Delivered at:: School of Politics and Governance

Course type:: Elective course

When:: 4 year, 2, 3 module

Instructor

Belenky, Alexander

Full Syllabus

Abstract

Procurement management is a field of management science and practice that actively develops, first of all, from the viewpoint of quantitative methods applicable in determining procurement strategies. Estimating the cost of goods and services, which has usually been considered as part of management problems to be solved in the fields in which these goods and services are produced, becomes a function of public administration, which spends taxpayers’ money to buy them within a limited budget. Based on the cost estimates, every public administration is interested in a) a high quality of the procured goods and services, and b) the lowest possible cost that can be paid for those selected for procurement. One of the effective ways to achieve these goals is associated with setting and running competition procedures, and acquainting course students with basic ideas and techniques of running such procedures taking into account reliable quantitative estimates of their expected results is one of the major parts of the present course. Another major part of the course is associated with analyzing approaches to finding partners in the private sector that every public administration may consider in financing large-scale projects requiring substantial investments. To succeed in this search, the public administration should be capable of engaging the private sector first in negotiations and then in cooperation, which is possible only if financial perspectives of this cooperation are made clear to potential investors and present interest to them. Achieving both goals requires quantitatively estimating these perspectives, and acquainting the course students with effective mathematical methods and techniques of this estimating is part of the present course.

Learning Objectives

The major goals of the course “Quantitative methods in procurement management and public-private partnerships” are to acquaint interested students with a) principles and basic techniques of mathematically modeling procurement management problems and problems associated with forming public-private partnerships, b) ideas of quantitative methods for analyzing and solving these problems, and c) standard software packages implementing these ideas. As a result of studying the course, the students are expected to a) understand ideas underlying the most popular basic approaches to mathematically modeling major procurement management problems, b) be familiar with all basic types of mathematical models formalizing these problems, c) be familiar with basic techniques of developing the simplest models of all these types
be able to quantitatively estimate the perspectives of forming public-private partnerships
be able to develop negotiation strategies aimed at convincing potential investors and potential partners to contribute to solving particular management problems in the framework of public-private partnerships, and f) be able to find financial and legal conditions of forming public-private partnerships acceptable to all the potential (negotiating) partners. In addition to that, the students are expected to understand basic concepts and ideas of systems analysis, robust optimization, game theory, and mathematical statistics as major tools for mathematically modeling, quantitatively analyzing, and solving practical procurement management and public-private partnerships problems.

Expected Learning Outcomes

understand ideas underlying the most popular basic approaches to mathematically modeling major procurement management problems
be familiar with all basic types of mathematical models formalizing these problems
be familiar with basic techniques of developing the simplest models of all these types
be able to quantitatively estimate the perspectives of forming public-private partnerships
be able to develop negotiation strategies aimed at convincing potential investors and potential partners to contribute to solving particular management problems in the framework of public-private partnership
be able to find financial and legal conditions of forming public-private partnerships acceptable to all the potential (negotiating) partners.
In addition to that, the students are expected to understand basic concepts and ideas of systems analysis, robust optimization, game theory, and mathematical statistics as major tools for mathematically modeling, quantitatively analyzing, and solving practical procurement management and public-private partnerships problems. ________________________________________
understand ideas underlying the most popular basic approaches to mathematically modeling major procurement management problems, b) be familiar with all basic types of mathematical models formalizing these problems
be able to find financial and legal conditions of forming public-private partnerships acceptable to all the potential (negotiating) partners

Course Contents

Topic 1. An introduction to basic mathematical concepts and facts from mathematical analysis, linear algebra, and multi-dimensional geometry necessary for successfully studying the course.
Basic concepts and definitions of set theory. Axioms for real numbers. Axioms for linear spaces. Linear independence of vectors in a linear space. Geometric interpretation of linear dependence and linear independence. The rank of a system of vectors, the rank of a matrix, a basis of a vector system, and a geometric interpretation of all these concepts. The formulation and the geometric interpretation of the Basic Theorem on two systems of vectors in a finite-dimensional linear space. The formulation of the Theorem on the Rank of a Matrix and that of its corollaries. The geometric interpretation of the Theorem on the Rank of a Matrix.
Topic 2. The geometry of linear homogeneous and non-homogeneous equations and inequalities.
Systems of linear homogeneous equations and the structure of the sets of their feasible solutions. Affine subspaces in finite-dimensional linear spaces, their connection with linear subspaces, and their geometric illustration. A multiplication of a matrix by a vector and a vector-matrix writing of systems of linear equations and inequalities in finite-dimensional linear spaces. A matrix multiplication. Degenerate and non-degenerate matrices with real elements. Unit matrices. Inverse matrices of non-degenerate matrices.
Topic 3. The solvability of systems of linear homogeneous and non-homogeneous equations and inequalities.
A scalar product of two vectors and orthogonal vectors in a finite-dimensional linear space. Conjugate subspaces of a finite-dimensional linear spaces. Systems of linear homogeneous and non-homogeneous equations. The solvability of systems of non-homogeneous equations . A geometric interpretation of the set of feasible solutions of a linear equation and a linear inequality on a plane and in a three-dimensional space. Non-negative solutions of systems of homogeneous and non-homogeneous linear equations and inequalities in finite-dimensional linear spaces. Basic and non-negative basic solutions of systems of linear non-homogeneous equations in finite-dimensional linear spaces.
Topic 4. Convexity in mathematical and economic systems.
Convex sets and convex cones in finite-dimensional linear spaces. Operations on convex cones and their geometric interpretation. A finite cone and the dual cone to a finite cone. Finite cones of non-negative solutions to systems of linear homogeneous equations and inequalities. Extreme points (vectors) and extreme solutions of systems of linear homogeneous inequalities. Convex polyhedral sets, convex polyhedra, and their extreme vectors. A representation of a polyhedral set via its extreme points, and extreme solutions of a corresponding system of linear equations and inequalities.
Topic 5. Basic concepts and ideas of nonlinear optimization and their geometric interpretation.
A statement and the mathematical formulation of a conditional extremum problem. The Lagrange function and the Lagrange multipliers. Necessary conditions for the extremum of a function of several variables and their geometric interpretation.
Topic 6. Linear programming models in procurement management.
Using linear programming models in choosing types of procurement contracts and approaches to their design, analysis, and execution. Principles of competitive tendering and some linear programming models for designing competitive tendering and conducting negotiations associated with procurement management. Linear programming models in analyzing competitive trades and for forming auction lots, batch-bidding, and basic elements of cross-market contracts. Linear programming models in developing strategies for fighting collusion and corruption phenomena in public procurement.
Topic 7. Minimax problems with nonlinear goal functions and games on polyhedral sets with nonlinear payoff functions in mathematically modeling public-private partnerships.
Federal (state) procurements and public-private partnerships: similarities and principal differences. Minimax and game mathematical models with linear constraints for a) estimating the volume of necessary investment in large-scale projects that cannot be financed in full by federal and local authorities, and b) estimating the risks associated with such investments investing and finding principles of cooperation between federal and local authorities and private partners in the framework of public-private partnerships. Developing and mathematically modeling fair mechanisms of sharing the expected profit among all the public-private partners.
Topic 8. Integer and mixed programming models in public administration problems associated with procurement management.
Examples of procurement management problems that are formulated as integer programming problems, mixed programming problems, and graph problems. The ideas and geometry of the basic exact methods of integer programming by transforming integer programming problems to auxiliary mathematical programming ones. Ideas of the exact methods of integer programming that are based on the use of the combinatorial nature of integer programming problems. Ideas of some variants of the branch-and-bound method for solving integer programming problems and for solving mixed programming problems. Examples of using the considered branch-an-bound methods for solving procurement problems mathematically formulated as knapsack problems. Graphs and extreme problems on graphs: basic definitions and underlying results.
Topic 9. Public-private partnership problems associated with the use of stochastic programming and queuing models
Examples of problems associated with forming public-private partnerships that are formulated as stochastic programming problems. Methods of passive stochastic programming that are based on the use of parametric programming ideas. Ideas underlying one-stage, two-stage, and multi-stage stochastic programming and their implementation in developing methods for solving stochastic programming problems. Forming public-private partnership in servicing systems, basic queuing models with multiple waiting lines, and the Poisson and the Erlang distributions in modeling service processes. Examples of solving queuing problems associated with analyzing the profitability of public-private partnerships.
Topic 10. Network models and their use in the quantitative analysis of the effectiveness of the public administration functioning.
Examples of problems associated with estimating the effectiveness of the functioning of a public administration that can be formulated as network flow problems. Simplex-type and combinatorial-type methods for solving network flow problems: basic ideas and major types of the most popular such methods. Primal, dual, and primal-dual methods of the simplex-type for solving network flow problems. Feasible trees, and dual feasible trees in these methods. The statement and mathematical formulation of the maximal network flow problem, and the Ford-Fulkerson method as a method of the combinatorial type for solving this problem. Statements and mathematical formulations of the shortest-pass, minimum-cost network flow, and the minimum spanning tree problems. Methods for solving these problems: underlying ideas and software packages.

Assessment Elements

Class work, activity
Tests are run in both the 2nd and the 3rd modules, and the scores for the tests are taken into con
The students do a group coursework (3 persons in a group) in the 3rd module
Согласно Положению НИУ ВШЭ
Tests are run the 3rd module, and the scores for the tests are taken into consideration in calcul
Class work, activity
Tests are run in both the 2nd and the 3rd modules, and the scores for the tests are taken into con
The students do a group coursework (3 persons in a group) in the 3rd module
Согласно Положению НИУ ВШЭ
Tests are run the 3rd module, and the scores for the tests are taken into consideration in calcul

Interim Assessment

Interim assessment (3 module)
0.1 * Class work, activity + 0.2 * Tests are run in both the 2nd and the 3rd modules, and the scores for the tests are taken into con + 0.3 * Tests are run the 3rd module, and the scores for the tests are taken into consideration in calcul + 0.4 * The students do a group coursework (3 persons in a group) in the 3rd module

Bibliography

Recommended Core Bibliography

Абанкина, И., Алескеров, Ф., Белоусова, В., Зиньковский, К., & Петрущенко, В. (2013). Оценка Результативности Университетов С Помощью Оболочечного Анализа Данных. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.F51E40DE
Альперович. В. Д. Качественные и количественные методы фзндаментальных исследований в психологии : учебное пособие / В. Д. Альперович : Южный федеральный университет. - Ростов-на-Дону : Таганрог : Издательство Южного федерального университета. 2017. - 114 с. - ISBN 978-5-9275-2389-4. - Текст : электронный. - URL: https://new.znanium.com/catalog/product/1020509 - Текст : электронный. - URL: http://znanium.com/catalog/product/1020509
Бинарные отношения, графы и коллективные решения : учеб. пособие для вузов, Алескеров, Ф. Т., 2006

Recommended Additional Bibliography

Базилевич С.В., Легчилина Е.Ю. - Количественные методы в управлении - КноРус - 2016 - 153с. - ISBN: 978-5-406-05502-1 - Текст электронный // ЭБС BOOKRU - URL: https://book.ru/book/920637

Bachelor’s Programme 'Public Administration'

Quantitative Analysis in Procurement and Public–Private Partnership