Mathematical methods in logistics. Georgy Prosvetov: Mathematical methods in logistics. Tasks and solutions. Educational and practical guide Prosvetov g and mathematical methods in logistics

Foreword

Chapter 1. What is logistics?

Chapter 2. Basic concepts of graph theory

Chapter 3. Factors of production and costs

• 3.1. Factors of production
• 3.2. Cost classification

Chapter 4

• 4.1. Weighing method
• 4.2. Full cost production location method
• 4.3. Gravity method
• 4.4. Costing method

Chapter 5 Placing Service Objects

Chapter 6

• 6.1. Labeling method
• 6.2. The problem of the shortest path between two points

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11 Branch and Bound Method

Chapter 12

• 12.1. Economic and mathematical model of the transport problem
• 12.2. Northwest corner method.
• 12.3. Minimum cost method
• 12.4. A special case
• 12.5. Distributive method for solving the transport problem
• 12.6. open model
  • 12.6.1. Fictitious consumer
  • 12.6.2. Fake supplier
• 12.7. Transport task and Excel

Chapter 13

• 13.1. What is a transport network
• 13.2. Initial supply plan
• 13.3. Checking the supply plan for optimality
• 13.4. Improvement of the supply plan
• 13.5. open model

Chapter 14

• 14.1. Minimization of the objective function
• 14.2. Objective function maximization
• 14.3. Assignment task and Excel

Chapter 15

Chapter 16

Chapter 17

• 17.1. Making decisions without using numerical values ​​of outcome probabilities
  • 17.1.1. Maximax and Maximin Solutions
  • 17.1.2. minimax solution.
  • 17.1.3. Hurwitz criterion
• 17.2. Decision making using numerical values ​​of outcome probabilities
  • 17.2.1. Rule of Maximum Probability
  • 17.2.2. Maximizing Expected Return
  • 17.2.3. Expected cost of complete information

Chapter 18

• 18.1. Additive model analysis
• 18.2. Analysis of the multiplicative model

Chapter 19 Exponential Smoothing

• 19.1. A simple exponential smoothing model
• 19.2. Trend Adjusted Exponential Smoothing

Chapter 20

Chapter 21 Network Planning and Management

• 21.1. Basic concepts
• 21.2. Rules for constructing network graphs
• 21.3. Critical Path Method
• 21.4. Project management with undefined lead times
• 21.5. Project cost. Network Graph Optimization
• 21.6. Ganges chart
• 21 7. Distribution of resources. Resource Graphs
• 21.8. Job parameters

Chapter 22

Chapter 23. Statistical Quality Control

• 23.1. Control cards
• 23.2. Control charts of arithmetic means of technological process
• 23.3. Process Variability Control Charts
• 23.4. Quantitative trait control charts
• 23.5. Quality control charts
  • 23.5.1. r-cards. Approximation by normal distribution
  • 23.5.2. r-cards. Approximation by the Poisson distribution
  • 23.5.3. from the map
• 23.6. Statistical acceptance quality control of qualitative features

Chapter 24

• 24.1. Basic concepts
• 24.2. Basic Inventory Management Model
• 24.3. Economic Lot Size Model
• 24.4. Quantity Discount
• 24.5. Batch production model
• 24.6. Deficit planning model
  • 24.6.1. Case of non-fulfillment of applications
  • 24.6.2. Application Fulfillment Case
• 24.7. Uncertainty and the basic inventory management model
• 24.8. Tiered reorder system
  • 24.8.1. Achieving the minimum cost
  • 24.8.2. Achieving the minimum service level
• 24.9. Cyclic reorder system
• 24.10. Other Inventory Management Issues

Chapter 25

• 25.1. Application of simulation models in the theory of inventory management

Chapter 26

• 26.1. FIFO stock valuation method
• 26.2. LIFO inventory method
• 26.3. The method of estimating reserves by weighted average
• 26.4. Influence of different inventory valuation methods on profit calculation

Chapter 27

Chapter 28

• 28.1. Possible Graphing Approaches
• 28.2. First come, first served rule
• 28.3. Rule of Shortest Execution Time
• 28.4. Early rule by due date
• 28.5. Longest Execution Time Rule
• 28.6. Rule of the most urgent work
• 28.7. critical attitude
• 28.8. The problem of two machines

Chapter 29

Chapter 30

Chapter 31, ABC Analysis

Chapter 32

• 32.1. The exponential law of probability distribution
• 32.2. The simplest flow
• 32.3. Basic concepts of queuing theory
• 32.4. State Graph
• 32.5. Kolmogorov's equations
• 32.6. Limit probabilities of states
• 32.7. The process of death and reproduction
• 32.8. Single-channel QS with failures
• 32.9. Multichannel QS with failures (Erlang problem)
• 32.10. Single-channel QS with unlimited queue
• 32.11. Multi-channel QS with unlimited queue
• 32.12. QS with a fixed service time
• 32.13. Single-channel QS with limited queue
• 32.14. Multi-channel QS with limited queue
• 32.15. Closed QS
• 32.16. CMO with limited waiting time
• 32.17. Application of simulation models in queuing systems

Chapter 33

• 33.1. Learning Curves
• 33.2. Level of study
• 33.3. Determination of production costs
• 33.4. Determining the level of training

Chapter 34

• 34.1. Advantages and disadvantages of leasing
• 34.2. Comparative analysis of the effectiveness of leasing and bank lending for the purchase of fixed assets

Chapter 35

• 35.1. Setting a price based on the value of the product
• 35.2. Setting a price based on current price levels
• 35.3. Psychology of price perception
• 35.4. Geographic pricing
• 36.5. Setting prices with discounts and offsets
• 35.6. Setting prices to promote sales
• 35.7. Dual Tariff Pricing

Chapter 36

• 36.1. Warehouse assignment
• 36.2. Warehouse activity
• 36.3. layout
• 36.4. Cargo handling
• 36.5. Packaging

Chapter 37

• 37.1. Way of transportation
• 37.1.1. Railway
• 37.1.2. Automobile transport
• 37.1.3. Water transport
• 37.1.4. Air Transport
• 37.1.5. Pipeline transport
• 37.1.6. Choice of transportation method
• 37.2. Intermodal transportation
• 37.3. Transportation and ownership issues

The program of the training course "Mathematical Methods in Logistics"

Tasks for the test on the course "Mathematical Methods in Logistics"

Teaching aid. - M.: RDL Publishing House, 2004. - 160 p. Sets.
Basic concepts of graph theory.
decision tree.
The problem of finding the shortest path.
Construction of a communication network of minimum length.
The problem of determining the maximum flow.
Network planning and management.
Basic concepts.
Rules for constructing network graphs.
Critical path method.
Project management with an indefinite lead time.
Project cost. Network graph optimization.
Gantt chart.
Resource allocation. Resource charts.
Work parameters.
Assembly line balancing.
Transport task.
Economic-mathematical model of the transport problem.
Northwest corner method.
Minimum cost method.
A special case.
Distribution method for solving the transport problem.
open model.
Assignment problem.
Minimization of the objective function.
Maximization of the objective function.
Making decisions.
Making decisions without using numerical values ​​of the probabilities of outcomes.
Making decisions using numerical values ​​of the probabilities of outcomes.
Inventory Management.
Basic concepts.
Basic inventory management model.
Economic lot size model.
Quantity discount.
Batch production model.
Deficit planning model.
Uncertainty and the basic model of inventory management.
Tiered reorder system.
Cyclic reorder system.
Other inventory management issues.
Simulation.
Application of simulation models in queuing systems.
Application of simulation models in the theory of inventory management.
Statistical quality control.
Control cards.
Control charts of the arithmetic mean of the technological process with known.
Control charts of technological process variability with known.
Control charts of quantitative traits with unknowns.
Control charts of qualitative features.
Statistical acceptance quality control of qualitative features.
Matrix games.
Basic concepts of game theory.
Formalization of the game. game matrix.
Optimal strategies.
Mixed strategies.
Duplication and dominance of strategies.
Solution of the game 2x2.
Solution of the game 2xn.
Solution of the game mx2.
An approximate method for solving matrix games.
Bimatrix games.
positional games.
Linear programming.
Basic definitions.
Geometric method for solving linear programming problems.
Simplex method (method of modified Jordan exceptions - MJI).
Excel. Search for a solution.
Dual tasks.
Properties of dual problems.
Duality theorems.
Reduction of a matrix game to a linear programming problem.
Leontief model.

In this tutorial, using simple examples, the following sections of logistics are revealed: transportation problem, assignment problem, shortest path problem, communication network of minimum length, maximum flow, traveling salesman problem, single average problem, coverage problem, basic concepts of graph theory, tasks production location, service facility location, plant and warehouse location analysis, production factors and costs, decision tree, decision making, time series, exponential smoothing, controlled forecasting, network planning and control, assembly line balancing, statistical quality control, inventory management, simulation modeling, inventory estimation, predictive equipment maintenance, material requirements planning, short-term schedules, just-in-time system, ABC analysis, mass production systems...

The purpose of this book is to teach the basic mathematical methods in logistics and introduce experience in this area.
In this tutorial, using simple examples, the following sections of logistics are revealed: transportation problem, assignment problem, shortest path problem, communication network of minimum length, maximum flow, traveling salesman problem, single average problem, coverage problem, basic concepts of graph theory, tasks production location, service facility location, plant and warehouse location analysis, production factors and costs, decision tree, decision making, time series, exponential smoothing, controlled forecasting, network planning and control, assembly line balancing, statistical quality control, inventory management, simulation modeling, inventory estimation, predictive equipment maintenance, material requirements planning, short-term schedules, just-in-time system, ABC analysis, queuing systems, manufacturing learning, leasing; pricing methods, warehousing and handling, transportation, distribution channels, wholesale and retail trade, surplus, coding, expert evaluation methods, supplier evaluation, justification of the decision "make or buy", competitive advantages, short-term decision making, futures contracts.
For teachers and students of economic specialties of higher educational institutions, specialists in the field of logistics.
3rd edition, enlarged.