Operation Research Tools

2023/2024

Academic Year

ENG

Instruction in English

3

ECTS credits

Delivered at:

Department of Economics

Course type:

Elective course

When:

1 year, 1 module

Course Syllabus

Abstract

The base of the “Operations Research Tools” course is developing and applying the optimal solution methods with mathematical modeling and different heuristic approaches. The major object of this course is to generate a system approach to solve economic problems for MA students. At the same time, the course has real-life applications. Students could apply different economic and math methods to solve challenging economic problems, estimate the efficiency of applied methods, and use new skills in IT or finance companies. The course is based on mathematical models such as linear programming, traveling salesman problems, integer programming, algorithms on the graphs (for searching the routing chains in transport scheduling), meta-heuristic algorithms (genetic algorithms, ant algorithms, immune algorithms), forecasting methods, and revenue management models. The task solution of acyclic directed graphs arrangement is based on linear programming, integer programming, the fundamentals of graphs theory, the graphs algorithms (depth-first search, breadth-first search), the sorting algorithms, and heuristic approaches. The program tools are Julia, Wolfram Mathematica or Python.

Learning Objectives

• At the end of the course, students will master the following knowledge and related disciplines: Operations Management Linear Programming Assignment Transportation Simulation Network Analysis Productivity Management Replacement Analysis Maintenance Management Total quality management Project management Layout Analysis / Management Forecasting Techniques Material Planning

Expected Learning Outcomes

• can use simplex algorithm to solve linear programming problem
• Explain and apply linear programming
• Students learn about linear programming problems in economics: transportation problem, monopoilist problem etc.
• Solves linear and non-linear optimization problems and interprets the results from the international business perspective
• Cake-eating problem: direct attack vs. DP approach
• Analytical solution of mathematical models. Dual problem. The Lagrange multiplier technique.
• Integer Programming. B&b method. Examples of Integer Programming Problems.
• . Open solvers for Linear Programming and Integer Programming problems: ortools, coin-or (cbc), glpk,… Performance comparison of benchmarks.
• Solve Randomized Linear Programming
• Solve Deterministic Linear Programming (DLP)
• Solve the task in any computer program: find the optimal booking limits and protection levels, using Littlewood’s rule and EMSRb for the model example. Find optimal booking limits using different types of nesting.
• Solve Simple Genetic Algorithm
• Solving combinatorial problems with metaheuristics
• Solve varying the mutation
• Solve crossover rates in Simple GA
• Solve Probabilistic Nonlinear Programming
• Solve Overbooking model
• Understand Principal of optimality

Course Contents

• Lesson 1. Introduction to Operations Research.
• Lesson 2. Linear programming.
• Lesson 3. Graphical method. Simplex method.
• Lesson 4. Advanced application of linear optimization.
• Lesson 5. Applications of integer programming: Revenue Management Systems.
• Lesson 6. Examples of NP-hard combinatorial optimization problems.
• Lesson 7. Genetic Algorithm for Partitioning Sets.
• Lesson 8. Nonlinear programming techniques.
• Lesson 9. Dynamic programming.
• Lesson 10. Indirect utility: firms and consumers

Assessment Elements

• Home task
• Class participation
• Individual assignment

Interim Assessment

• 2023/2024 1st module
  0.33 * Class participation + 0.45 * Home task + 0.22 * Individual assignment

Bibliography

Recommended Core Bibliography

• Introduction to algorithms, Cormen, T. H., 2009
• Taha H.A. Operations Research: An Introduction, 10-th Edition, Pearson Education Limited, 2017. – 849 p. – ISBN: 9781292165561
• The theory and practice of revenue management, Talluri, K. T., 2004

Recommended Additional Bibliography

• Bertsekas, D. P. (2017). Stable Optimal Control and Semicontractive Dynamic Programming.
• Cormen, T. H., Leiserson, C. E., Rivest, R. L., Stein, C. Introduction to Algorithms (3rd edition). – MIT Press, 2009. – 1292 pp.
• Pricing and revenue optimization, Phillips, R. L., 2005