5  11.6 \u003d 46.8 y. d. e. / t. Table 2 Indicators 1. Volume of material flow, thousand tons 2. Electricity costs, thousand y. E. E. The value of the indicator The maximum minimum 21.5 5253.9 11.6 4790.5 3. Using formula (6), we define the total amount of constant costs: Fc \u003d 5253.9 - 46.8 21.5 \u003d 4247.7 you Su. e. 4. The dependence of the total costs of the volume of the material flow will have the following form: TC \u003d 4247.7 + 46.8 * Q. 2. The graphic method of finding the amount of constant costs. Two points are postponed on the chart, corresponding to the total costs for the minimum and maximum volume of Mate8 Copyright OJSC TsKB "Bibcom" & LLC "Agent KNIG-CERVIS" of the Rial Flow. Then they connect to the intersection with the axis of the ordinate on which the levels of costs are postponed. The point where the straight line crosses the ordinate axis shows the amount of constant costs, which will be the same for both maximum and the minimum volume of the material flow, since at this point the volume of the material stream is zero. The size of the average variable costs is determined by the formula AVC  TC MAX  FC, Q (8) where the TC is the average gross costs for the period, y. e.; Q is the average size of the material flow for the period, pcs. Example 2. Using the data of Example 1, allocate from the total cost of electricity constant and variable costs with a graphic method. Decision. According to the graph, we determine the level of level of constant costs at the volume of material flow, equal to zero. : TC \u003d 4250 thousand y. e. The rate of variable costs, determined by formula (8), will be AVC  5006.1  4250 \u003d 46.8 y. d. e. / t. 16,16 The dependence of the total cost of the volume of the material flow will be of the following form: TC \u003d 4250 + 46.8 * Q, thousand y. E. E. To distribute the total costs of variables and constant methods of least squares requires statistical data for several consecutive periods of time. The dependence of the total costs of the volume of material flow can be recorded in the following form: 9 Copyright OJSC TsKB Bib's & LLC "Agent KNIGA-CERVIS" TC \u003d FC + AVC * Q. (9) The rate of variable costs can be determined by the formula AVC   (Q)  (TC  T C)  (q  q) 2 (10) The total amount of variable costs will be: VC \u003d AVC * Q. (11) Then constant costs are determined by the FC \u003d TC - VC formula. (12) The use of the least squares method Although complicates the calculation procedure, but allows you to more accurately make the distribution of gross costs for variables and constant, as the initial data are used in the calculations for the entire period of the enterprise included in the logistics system. Example 3. Based on the data from Example 2, it is necessary to distribute the total costs to constant and variables using the least squares method. Decision. The sequence of determining the coefficients of equation (9) and the results of calculations to submit (students themselves) in Table. 3. Table 3 month Volume of production Q, thousand tons (q- q) (Q- Q) 2 January ......... Total average value of 10 TS gross consumption (TS) (TSK) 2 Copyright OJSC TsKB BBCOM "& LLC" Agent KNIGA-SERVIS "Determine the rate of variable costs: AVC \u003d 5315,24 / 113,56 \u003d 46.8 y. d. e. / t. The total amount of variable costs will be: vc \u003d 46.8 * 16,18 \u003d 757.2 thousand y. E. E. Then the constant costs will be equal: Fc \u003d 5006.1 - 757.2 \u003d 4248.9 thousand. E. E. In analytical form, total electricity costs can be represented as follows: a) according to the method of maximum and minimum point: TC \u003d 4247.7 + 46.8 * Q; b) according to the graphical method: TC \u003d 4250.4 - 46.8 * Q; c) according to the least squares method: TC \u003d 4248.9 + 46.8 * Q. Minor deviations in the magnitude of constant expenses occurred due to rounding intermediate calculations. 2. Determination of the optimal volume of material flow The main goal of the activity of any link Logistics system is the profit maximization. Therefore, the company is more profitable if the unit of material flow accounts for a smaller amount of constant costs. This can be achieved by increasing the volume of production and sales of products on existing production facilities. But, making a decision to increase production volumes, the manager must remember that it is impossible to increase the number of variable factors per unit of permanent, since in this case the law of decreasing return comes into account. 11 Copyright OJSC TsKB BIBKOM & LLC "KNIIG-CERVIS" LLC According to this law, starting from a certain moment, the consistent attachment of the units of the variable factor to the unchanged fixed factor will lead to the discontinuation of the growth of returns from it, and then to its termination. The cost of costs associated with the production of an additional unit of material flow, i.e., the ratio of the increase in the costs of the costs caused by their increase in the material strength is called limiting costs (MS, English. Marginal Cost). MS \u003d ΔVC / ΔQ (13) where ΔVc is an increase in variable costs; ΔQ - the increase in the material strength caused by changes in variable costs. Obtaining maximum profit is possible only under certain conditions: a combination of the volume of material strength, costs for its production and progress to the end user, as well as the sales price of the material strength should be such that the limiting costs for production and implementation have been equal to the utmost income (MR, English Marginal Return). Revenue income is an increase in revenue per unit of growth of material flow. Mr \u003d ΔTr / ΔQ, (14) where tr is the income of the enterprise for the period, d. E. Tr \u003d p * Q, (15) where p is the price of the implementation of the unit of material strength. It should be borne in mind that not any expansion of production entails an adequate increase in profits, since the change in costs occurs in different ways and the increase in production increases prices. 12 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" There are several ways to determine the optimal volume of material flow, in which the company will receive maximum profits: 1) accounting and analytical; 2) graphic; 3) Method of least squares. The essence of the accounting and analytical method consists in comparison of maximum income and limit costs. If the maximum income is more limit costs, then further growth increases increases the total amount of profit, and vice versa. Therefore, to maximize profits, the enterprise should increase the volume of the material flow produced until the marginal income above the limit costs, and stop its increase, as soon as the limit costs begin to exceed the final income. With a graphical method, it is necessary for one schedule to apply the curves of the limit costs and the limiting costs from the volume of material flow. The maximum profit is the point of intersection of the limiting curve with the limit income curve. After this point, the limiting curve is located above the limit income curve, from which it follows that each additional unit of material flow reduces profits and its production is ineffective for the enterprise. The essence of the method of least squares is that on the basis of mass data and using correlation-proof analysis, the dependence of the maximum income and limit costs from the volume of material flow are investigated. Example 4. Based on data on the work of the warehouse (Table 4), it is necessary to determine the optimal freight turnover (natural voluminous performance of the warehouse (bases, enterprises for supply), showing the amount of products sent for a certain period of time), in which the warehouse will receive the maximum profit . Data Table. 4 shows that the most favorable amount of cargo turnover is 8 thousand tons. The limit costs are then superior to the marginal income, which is clearly unfavorable for the enterprise 13 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIG-SERVIS". Consequently, the warehouse is economically beneficial to post up to 8 thousand tons of material resources. The graphic method also gives the same result. Up to 8 thousand tons of limiting curve (MC) is lower than the maximum income curve and therefore each additional unit of cargo turnover increases the amount of profit. Table 4 Initial data for calculating the optimal cargo turnover of automatic transaction, the proportion of the incidence of costs, thousand-like thousand tons of storage (reversals. U. E. E. income, which has a year 1 t, ka), thousand . d. e. thousand ki, thousand y. d. e. y. d. e. y. d. e. y. d e. 1 0 1 2 3 4 5 6 7 8 9 10 2 310 300 290 280 270 260 250 240 230 220 210 3 0 300 580 840 1080 1300 1500 1680 1840 1980 2100 4 205 385 550 705 850 985 1125 1275 1430 1615 1805 5 6 7 Table data and graphics make it possible to conclude that the relationship between the limit income and the volume of cargo turnover can be described by the straight equation: Mr \u003d a + b * Q, where Mr is a marginal income per unit of production; Q is a warehouse cargo in physical terms. Using the method of least squares, we define unknown parameters A and B. 14 Copyright OJSC TsKB Bib's & BBC & Agent LLC Mr \u003d 320 - 20 * x. The dependence of the limit costs from the production volume can be described by the Parabola equation: MC \u003d A + B * Q + C * Q2. In our example, it will have the following form: MS \u003d 203.75 - 24.527 * Q + 2.3674 * Q2. Having equated marginal income and limit costs, you can find the value of the optimal cargo turnover, which will ensure the maximum amount of profit: 320 - 20 * Q \u003d 203.75 - 24,5270 + 2,3674 * Q2; Q \u003d 8.028 thousand tons. These calculations show that the optimal volume of cargo turnover is 8 028 tons. With this volume, the revenue will be: r \u003d 230 8.028 \u003d 1846.44 thousand y. e. The dependence of the total amount of costs from the volume of cargo turnover is the following form: TC \u003d 67.727 + 154.32 * Q. Storage costs will be: TC \u003d 67,727 + 154.32 * 8.028 \u003d 1306.61 thousand. e. Profit will be equal to: p \u003d tr - Tc \u003d 1846,44 - 1306.61 \u003d 539.83 thousand y. D. E. 15 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" Consequently, this warehouse can increase the volume of cargo turnover to 8 028 tons, provided that the cost of storage 1 tales will not increase. 3. The calculation of the break-even point of the functioning of the microloistic system in the process of planning production activities The management of the enterprise included in the logistics system is to be answered by the following questions: - What amount of products must be produced to not only cover all costs for production, but also profit; - What the price must be installed on realized products; - At what level it is necessary to maintain costs to remain competitive in the market. Logistics Manager can get an answer to the questions set by calculating the break-even point of production and sales of products. This point is also called "dead point", "critical point", "threshold of profitability", "point of self-sufficiency". The break-even point corresponds to such a volume of material strength, in which the firm covers all constant and variable costs, without any profit. In terms of value, the break-even point is determined by the formula Q * Condition \u003d Fc / (1 - VC / TR)), (16) where Q * is the optimal volume of material strength in terms of value; FC - constant costs in monetary units; THR - the income of the enterprise in monetary units; VC - full variable costs in monetary units, Vc \u003d zq; Z - Specific value costs (per unit Mate16 Copyright OJSC TsKB Bibsky & Agency "Agent KNIG-SERVIS" Rialopotok), in monetary units; Q is the volume of material strength in kind (pcs., T, etc.). In kind of material strength at the break-even point, Q * NAT \u003d Q * We / P or Q * NAT \u003d FC / (P - Z). (17) Determine the break-even point can also be using a graphical method. To do this, you need to combine four lines on one chart: FC - line permanent costs , VC - line of variable costs, TC - line of common costs, TR - line of general revenue (Fig. 1). TS TC VC FC Q * Fig. 1. Determination of the break-even point Example 5. The production company "Grand" plans to release new products. The predicted annual demand is 600 units. The constant costs associated with the release of such a volume of products are at the level of 12,000 y. e. a year. The planned variable costs per unit product range to 42 y. E. E. Analysis of competitive firms producing similar products showed that the average level of vacation tax is 67 y. d e. per unit. It is necessary to define the "break-even point" in kind and value terms. Decision. Cumulative variable costs associated with the release of 600 units. Products will be: vc \u003d z q \u003d 42 600 \u003d 25 200 y. E. 17 Copyright OJSC TsKB BIBKOM & Agent "Agent KNIG-SERVIS" After the sale of products, the company will receive a revenue in the amount of R \u003d p Q \u003d 67 600 \u003d 40 200 y. E. E. Then in the value-readability point of the activity of this enterprise can be determined by formula (16) Q * cost \u003d 12,000 / (1 - 25 200: 40 200) \u003d 32 160 y. e. In the natural expression "break-even point" equal to Q * NAT \u003d 32 160/67 \u003d 480 units. The approximate value of the optimal volume of production can be defined graphically. The definition of "break-even point" is very relevant in market conditions, as it allows enterprises included in the logistic chain to reasonably predict break-even activities. Moreover, when determining the development strategy of the enterprise, the logistics manager must take into account the value of the stock of financial strength (TWF), i.e., assess the volume of material strength over the level of break-even. Assessment of the stock of financial strength is carried out according to the following formulas: - in value terms: SFP \u003d R - Q * Cost - as a percentage: ZFP  R  q  Cost  100 0 0 R (18) (19) Another important value you can Use to characterize the cost of the logistics system, is the value of the deposit on the coating. The contribution to the coating is defined as the difference between the revenue of the enterprise (the link of the logistic system) from the sale of products for a certain period and rear. The values \u200b\u200bof the total contribution are distinguished and the specific contribution per unit of production (CONST) const \u003d R - Vc \u003d pq- zq \u003d (p - z) q, Сont \u003d p - z (20) (21) Using the "Contribution to the coating ", It is possible to determine the effect of changes in variable and constant costs of the functioning of the logistics system by the magnitude of the profit obtained by this system. To do this, it is necessary to calculate the so-called effect of the production lever. The effect of the production lever is called such a phenomenon when any change in sales revenue generates an even stronger change in profits. The quantitative impact of the operational lever can be expressed by the following formula: EPR \u003d const / P, (22) where P is a profit gained by the company, y. E. E. Knowing the value of the surgical lever can be determined by how much interest will increase the profit of the enterprise if the percentage of income growth is known:% n \u003d EPR% TR, (23) where% P is the percentage of enterprise profits; % Tr - percentage of income growth. Example 6. Using the data of Example 5, it is necessary to calculate the stock of the financial strength of this enterprise (in value terms and percentage), as well as the impact of the production lever for profit, if it is known that income growth will be 7.2%. 19 Copyright OJSC TsKB BIBKOM & Agent LLC KNIG-CERVIS. The supply of financial strength Determine by formulas (18), (19): SFP \u003d 40 200 - 32 160 \u003d 8 040 y. e.; SFP \u003d 20%. The profit received by the company "Grand" from the release of new products at a volume of implementation of 600 units will be: n \u003d 40 200 - 12,000 -25 200 \u003d 3,000 y. E. E. The effect of the impact of the production is determined by the formula (22) and is equal: the EPR lever \u003d (40 200 - 25 200) / 3,000 \u003d 5. Therefore, under the effect of the effect of the production lever, with an increase in income on 7.2% enterprises It will increase by 36%:% n \u003d 5 * 7.2% \u003d 36%. Having determined the impact of the cost of profit costs using the effects of the operational lever, it can be concluded: the higher the specific weight of the constant costs and, accordingly, below the proportion of variable costs with a constant sales volume, the stronger the effect of the operational lever. Therefore, constant costs must be all the time under the close attention of the manager, since the increase in their specific gravity increases the operation of the operating lever, and this is a decrease in business activity of the enterprise can lead to large profits. However, when making a decision on an increase in production volumes, it is necessary to remember the following: as the effect of the production lever is removed from the break-even point, the effect of the production lever will be reduced until the increase in the volume does not require an increase in constant costs. This is due to a decrease in permanent cost per unit of products. In this case, it will be necessary to calculate the new threshold of profitability of the micro-system system. 20 Copyright OJSC TsKB "Bibcom" & LLC "Agent KNIG-CERVIS" 4. The adoption of logistics solutions in conditions of uncertainty and risk Even under the most favorable economic conditions for the functioning of the logistics system, the possibility of occurrence of crisis phenomena is always preserved. Such an opportunity is associated with risk. In the most general form, the concept of "risk" is characterized as uncertainty associated with the possibility of occurrence during the implementation of the project of adverse situations and consequences. The source of risk is uncertainty, under which the absence of complete and reliable information is understood. On this basis, all logistic decisions are divided into three groups: 1) adopted under certainty; 2) accepted in probabilistic definiteness (risk-based); 3) taken in conditions of complete uncertainty. 4.1. Analysis and adoption of logistics solutions in conditions of certainty is the easiest case. The number of possible situations (options) and their outcomes are known. The probability of each event is equal to one. You need to choose one of the possible options. The degree of complexity of the selection procedure in this case is determined only by the number alternative options . Mathematical models of the studied phenomena or processes can be given in the form of tables, whose elements are the values \u200b\u200bof the private criteria for the efficiency of the logistics system calculated for each of the compared strategies with strictly specified external conditions. For the conditions under consideration, decision making can be made: - one criterion; - in several criteria. 21 Copyright OJSC TsKB BIBKOM & LLC "KNIIG-CERVIS Agent" example 7. One of the firms need to choose the optimal strategy to ensure new production with equipment. With the help of experimental observations, the values \u200b\u200bof the private criteria for the functioning of the corresponding AIJ equipment manufactured by three plants were determined. The source data is presented in Table. 5. Table 5 Data for selecting an optimal strategy in conditions of complete definiteness Equipment options (strategies, solutions) Private equipment efficiency criteria * Productivity, equipment, equipment. d. e. y. d. E. Factory A11 \u003d 5 A12 \u003d 7 Energy intensity, y. e. A13 \u003d 5 Equipment number 1, (x1) Equipment of the plant A21 \u003d 3 A22 \u003d 4 A 23 \u003d 7 No. 2, (x2) Equipment of the plant A31 \u003d 4 A32 \u003d 6 A33 \u003d 2 No. 3, (x3) * Private values Criteria are given in conventional units. reliability, y. e. A14 \u003d 6 A24 \u003d 3 A34 \u003d 4 Based on expert estimates, the weight of the private criteria λ i, j \u003d 1.4: λ1 \u003d 0.4 was also determined; λ2 \u003d 0.2; λ3 \u003d 0.1; λ4 \u003d 0.3. The choice of an optimal strategy (equipment option) by one criterion in this task does not cause difficulties. For example, if you evaluate equipment for reliability, the equipment of the plant No. 1 (strategy X1) will be recognized as the best. The choice of the optimal solution on a set of several criteria (in our example in four criteria) is a multi-criteria problem. 22 Copyright OJSC TsKB BIBKOM & Agent "Agent KNIG-SERVIS" One approaches to solving multi-criteria management tasks is associated with the procedure for formation of a generalized function, monotonically dependent on criteria. This procedure is called the procedure (method) of criteria coagulation. There are several coagulation methods, for example: - the method of additive optimization; - Method of multipurpose optimization, etc. The generalized function function can be used to coagulate the private optimality criteria, if: 1) private (local) criteria are quantitatively commensurate by importance, i.e., each of them can be put into line with a number of λj, which is numerically characterizes its importance in relation to other criteria; 2) Private criteria are homogeneous (have the same dimension. In our example, the criteria for the equipment and performance of equipment in the conditional monetary units will be homogeneous). In this case, to solve the problem of multicriterial optimization, the application of an additive optimality criterion is fair. The task. Suppose, in example 7 it is necessary to choose the optimal version of the equipment in two homogeneous local criteria: - performance, y. e.; - cost of equipment, y. D. E. On the basis of expert estimates, the weight coefficients of these two private criteria were determined: λ1 \u003d 0.667, λ 2 \u003d 0.333. Calculate an additive optimality criterion for three options. Using the example 7, to determine the optimal strategy for selecting equipment from three possible (T \u003d 3), taking into account the four local criteria (n \u003d 4). Decision. 1. Determine Max and Min of each local criterion: 23 Copyright OJSC TsKB "Bibcom" & LLC "KNIIG-SERVIS" LLC 2. When solving the problem, the first (performance) and the fourth (reliability) criteria are maximized, and the second (equipment cost) is minimized. and the third (energy intensity. 3. Based on the principle of maximizing the effectiveness to normalize the criteria. 4.2. Forecasting of material stream and turnover from a regional warehouse for predicting turnover and material stream of a regional warehouse should be selected suitable from known mathematical equations (direct, hyperbola, parabola, etc.) . These equations are determined on the basis of the graphs that are built under the reporting data (dynamic rows). Consider these equations. The equation direct has the following form: Wow \u003d a + b x, where Wow is a resulting feature; x - time period; a and b - Parameters direct. Finding parameters A and B is made on the basis of alignment by the method of smallest squares, which leads To the system of two linear equations with two unknowns. To facilitate finding parameters A and B, you can simplify the system. For this, the countdown should be guided so that the sum of the time indicators of the row (σx) was zero. Such a convention is quite admissible due to the fact that the beginning is selected arbitrarily. In order for σx to zero, in the ranks with an odd number of members, the central member is taken for zero, and members coming from the center (in the column) are obtained from -1, -2, -3 (with a minus sign), and down + 1 , +2, +3 (with a plus sign). For example, a row is seven members (-3, -2, -1 up) (+ 1, +2, +3 down). If the number of members of a series is even (for example, six), it is recommended to increase the members of the upper half of the series (from the middle) of 24 Copyright OJSC TsKB Bibkom & Agent "Agent KNIG-SERVIS" numbers -1, -3, -5, etc. d., members of the lower half (from the middle) +1, +3, + 5, etc. in both cases σx \u003d 0. It is necessary to know the values \u200b\u200bσu, σx2, σhu. Example 8. For the period from 1998 to 2004. There is a dynamic series of material stream of regional warehouse (Table 6). Make a forecast of material stream for 2005-2007. Table 6 Material flow for the period 1998-2004. (Usl. Unit.) 1998. 130 1999 148 2000 170 2001 190 2002 210 2003 225 2004 250 decision. According to Table. 6 Build a schedule for the dynamics of changes in the material strength for the period 1998-2004. From this schedule you can see a trend change in turnover. She walks in a straight line. Therefore, the relationship between these features can be described by the Equation of Wow \u003d a + BX, where Wow is the material strength of the regional warehouse, SL. units; x - period under review; a - turnover at zero period (x \u003d 0); B - annual increase. To calculate these values, we will be Table. 7 (Lines Fill out students independently). Table 7 Calculation of the parameters of the equation direct to predict the material strength in 2007. Year turnover, SL. units, in x x2 Hu uh \u003d 189 + 19.8 x found values \u200b\u200bwe substitute in formula A and B, we get: the equation of our direct will be 25 Copyright OJSC TsKB "Bibcom" & LLC "KNIG-SERVIS" LLC \u003d 189 + 19.8 * x. Calculate the theoretical levels of the number for each year. Almost complete coincidence of the results of empirical and theoretical equations (incontrollence of 1 unit. Units) indicates the correctness of the calculations produced. The comparison of the second and sixth columns for each year shows very minor deviations of the calculated levels from the actual, which confirms the correctness of the choice of the mathematical equation. To predict the material strength, it is necessary to continue the third column (period under review) by the numbers following the specified number. In our case, this is 3, then the period under consideration will be 4, 5, 6, etc., for 2007 x \u003d 6, then U2007 \u003d 189 + 19.8 - 6 \u003d 307.8. Example 9. Task on best use Available rolling stock. Of the two terminals, the same type of cargo on tractors with trailers is exported. It has been established that for the export of cargo from the first terminal, one tractor must have two trailers, and the second is four. The amount of cargo transported by one tractor from the first terminal is 12 tons, and from the second - 20 tons. Autorashide has 8 tractors and 24 trailers. It is required to place the tractor and trailers in such a way as to ensure their maximum performance. Information about vehicles is given in Table. 8. Table 8 Vehicle information Name Realization of vehicles transport Terminal 1 Terminal 2 Tractor means 1 1 Trailers 2 4 26 Availability of vehicles 8 24 Copyright OJSC TsKB Bib's & Agent "Agent KNIG-CERVIS" Condition of the task can be recorded by equations : x + y \u003d 8 - equation for tractors; 2x + 4u \u003d 24 - equation for trailers, where X is the number of tractors on the terminal 1; U - the number of tractors on the terminal 2. Numerous studies show the effectiveness of the implementation of the main logistics concepts. Thus, the introduction of the system of "Planning the need for materials" (MRP), in which a flexible mechanism is formed on the basis of computers, which provides dynamic management of material flows in real time, allows:  to increase the timeliness of providing materials to 95-97% (instead of 85-90 %);  reduce the level of finished products in warehouses by 10-12%;  reduce incomplete production by 20-30%;  Reduce the number of distribution disorders by 30-25%. The cost of implementing the specified system in a large firm amounted to 200 thousand dollars, and savings over the year of operation - about 1 million dollars. The results of the analysis for the implementation of the concept of "exactly on time" in 100 enterprises, where the specified system functioned from 2 to 5 years, allowed to establish:  Incomplete production reserves decreased by more than 80%;  reserves of finished products decreased by about 33%;  Volumes of non-productive reserves (materials and obtained on partitions) range from 4 hours to 2 days. Compared with 5-15 days. before the introduction of the method;  The duration of the production cycle (the term for the implementation of the tasks of the entire logistics chain) decreased by 40%;  Production flexibility has significantly increased. The ratio of natural indicators at the automotive plants using traditional methods of production organization ("General Motors") and the logistics concept "exactly on time" ("Toyota" illustrates the advantages of a new approach. 27 Copyright OJSC TsKB Bib's Bib's & LLC "KNIGA-CERVIS" LLC 5. The ABC method in logistics is widely used by the method of control and stock management - the ABC method that also received the name "Pareto rule" or "Rule 80/20". The ABC method is a method for forming and monitoring the state of reserves, which consists in dividing the nomenclature of N realized inventive material values \u200b\u200binto three unequal subsets A, B and C on the basis of a certain formal algorithm. The essence of this method is that the entire nomenclature of material resources is located in descending order of the total value of all positions in the warehouse. At the same time, the price of the unit is multiplied by total amount And make up a list in descending order of works. Next, all positions of the nomenclature are subdivided into three groups - A, B and C. The positions of the nomenclature, attributed to the group A, are few, but they account for the prevailing part of the funds invested in stocks. This is a special group from the point of view of determining the value of the order for each position of the nomenclature, control of the current stock, delivery costs and storage. The group B belongs to the positions of the nomenclature, occupying the average position in the formation of stocks of the warehouse. Compared to the positions of the group's nomenclature, they require less attention, the normal control of the current stock in the warehouse and the order time is performed. The group C includes the positions of the nomenclature, which make up most of the stocks: they account for a slight part of the financial resources invested in stocks. As a rule, the positions of the group with no current accounting are carried out, and the availability check is carried out periodically; The calculations of the optimal value of the order and the order period are not performed. Task 1. Based on data 2, 3, 4 columns Table. 9 distribute the range of spare parts and aggregates of Savropol-Lada OJSC using the ABC graphic method. The results obtained are calculated in 5, 6, 7 columns. 28 Copyright OJSC TsKB BIBKOM & Agent "Agent KNIGA-CERVIS" Table 9 Example of using the ABC method for separating the range of spare parts and aggregates of Zavropol-Lada OJSC Details 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 25 NAME DETAILS 2 PPC valves cylinder block piston cylinder head finger piston crankshaft shaft generator steering rod pulley steering shaft disc clutch battery filter oil pads brake carburetor bushing guide liners connecting rolled large pump thermostat Steering Tree Pillow Water Pump Chain Candle Roller Tension Zibler Consumption Price Caller Qi Σi,% of parts, Details, price, price (qi), pcs. rub. rub. % 3 4 5 6 7 510 4818 690 298 58 2791 903 170 25 4500 1091 117 87 597 145 101 866 1085 110 316.67 180 68 1490 250 641 26,67 585 66,92 40 8704 806,67 3,44 330 89 138 279 84 944 174 180 603 265 3443 208 100,83 333 29,17 158 151 41,67 94 7 29 Copyright OJSC TsKB Bibsky & Agent KNIGA-SERVIS LLC 1 27 28 29 30 31 32 33 34 35 16 37 38 39 40 44 42 43 44 45 47 48 49 50 54 52 53 54 55 56 57 58 2 3 Gasket 1256 gear small 783 pump fuse 105801 shaft primary 79 connecting rod 181 relay 385 wiper ramp 14 rings 82 25 belt gear 166 hose Brake 505 small pump 91 gear 158 intermediate 139 shaft drive left 10 rings 301 piston shock absorber 179 clamp 5838 sprinkler 66 drive right 8 straps 384 fan sleeve 27 plug 1329 pistons 8 tube 2454 Drainage bolt 1262 bearing 1177 puck 2326 nut 2383 crankshaft yard- 5344 Shaft sleeve 10522 restrictive hairpin 1620 fitting 1014 total 167565 4 18.4 27.5 0.2 261.25 112 50 1363 760 110 33,33 175 95 , 28 100.83 1161 37.2 60.61 1,67 146.67 1170 21.67 238 3,33 466 1.34 1.1 0.86 0.33 0.24 0.02 0.01 0, 02 0.02 30 5 6 7 Copyright OJSC TsKB "Bibcom" & LLC "KNIIG-CERVIS" Agent "Task 2. Calculate the calculation according to the ABC method using the analytical technique. Table 10 Source Data No. П / n argument, xi 1 2 1 0.02 2 0.03 3 0.05 4 0.07 5 0.09 6 0.1 7 0.12 8 0.14 9 0,16 10 0.17 11 0.19 12 0.21 13 0.22 14 0.24 15 0.26 16 0.28 17 0.29 18 0.31 19 0.33 20 0.34 qσi, 3 0.57 0.61 0.65 0.69 0.71 0.74 0.76 0.82 0.83 0.84 0.85 0.85 0.86 0.87 0, 87 0.88 0.89 № The value of p / n argument, xi 4 5 21 0.36 22 038 23 0.40 24 0.41 25 0.43 26 0.45 27 0.47 28 0.48 29 0, 5 30 0.52 31 0.53 32 0.55 33 0.57 34 0.59 35 0.6 36 0.62 37 0.64 36 0.66 39 0.67 40 0.69 qσi, No. P / P 6 0.89 0.90 0.91 0.91 0.92 0.92 0.93 0.93 0.94 0.94 0.95 0.95 0.96 0.96 0.96 0.97 0.97 0.98 0.98 0.98 7 41 42 43 44 51 52 53 54 55 56 57 58 The magnitude of the argument, xi 8 0.71 0.72 0.74 0.76 0, 78 0.79 0.81 0.83 0.84 0.86 0.88 0.95 0.97 0.98 1 qσi, 9 0.98 0,986 0,988 0,991 0,993 0,995 0,996 0,997 0,998 0.9999 0.999 0.9999 0.999 0.9996 6. Selection of logistics intermediaries The most common task for most functional logs Sticks ("basic and key logistics activities") is the choice of logistics intermediaries (LP): suppliers, freight forwarders, carriers, etc. It is obvious that if there is a competition in all links of the logistics system31 Copyright OJSC TsKB Bibkom & Agent LLC KNIG-SERVIS "We (ZlS) there is a multivariate, expressing both in a large number of LPs that can perform appropriate logistics operations and the presence of alternative solutions formed from various ZLS. Issues of the choice of LP, discussed in detail in almost all logistics works, differ mainly in the depth of study and the presence of examples of calculations. The calculation includes two stages. At the first stage, each criterion is assigned a certain "weight", reflecting its relative importance for the shipper. In this example, the most important criterion has "weight" or a discharge equal to 1. At the second stage, the carrier's effectiveness for each criterion is also estimated, and a three-point scale is also used. The rating for each criterion is determined by multiplying the estimates of "relative importance" and "efficiency", and the final rating of the carrier - the addition of estimates. Task 1. During the first two quarters of the year, the company received from suppliers No. 1 and 2 products A and B. It is necessary to decide on the extension of the contract with one of the suppliers by the quality criterion, reliability and delivery price. The weight of the criteria is established by the expert and amounted to 0.35 respectively; 0.25 and 0.4. The weighted average price increase for the supplied goods supplied goods was 115 and 124%; The growth rate of the supply of goods inadequate quality - 96 and 105%; The growth rate of medium late is 111 and 115%, respectively. Task 2. Table 11 Criterion Price quality Reliability Evaluation of suppliers for this criterion Supplier A Supplier B 2 10 7 8 4 3 32 Copyright OJSC "TsKB" Bibcom "& LLC" Agent KNIGA-CERVIS "To evaluate suppliers A and B criteria: Price (0.6), quality (0.2), delivery reliability (0.2). In brackets indicated the weight of the criterion. Estimation of suppliers According to the results of work in the context of the listed criteria on the 10-point system is given in Table. 11. Which suppliers should prefer? Task 3. The logistics service of the industrial enterprise "Corkun", which produces consumer goods, the market of timber market was conducted. As a result, the three most attractive suppliers were selected. The assessment of the suppliers was carried out on a 10-point scale for seven criteria: I - the timeliness of the supply; II - the quality of the supplied goods; III - terms of payment (cash, cashless payments, notes, etc.); IV is the financial state of the supplier; V - price factor; VI - the safety of the cargo; VII - the possibility of unscheduled supplies. The results of the selection and weight of the private criteria obtained by the expert route are presented in Table. 12. Table 12 Results of expert selection of suppliers No. Criterine II III IV V VI VII Specific value Criterody A at 0.15 0.13 0.08 0.15 0.20 0.12 0.17 7 8 6 9 10 7 6 8 6 9 7 8 10 7 With Supplier D E FG H 7 6 9 8 7 6 8 10 8 7 7 5 9 6 7 8 9 10 9 8 6 6 9 6 8 9 6 7 9 10 5 6 8 9 7 33 8 9 8 6 7 9 10 Copyright OJSC TsKB BIBCOM & Agent LLC KNIIG-SERVIS It is necessary to decide on the conclusion of a contract with one of the suppliers (Table 13). Table 13 Option number Supplier Number 1 2 3 1 A, B, C 16 2 A, B, D 17 3 A, B, E 18 4 A, B, F 19 5 A, B, G 20 6 A, B, H 21 7 B, C, D 22 8 V, C, E 23 9 B, C, F 24 10 B, C, G 25 11 V, C, H 26 12 C, D, E 27 13 C, D, F 28 14 C, D, G 29 15 C, D, H 30 supplier 4 D, E, FD, E, GD, E, HA, C, DA, C, EA, C, C, DA, C, EA, C, FA, C, GA, C, C, HB , D, eb, d, fb, d, gb, d, ha, d, fb, e, fd, f, d, fb, e, fd, f, h 7. Tasks and business games Task 1. At the Woodworking Plant "Sunrise" One of the cost of the cost of finished products is made up Water costs. In this case, part of these costs is a constant value and includes the cost of maintaining the territory and auxiliary premises, and the other part is variable, includes the cost of processing timber. It is necessary using the data on the operation of the plant for six months (adj. 1), to allocate water supply costs from the total amount of constant and variable costs: - using the maximum and minimum point method; - using the graphical method; - Based on the method of smallest squares. 34 Copyright OJSC TsKB BIBKOM & Agent "KNIGA-SERVIS LLC" Task 2. Fenix \u200b\u200bcompany, providing warehouse services to the city's trade firms, decided to open a new warehouse. The projected data on the work of the new warehouse is presented in the ad. 2. It is necessary to determine the optimal volume of cargo turnover in the warehouse, in which the company "Phoenix" will be able to obtain the maximum profit level: - accounting and analytical method; - graphic method; - method of smallest squares. Task 3. The company "North" owns a network of warehouses, leased to organizations engaged in wholesale trade. The analysis of the city's transport markets market showed that you can create your own vehicle fleet. Predicted transport work (P); constant costs (FC) associated with the content of vehicle park; Variable costs (z) per unit of transportation work and transport tariff (T) per ton-kilometer are shown in ad. 3. It is necessary to determine using the "break-even point" the feasibility of creating a fleet of rolling stock: - in value terms; - in physical terms. Task 4. In paragraphs A and B are 150 and 90 tons of fuel, respectively. Paragraphs 1, 2, 3 are required, respectively, 60, 70, 110 tons of fuel. The cost of transporting 1 tons of fuel from paragraph A to paragraphs 1, 2, 3 is 60, 10, 40 thousand rubles. For 1 t, respectively, and from point in paragraphs 1, 2, 3 - 120, 20, 80 thousand rubles. For 1 t, respectively. Make a combustion plan, minimizing the total amount of transportation costs. Task 5. Three plants produce trucks that are sent to four consumers. The first plant supplies 90 truck platforms, the second - 30, the third - 40 platforms. For consumers required: the first - 70 platforms, the second - 30, the third - 20, the fourth - 40 platforms. The cost of transporting one platform between each supplier and each consumer (y. D.) Is indicated in Table. 14. 35 Copyright OJSC TsKB BIBKOM & LLC "KNIIG-SERVIS Agent" Table 14 Supplier II III III 1 Consumer 2 3 4 18 10 16 20 20 22 10 30 20 14 40 10 Make an optimal delivery plan for trucks. Task 6. When building a trunk road, it is necessary to align the ones on the highway to the level of the main road and cut the protrusions in some places. Cutted soil are filled with potholes. Pound transport is carried out by trucks of the same load capacity. The distance in kilometers from sections to chosel and the scope of work is indicated in Table. 15. Create a transport plan that minimizes the overall mileage of trucks. Table 15 supplier A B with the required amount of soil, T consumer II III III 1 2 2 1 1 2 100 140 3 3 4 60 Availability of soil, T 110 130 20 Task 7. Cargo stored in three warehouses and requiring transportation 60, 80 , 106 cars, respectively, need to be transported to four stores. The first store requires 44 cargo machine, the second - 70, the third - 50 and the fourth - 82 cars. The cost of a mileage of one vehicle for 1 km is 10 thousand rubles. The distance between the warehouses and shops are shown in Table. 16. Make an optimal shipment plan from warehouses in stores. 36 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" Table 16 Warehouse 1 2 3 1 Shop 2 3 4 13 2 12 17 7 18 6 10 2 8 41 22 Task 8. In warehouses A, B, with A varietal grain, respectively, in the amount of 100, 150, 250 tons, which you need to deliver into four points. Paragraph 1 requires 50 tons, paragraph 2 - 100, paragraph 3 - 200, paragraph 4 - 150 tons. The cost of delivery of 1 tons of grain from the warehouse A to these items, respectively, 80, 30, 50, 20 thousand rubles; From the warehouse in - 40, 10, 60, 70 thousand, from the warehouse C - 10, 90, 40, 30 thousand rubles. Make up the optimal plan for transportation of grain subject to the minimum cost of transportation. Task 9. The plant has three shops A, B, C and four warehouses 1, 2, 3, 4. Workshop A produces 30 thousand products, shop 5-40 thousand, C - 20 thousand products workshop. The capacity of the warehouses is still characterized by the following indicators: a warehouse 1 - 20 thousand products, a warehouse 2 - 30 thousand, a warehouse 3 - 30 thousand and a warehouse of 4 -10 thousand products. The cost of transportation of 1 thousand products from the workshop A in warehouses 1, 2, 3, 4, respectively, 20, 30, 40, 40 thousand rubles, from the workshop for 1 thousand products, respectively, 30, 20, 50, 10 thousand rub., And from the workshop of C - respectively, 40, 30, 20, 60 thousand rubles. To make a plan for transportation of products, in which the cost of transporting all 90 thousand products would be the smallest. Task 10. There are five brick plants on the construction site, the production of which is 600, 600, 500, 650, 700 tons per day. These plants satisfy the needs of seven construction sites, respectively, in the amount of 350, 450, 300, 450, 300, 200, 200, 450 tons. The remaining brick is sent by railway In other areas. Brick on construction objects is delivered by car. The distance in kilometers from plants to objects is given in Table. 17. 37 Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" Table 17 Factory 1. 2. 3. 4. 5. B2 B2 B3 Object B4 14 13 18 14 11 5 4 8 7 15 10 11 14 13 14 8 9 18 19 25 B5 B6 B7 16 20 23 15 19 10 12 13 16 15 25 23 21 23 20 Determine from which plants and which objects should be delivered to the brick, as well as what plants and in what quantity you should send brick to other Areas for transportation costs for brick delivery by motor transport were minimal. The cost of carriage of 1 tons of brick vehicles satisfies the condition C \u003d A + D * (L - 1), where a \u003d 25 thousand rubles., D \u003d 5 thousand rubles, L - mileage, km. 7.1. Business game 1 "Productivity, investment, division of labor" Economic model. Performance growth can be achieved by various methods, among which primarily allocate: 1) specialization and division of labor; 2) the introduction of new technologies; 3) Investments in human capital. The concepts of division of labor and specialization are closely related to each other. The separation of the production process on the operation, on the execution of which a separate worker specializes, shop, firm, etc., allows the goods to produce the most rationally, with the lowest costs. Specializing in, i.e., participating in the division of labor, people refuse the desire to independently produce all the necessary benefits and focus on those that manage to produce with the smallest costs. Producing these benefits in larger quantities Than 38 Copyright OJSC TsKB Bibsky & Agency "Agent KNIG-CERVIS" required, participants in market relations are calculated in return for other necessary goods and services. Another important factor affecting productivity is the improvement of machinery and equipment, the introduction of new technologies. The use of technology, new materials and technologies expands the physical possibilities of a person, increasing productivity repeatedly. At the same time, the purchase of new equipment requires additional investments of resources distracted from current consumption per future return. The quality of labor resources also affects performance. The effectiveness of the performance of production tasks depends on the level of education, training, the health of the employee. Therefore, the investment of resources into human capital (education, advanced training, medical care of employees) is the main factor in improving productivity. Performance is one of the most important indicators illustrating the cost ratio and obtained results. Under costs it is understood as the use of a certain amount of resources in production. Total production costs make up the cost of production, often called costs. With the change in production, the cost of production unit changes. This is due to the fact that in the structure of production costs, fixed costs are distinguished, which do not vary depending on the production volume, and variable costs, the size of which depends on it. Description of the game. The exercise is based on the business game "Book Factory", in which the production of books is simulated. Comparison of the results of book publishing activities in various ways of organization of production makes it possible to demonstrate the benefits of division of labor and specialization, to introduce listeners with some important concepts necessary for analyzing production activities (cost of production, investment, etc.). 39 Copyright OJSC TsKB "Bib's" & LLC "Agent KNIIG-CERVIS" course of the game. At the beginning of the class it is necessary to remind students the concept of limited resources. It is important to pay attention to how people take into account the fact of limited resources in their economic activity. It should be discussed that in business people always try to achieve the greatest return on the smallest number of resources; Let students prove (or refute) this idea on the examples. To spend the business game "Book Factory", the audience needs to be divided into groups of 4-5 people. Each of the groups is a publishing company and should choose the name of the company. The purpose of the established companies is the manufacture of the maximum number of books. At the same time, at the end of each period of the game (duration of 3 minutes), only ready-made quality products are taken into account, the remaining semi-finished products are withdrawn. The technology of manufacturing a book is as follows: a sheet of paper is folded in half and then bursts on the collar; It takes shape again and breaks again. The resulting 8 leaves fold again in a 16-page book. It is necessary to numbered all even internal pages (from the 2nd to 14th), on the cover to write the company's name and bore the pages of the paper. Students must remove all things from the tables, get paper and paper clips and try making a book yourself. After each will make his book, students explain the procedure for taking into account production results. The beginning of the first stage of the game is announced. At this stage, all students produce books on their own from beginning to end, specialization is not permitted. At the same time, each company accounts for each company only one handle. After three minutes, production stops. The quality of customized books is checked, compliance with technological requirements (this work can also be entrusted with quality controllers previously selected in each company, sending them to check competing companies). After counting the results, all produced products and semi-finished products are collected. Students must fill out a table 40 Copyright OJSC TsKB Bib's & Agent "KNIIG-CERVIS" LLC for calculating labor productivity, the presenter checks the correctness of its fill. The beginning of the second stage of the game is announced. At this stage, students independently organize the production process (divide it on operations, specializing in the implementation of the Operations). The number of handles does not change. After three minutes, the same procedures for monitoring and counting the results are carried out as in the first stage. At the third stage of the company get the opportunity to use as many handles as they find it necessary for a more efficient organization of production. It should be emphasized that the cost of each handle (50 rubles) is included in the total cost of production. (In the game handles personify capital resources - machines and equipment - which the company uses.) At the fourth stage, it is added to reduce the number of employees in the company if the players come to the conclusion that there are more employees in its composition than it is necessary to achieve maximum performance. The dismissed workers can unite into new companies or to go to work in a company experiencing difficulties with workforce. The game may include another one or two stages, each of which is added any new conditions (environmental protection - control of the amount of production waste; partial employment of employees is a reduction in working time for part of employees, etc.). At the end of each stage, it is necessary to calculate the results. At the end of the game, students should analyze the results of their book factories. Attention should be paid to the performance assessment methods used during the game, and their connection with the definition of performance as a ratio of the amount of goods produced to the number of resources used. (In the game we are talking about productivity, and the amount of the manufactured product is correlated with the total number of working time books spent.) Discussion Students must carefully examine the recorded results of each stage of production and compare them. It is necessary to find out what the effect gave the division of labor on the second 41 Copyright of OJSC TsKB Bib's Bib's & LLC "Agent KNIG-CERVIS" stage. Students can demonstrate on the basis of data from the tables filled with them (Table 18) increase performance as a result of labor separation. Students are invited to discuss the following questions. 1. What are the advantages (performance growth) and disadvantages (monotony of work) of labor separation and narrow specialization? 2. What do students themselves prefer - to fulfill all the work and respond to only one operation? 3. Why, entering the conveyor at its plants, D. Ford almost doubled the workers' wages? 4. What is the connection between labor separation and standardization? 5. Differences decreased between the made samples at the second stage compared to the first? (They had to decrease, since each student performed only one or two operations.) 6. The results achieved in the third stage should be analyzed after purchasing additional handles. Did the growth in capital benefits affected the level of performance? Does the additional investment on production efficiency be unambiguously affected? Table 18 Table for calculating labor productivity No. P / P 1 1 2 3 4 Production indicator 2 Sample 1st stage 2nd stage 3rd stage 4th stage 5th stage NAT. rub. nat. rub. nat. rub. nat. rub. nat. rub. nat. rub. units. units. units. units. units. units. 3 4 5 6 7 8 9 10 11 12 13 14 Quantity of 4 manufactured books The cost of materials (25 rubles. For each book) Number of 4 wages (100 rubles per employee) 100 400 42 Copyright OJSC TsKB Bib's Bib's & LLC "Agent KNIG-SERVIS" 1 5 6 7 8 9 10 2 3 4 Rent for slave 200 (Table) Capitalic 50 Zhenium (50 rubles. for the handle) General Stoy750 production (folded right speakers) Cost 12 production min. One book (clause 7 / p. 1) Total time spent (3 min. x Number of employees) The output of finished products per minute (clause 1 / p. 9) 5 6 7 8 9 10 11 12 13 14 It is known that expenses For the purchase of additional capital goods, it is not always possible to be justified from the point of view of productivity. As an example, the situation in which the acquisition of an additional fifth handle on a group of five does not lead to the same increase in productivity as the purchase of the second or third. In addition, it must be remembered that the decision on investment has, as a rule, a high alternative value due to the fact that capital benefits of the road and pay off over a long time. What effect gave the abbreviation of employees at the fourth stage? First of all, the effect depends on the contribution of the disadvantaged employee into production: if this contribution was insignificant, productivity will increase, and otherwise it will decrease. Students need to determine which production costs do not depend on the volume of manufactured products (refer to 43 Copyright OJSC TsKB BBC & Agent-Servis Agent LLC to fixed costs), and which changes depending on production volume (variable expenses). When summing up the discussion, it is necessary to once again formulate possible ways of increasing productivity: division of labor, additional investment, investments in human capital. 7.2. Business game 2 "Determining the need for gasoline for the fleet of trucks in the conditions of limiting fuel and lubricants" The characteristic of the game. The game simulates the activities of the planned group of the logistics department (OMTS) of an enterprise that has a private fleet of trucks, such as a motor transport enterprise. The definition of the need for gasoline allows several options for scheduled calculations. These options differ from each other complexity, the volume of computational works, and therefore the result obtained. The choice of this or that method of calculating the need is due to the traditions of this enterprise, its relations with superior organizationsacting by the system of economic stimulus, the qualifications of workers, the level of use of the computer. Up to 7 groups can participate in the game (3-4 people each) representing the logistics department. The content of the game. The goal of the game. To determine the need for gasoline for the fleet of trucks in the conditions of limiting flangeous materials. Conditions for achieving the goal of the game: M< = L, где M – расчётная потребность в бензине; L – установленный лимит. 44 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Средством достижения цели является рациональная организация работ. Методические указания для участников игры. Методы определения потребности в бензине подразделяются в зависимости от ряда факторов. 1. В зависимости от числа грузовых автомобилей: M = Hn*N, где Hn – норма расхода бензина в расчёте на один автомобиль в год, т; N – списочное число автомобилей. 2. В зависимости от уровня расхода бензина в отчётном году: M = M0*K1*K2, где M0 – расход бензина в отчётном году, т; K1 – коэффициент изменения объёма транспортной работы в планируемом году; K2 – коэффициент снижения нормы расхода. 3. В зависимости от общего пробега парка грузовых автомобилей: M = Hl*Σl, где Hl – норма расхода бензина в расчёте на 100 км пробега, л; Σl – общий пробег парка автомобилей, км. 4. В зависимости от объёма перевозимого груза: M = Hq*Q, где Hq – норма расхода бензина в расчёте на 1 т перевозимого груза на весь планируемый период, т; Q – объём перевозимого груза, тыс. т. 5. В зависимости от объёма транспортной работы: M = Hw*W, где Hw – групповая норма расхода бензина, г/т*км; W – общий объём транспортной работы, тыс. км. 45 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Групповая норма расхода бензина определяется на основе линейных (индивидуальных) норм расхода по следующей формуле: Hw = 10γ*(Hl / q*ż), где Hl – средневзвешенная норма расхода бензина на пробег, л/100 км; определяется исходя из линейных (индивидуальных) норм расхода; q – средневзвешенная грузоподъёмность автомобилей; ż – коэффициент полезной работы автомобилей; γ- плотность бензина, 0,74 г/л. Исходные данные игры. Автотранспортное предприятие согласно договору осуществляет перевозки с трёх баз снабжения 24 предприятиям-потребителям. 1. Ресурсы баз. База № 1 – 220 тыс. т; база № 2 – 380 тыс. т; база № 3 – 400 тыс. т. 2. Потребность предприятий-потребителей, тыс. т. Таблица 19 № предприятия 1 2 3 4 5 6 7 8 Потребность 18 24 37 84 94 75 45 16 № предприятия 9 10 11 12 13 14 15 16 Потребность 18 81 13 19 54 64 41 32 № предприятия 17 18 19 20 21 22 23 24 Потребность 18 20 20 13 25 75 35 79 46 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 3. Расстояние между базами и предприятиями, км. Таблица 20 № предприятия 1 2 3 4 5 6 7 1 8 9 10 11 12 1 5 7 10 18 13 15 17 2 12 13 18 24 11 № базы 2 3 14 17 24 17 16 15 3 15 12 18 21 16 № предприятия 3 8 20 13 18 16 18 19 4 15 7 13 18 17 13 14 15 16 17 18 19 5 20 21 22 23 24 1 19 21 15 18 12 13 16 6 23 14 12 18 17 № базы 2 21 20 16 19 14 14 17 7 18 16 17 17 21 3 18 10 17 13 18 15 22 8 17 18 31 19 18 4. Показатели работы автотранспортного предприятия. Таблица 21 № Показатели Обозначение 1 2 3 4 Списочное число автомобилей Коэффициент полезной работы Объём перевозок (план) Объём транспортной работы: (а) отчёт (б) план на следующий год Общий пробег (отчёт) Израсходовано бензина (отчёт) Задание по снижению нормы расхода бензина Нормы расход бензина: (а) на автомобиль (годовая) (б) на перевозимый груз N z Q W 5 6 7 8 47 Σl M0 Hn Единица Значение измерения Ед. 342 0,5 Тыс. т 1000 Тыс. т*км 16781 17300 Тыс. км 7425 т 1929,3 % 5,0 Hq т л/т 5,64 1,98 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» 5. Сведения об автопарке. Таблица 22 Наименование марок и моделей автомобилей ГАЗ-51 Урал-355 ГАЗ-53Ф ГАЗ-53А ЗИЛ-130 Урал-377 Списочное число Грузоподъёмность, т 56 21 14 64 124 63 2,5 3,0 3,0 4,0 5,0 7,5 Линейная норма расхода, л/100 км 24 33 29 29,5 36,5 55,5 Задания. 1. Рассчитайте possible options definitions of gasoline needs. 2. Apply the linear programming transport task model to find the optimal transport plan with a minimum of transport work using Table. 19, 20, 21. 3. Calculate savings (absolute and percentage) if the limit is set in the amount of 1722 tons of 7.3. Business game 3 "Planning the need for spare parts for repair and operational needs" Characteristic of the game: The game simulates the activities of the logistics department for the provision of an industrial enterprise with spare parts of general purpose: bearings, coupling, gears and gears, electrical products. The transition of enterprises to market relations based on commercial calculation requires providing spare parts with the minimum possible costs. The essence of the conflict is to provide an enterprise with reserve enterprises with minimal cost. 48 Copyright OJSC TsKB BIBCOM & Agent LLC KNIG-CERVIS in the game can participate up to 7 groups (3-4 people each). Winning becomes a group that will find best option Prevention modes and, accordingly, the minimum number of spare parts. The content of the game. The goal of the game. Determine the number of spare parts with minimal costs that ensures the operation of the equipment at a given level of reliability. Condition for achieving the goal of the game: C< L, где C – суммарные расходы по эксплуатации оборудования; L – лимит расходов, включая материальные затраты на запасные части. Достижение цели игры возможно только при использовании научных методов нормирования расхода запасных частей, основанных на выводах теории надёжности:  Наработка на отказ – Т0.  Интенсивность отказов – λ = 1/Т0.  Надёжность R как вероятность безотказной работы.  Экспоненциальный закон надёжности: R=e– λt.. Методические указания для участников игры. Методы определения потребности в запасных частях подразделяются в зависимости от ряда факторов: В зависимости от достигнутого уровня отчётного года: M = k*M0, где M0 – расход запасных частей данного наименования и типоразмера в отчётном году; k – коэффициент изменения режима работы оборудования в планируемом году. 2. В зависимости от периодичности выполнения профилактических работ: M = (T/t0)*n, где T – общее время работы оборудования в году, час; 49 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» t0 – периодичность профилактики, час; n – количество заменяемых запасных частей в ходе одного цикла профилактических работ. 3. В зависимости от трудоёмкости ремонтных работ: M = ΣAm, где ΣA – трудоёмкость ремонтных работ, чел./час; m – количество заменяемых запасных частей в расчёте на 1 чел./час ремонтных работ. 4. В зависимости от объёма выпускаемой продукции: M = S*m΄, где S – объём выпускаемой продукции на данном оборудовании за год, тыс. руб.; m΄ – количество запасных частей данного вида и типоразмера в расчёте на 1 руб. выпускаемой продукции 5. В зависимости от допустимого уровня надёжности: n = (ln(1 – R0) / ln q, где R0 – допустимый уровень надёжности; q – вероятность отказа (q = 1 – R) Задания. 1. Найти минимальную величину суммарных расходов по эксплуатации агрегата. 2. Определить, при какой потребности в запчастях на весь агрегат суммарные расходы по эксплуатации агрегата составляют минимальную величину. 3. С какой периодичностью ремонтная служба должна проводить профилактику? 50 Copyright ОАО «ЦКБ «БИБКОМ» & ООО «Aгентство Kнига-Cервис» Исходные данные игры. Таблица 23 1 1. Оборудование: агрегат ПКИ-3 2. Наименование запасной части: подшипник №6 3. Количество подшипников № 6 в агрегате 4. Цена одного подшипника № 6 (плановая) 5. Плановое время работы агрегата в год (T) 6. Объём производимой продукции за год: (S) отчёт план 1 7. Заявленная потребность в отчётном году на подшипник №6 8. Получено подшипников № 6 в отчётном году: – по фондам – техническая помощь со стороны 9. Трудоёмкость ремонтных работ (без профилактики) (ΣA) 10. Стоимость одной профилактики 11. Убытки от внеплановых простоев агрегата 12. Permissible level Reliability (R0) 13. Working on bearing failure No. 6 (q) 14. Bearing output under the allowable level of reliability 15. Wage costs (with charges) at repair work 16. Expenses for maintenance for repair work (without spare parts - Bearings),% of wages 17. The limit of the cost of operation of the unit, including the cost of spare parts (L) 51 2 1 unit. 10 pieces. 5.2 rubles. 6000 hour 91.8 thousand rubles. 96.4 thousand rubles. 2 60 pcs. 18 pcs. 38 pcs. 360 people / hour 15 rubles. 402 rub / day. 0.9 500 hours / OTV 0.2 1,05 rubles / person / hour 35% 450 rub. Copyright OJSC TsKB BIBKOM & LLC "Agent KNIGA-SERVIS" 8. Topics of reports for seminar classes 1. Classification of models and methods of logistics theory. 2. The ABC method. 3. Selection of logistics intermediaries using expert assessments. 4. Model "exactly on time". 5. Calculation of the optimal order size. 6. Application of forecasting methods in logistics. 7. The main provisions of the theory of forecasting. 8. An example of the forecast of the current stock in the warehouse. 9. Combined forecast. 10. An example of the forecast of the number of containers. 11. Determination of the number and coordinates of the location of warehouses in the region. 12. Determination of the location of the warehouse. 13. Transport component of logistics costs depending on the number of warehouses in the region. 14. Algorithm for assessing the impact of the placement of the warehouse network for transportation costs. 15. Calculation of the insurance reserve (example). 16. Common dependencies for calculating reserves. 17. Analysis of the formula BauerSox-Closse for calculating the insurance stock. 18. Transport logistics: solving the tasks of road transport. 19. The overall algorithm for planning freight road transport. 20. Algorithm of accelerated road planning. 21. Mixed carriage: selection of the type of transport. 52 Copyright OJSC TsKB Bib's Bib's & Agent "KNIIG-SERVIS LLC" 9. Questions to the offset 1. Logistics as an infrastructure component of a market economy. 2. Logistics: concepts and principles. 3. Main categories logistics. 4. Logistic process and logistics systems. 5. Supply chain management. 6. The concept and objective nature of material reserves. 7. Material reserves and flows as logistics management objects. 8. Classification of stocks and interpretation of changes in their magnitude. 9. Parameters of stocks and indicators of their turnover. 10. Principal stock control systems. 11. Economic and mathematical models of stock management and their classification. 12. Analysis feature in logistic management. 13. The ABC analysis method. 14. XYZ analysis method. 15. Positioning of inventory resources. 16. Problems of integrated logistics management. 17. Classical stock management model. 18. Models of the optimal order size under conditions of periodic accumulation of stock. 19. The deficit planning model. 20. A generalized deterministic model of the optimal order size. 21. Special cases in constructing stock management models. 22. Methods for normalization and optimization of insurance stock. 23. Dynamic and stochastic stock management models. 24. Conceptual approaches to the management of logistics processes and logistics management systems. 25. Information support for organizational and economic activities of enterprises. 26. Specificity of approaches to the creation and application of software. 53 Copyright OJSC TsKB Bib's & Agent-Cervis LLC List of recommended literature Basic 1. Gadzhinsky, A. M. Logistics Basics / A. M. Gadzhinsky. - M.: Marketing, 2006. - 124 p. 2. Gadzhinsky, A. M. Logistics: Textbook / A. M. Gadzhinsky. - 6th ed. - M.: Dashkov and K O, 2003. 3. Dybskaya, V. V. Logistics of storage / V. V. Dybskaya. - M.: GU HSE, 2006. 4. United transport system / Ed. prof. V. Glabourds. - M.: Transport, 2006. 5. Kolobov, A. A. Basics of industrial logistics: studies. Allowance / A. A. Kolobov, I. N. Omelchenko. - M.: MGTU, 1998. - 116 p. 6. Logistics / Ed. B. A. Anikina. - M.: Infra-M, 2001. - 352 p. 7. Logistics in examples and tasks: studies. Manual / Sost: V. S. Lukinsky, V.I. Berezhnaya, E. V. Berezhnaya et al. - M.: Finance and Statistics, 2009. - 288 p. 8. Logistics: Control in freight transport and logistics systems: studies. Manual / Ed. L. B. Mirotina. - M.: Lawyer, 2002. 9. Nikolaichuk, V. E. Logistics / V. E. Nikolaichuk. - SPb.: Peter, 2001. - 159 p. 10. Novikov, O. A. Logistics: studies. Manual / O. A. Novikov, S. A. Uvarov. - SPb.: Business press. - 2000. - 159 p. 11. Industrial logistics. - St. Petersburg: Polytechnic, 2006. - 165 p. 12. Stepanov, V.I. Logistics: Textbook / V.I. Stepanov. - M.: Velby, Prospekt, 2006. - 488 p. 54 Copyright OJSC TsKB BIBKOM & LLC "KNIIG-SERVIS Agent" LLC Additional 1. BauerSoks, D. J. Logistics. Integrated supply chain / D. J. Bowersoks, D. J. Kloss. - M.: Olympus Business, 2001. 2. Brodetsky, G. L. Methods of stochastic optimization. Mathematical model of stock management: studies. Manual / G. L. Brodetsky. - M.: Raa, 2004. 3. Volgin, V.V. Warehouse: Pratte. Manual / V. V. Volgin. - M.: Dashkov and K O, 2001. 4. Karnukhov, S. B. Logistics concept. System analysis / S. B. Karnukhov. - M.: REA, 2003. 5. Sergeyev, V. I. Management in Business Logistics / V.I. Sergeev. - M.: Filin, 2006. 6. Transport logistics: textbook / under the general ed. prof. L. B. Mirotina. - M.: Exam, 2002. Software and Internet resources In the process of studying discipline students from a personal computer can get acquainted with Internet sites of leading universities in Russia, where there is training on this discipline or disciplines related to it (for example, through the Rambler server) , Get new information and familiarize yourself with electronic versions of periodic publications in digital processing in Russian and English. The existing website discipline on the Internet represents remote access to educational and methodological and software Disciplines and makes it possible to train students using remote technologies. 55 Copyright OJSC TsKB "Bibcom" & LLC "Agent KNIGA-CERVIS" Appendix 1 Data on the work of the plant "Sunrise" Number of option 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 January 30 q TS 2 15.4 17.3 19.5 22.0 24.7,78,33,4,5,3,33,7 34,5 30.0 26,1 22 , 7 19.7 17, 14.9 18.1 22.0 26.7 32.4 39.4 28.6, 20.8 15.1, 19.8 26, 34.3 45.1 59.2 77.9 3 2043,4,204,12,209,92,04,92,239,2304,92,554,4,245,12,254,4,245,1,23,12,227,6,195,92,267,2,29,92,233,5,079,3,2032 , 3 2099.4 2181.0 2280.1 2400.5 2546.8 2320.3 2155.8,036,4,213,21,267,12,24,12,266,1,264.1,2356,0 February q TC 4 16, 3 18.4 20.7 23.3 26.2 29.5 33.2 37.4 42.1 36.5 31.8 27,6 24.0 20.8 18.1 15.7 19,1 23 , 2 28.2 34.3 41.7 30.3 22.0 15.9 21.0 27.6 36,3 47.7,62.7 82.5 5 2062.3 2105.4 2153.8 2208, 4 2269.8 2339.0 2416.9 2504.5 2603.2 2487.5 2387.0 2299.6 2223.7 2157.7 2100.3 2050.5 2121.6 2207,92,12,8,2440,3,2595 , 2 2355.4 2181.3 2054.9 2160.4 2299.1 2481.5 2721.6 3036.8 3451.6 March Q TC 6 17.2 19.4 21.8 24.5 27.6 31.1 35.0 39.4 44.4 38.6 33.5 29.1 25, 22.0 19, 16.6, 20.2 24.5 29.8 36.2 44, 0 31.9 23.2 16.8 22.1 29, 38.3 50,3,66.2 87.0 7 2081.2 2126.6 2177.8 2235,4 2300.2 2373.2 2455.3 2547.8 2652.0 2529.9 2423.8 2331.6,251,5,128,921.3,280,92,243,8,24,92,245,6,2480,22,243,5,290,4,2406,73,290,4,2306,73, 4 2184,7,231,1,523,5,276,7 3109,547.2 April q Tc 8 18.5 20.8 23,4,64,97,73.5 37.7,42.4 47.7 41.5 36.0 31.3 27.2 23.7 20.6,79,27,24,32.0 38.9 47.3 34.3 24.9 18.1 23.8 31, 3 41.2 54.1 71.2 93.6 9 2108,12,257,4,212,4,242,22,244,22,22,52,29,2610,4,252,4,2591,22,22,25,11,8 2291.6 2216.8 2151.7,273,8,2975,8,273,8,292,8,241,22,213,3,241,22,243,12,12,2219,8,277,25,284.3 2856,5214, 5 3685.3 May q Ts 10 19.2 21,6 24.3 27.4 30.8 34.7 39.1 44.0 49.5 43.1 37,4 32.5 28.3 24.6 21.3 18.5 22.5 27.4 33.3 40.4 49, 35.6 25.9 18.8,23,26,5,42.7,26,2,23,99,21,12,123 , 2 2173.9 2231.0 2295.3 2367.7 2449,12,240,84,1,22,22,222,2,250,22,22,22,2,213,3,2235,6,168.0 2109.3 2193 , 0 2294.7 2418.3 2568.4 2750.9 2468.4 2263.3 2114.5 2238.7 2402.1 2617.0 2899.5 3271.1 3759,7 June Q TC 12 21.3 24, 0 27.0 30.4 34.2 38.5 43.4 48.8 55.0 47.8 41.5 36, 31.3 27.2 23.7 20.6 25.0 30,46 36 , 9 44.8 54.5 39.5 28.7,08,74,46.0 47.4 62.3 81.9 107.8 13 2167.3 2223.6 2286.9 2358.2 2438, 5 2528.9 2630.6,252,22,274,12,22,95,91,6,257,4,278,2,291,92,217,22,291,9244.8,257,22,244,2,261,28,63,7,261,28,63,6,250,250 , 3 2322.8 2157.6 2295,5,2476.7,215,130,24,5,3440,7,3982.8 Note: Q is the volume of material flow when processing timber, thousands etc. TC - total water supply costs, thousand y. D. E. 56 Copyright OJSC TsKB "Bibcom" & LLC "Agent KNIGA-SERVIS" Appendix 2 Data on the work of the firm of the company "Phoenix" Option number 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 q \u003d 0 Q \u003d 1 Q \u003d 2 Q \u003d 3 Q \u003d 4 Q \u003d 5 Q \u003d 6 Q \u003d 7 Q \u003d 8 p Tc p Tc p Tc p Tc p Tc p Tc p TS R TS R TS 2 190 200 205 212 215 212 209 203 197 201 205 209 213 198 203 207 3 215 232 251 271 293 275 254 293 228 215 297 284 298 313 305 298 4 180 190 195 202 205 202 199 193 187 191 195 199 203 188 193 197 5 351 368 387 407 429 411 394 379 364 351 383 420 434 180 185 192 195 192 189 183 177 181 185 189 193 178 183 187 7 447 464 483 503 525 507 490 475 545 537 530 8 160 170 175 182 185 182 179 173 167 171 175 179 183 168 173 177 9 515 532 551 571 593 575 558 584 528 515 547 584 598 160 165 172 175 172 169 163 157 161 167 169 173 158 163 167 11 567 584 603 623 645 627 610 595 580 567 599 636 650 665 657 650 12 140 150 155 162 165 162 159 153 147 151 155 159 163 148 153 157 13 610 627 646 666 688 610 642 679 693 708 700 693 14 130 149 145 152 155 149 149 143 137 141 145 149 153 138 143 147 15 653 670 689 709 731 713 696 681 666 653 685 722 736 751 743 736 16 120 130 135 142 145 142 139 133 127 131 135 139 143 128 133 137 17 733 70 769 789 811 793 769 761 746 733 765 816 816 831 823 816 18 to 120 125 132 135 132 129 123 117 121 125 129 133 118 123 127 19 799 816 835 855 877 859 842 827 812 799 831 868 882 897 889 882 57 Copyright OJSC "TsKB" BIBKOM "& LLC" Agent KNIIG-SERVIS "Appendix 3 Data on the work of the company" North "number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 P, TKM Fc, y. e. 300 316 334 352 371 392 413 436 460 430 435 420 370 395 430 3700 4063 4461 4898 5378 5300 5224 5149 5075. 5002 4930 4859 5430 5628 5009 4458 3968 3531 3143 58 Z, y. d. E. / TKM T, y. d. / Tkm 57 58 61 63 66 68 71 74 77 80 83 86 152 158 140 125 111 99 88 68 73 77 81 85 89 93 92 91 94 97 96 168 174 155 138 123 109 97 Copyright OJSC TsKB Bibkom "& LLC" Agent KNIG-SERVIS "Table of contents Introduction ......................................... .................................................. ...................... 3 1. Evaluation of economic costs of production of logistics services ................... .................................................. ......... 5 2. Determination of the optimal volume of material flow ..................... 11 3. Calculation of the break-even point of the micro-system system. .................................................. ......... 16 4. Taking logistics solutions in conditions of uncertainty and risk .............................. .................................... 21 4.1. Analysis and adoption of logistics solutions in conditions of certainty .......................................... .......................................... 21 4.2. Forecasting of materials strength and turnover from a regional warehouse ............................................. .................................................. ....... 24 5. ABC method ...................................... .................................................. ............. 28 6. Choosing logistics intermediaries ................................. ............................. 31 7. Tasks and business games .............. .................................................. ................. 34 7.1. Business game 1 "Productivity, investment, division of labor" ....................................... ......................................... 38 7.2. Business game 2 "Determining the need for gasoline for a fleet of trucks in the conditions of limitation of flammable materials" ................................ ...................................... 44 7.3. Business game 3 "Planning the need for spare parts for repair and operational needs" ................................... ....... 48 8. Topics of reports for seminar classes ......................................... ................. 52 9. Questions to test ........................... .................................................. .............. 53 List of recommended literature ................................ ................................ 54 Software and Internet resources ........... ................................. 55 applications ............... .................................................. ...................................... 56 59 Copyright OJSC TsKB Bibsky & LLC " KNIGA-SERVIS Agent "Educational publication Abakumova Julia Anatolyevna Mathematical models in logistics solutions Methodical instructions Editor, Corrector I. V. Bunakova Lestka E. L. Shelekhova signed in print 01/20/2011. Format 6084 1/16. Boom. offset. Headset "Times New Roman". Sl. Pechs. l. 2.79. Ud. l. 2.0. Circulation 150 copies. Order Original-mock-up prepared in the editorial and publishing department of the Yaroslavl State University. P. G. Demidova. Printed on a risograph. Yaroslavl State University. P. G. Demidova. 150000, Yaroslavl, ul. Soviet, 14. 60 Copyright OJSC TsKB BIBKOM & Agent LLC KNIG-SERVIS 61 Copyright OJSC TsKB Bibsky & Agent KNIGA-SERVIS LLC Yu. A. Abakumova Mathematical models in logistics solutions 62

The use of economic and mathematical modeling in logistics systems. Application of mathematical models in logistics

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