This class exists in these courses :
• IÉSEG > IESEG Degree - Programme Grande École > Semester 2 > 2,00 ECTS

Prerequisites

Course presupposes an understanding of optimisation without and with equality or inequality constraints (basic optimisation course for business, or basic linear programming course).

Learning outcomes

This course provides an applied perspective on Mathematical Programming (MP), instead of focusing on algorithms. In particular, it serves 3 purposes:
(i) providing a selective catalogue of practical MP problems faced by managers,
(ii) linking these problems to the different types of mathematical optimisation methods,
(iii) formulating MP problems and interpreting their solutions within a spreadsheet.

At the end of the course, the student should be able to:
- understand the concepts of MP-based optimisation
- interpret the solutions of MP, thereby distinguishing between (i) the optimal values of decision variables and (ii) the optimal value of the objective function
- interpret sensitivity analysis on (i) objective function coefficients (ii) parameters of the constraints on the left and right hand sides, and (iii) adding or discarding constraints or decision variables
- understand the notion of a shadow price
- recognise a practical business problem as amenable to MP formulation due to a knowledge of a catalogue of MP problems

Course description

The course follows Hillier & Hillier (2008) closely: Ch. 1-8 (except Ch.4) are covered completely:
Ch. 1: Introduction
Ch. 2: Linear Programming: Basic Concepts
Ch. 3: Linear Programming: Formulations and Applications
Ch. 5: What-If Analysis for Linear Programming
Ch. 6: Network Optimization Problems
Ch. 7: Using Binary Integer Programming to Deal with Yes-or-No Decisions
Ch. 8: Nonlinear Programming

MP techniques discussed are linear, non linear, integer (general and binary) programming, non linear integer programming, and sensitivity analysis for small changes (parametric programming for large changes).

A series of additional topics are discussed based on course notes: heuristics vs. optimisation, some guidelines for MP-based consulting projects, cutting stock, Travelling Salesman Problem (TSP), a variety of basic portfolio optimisation models, etc.

Lectures are based on a textbook, additional lecture notes, and class discussion.

Students prepare lectures (read the textbook) according to the guidelines communicated at the end of each session.

The course consists of 16 hours study. These include some common practice sessions in the PC labs (depending on PC's available to students).

Class type

Class structure

Teaching methods

• E-learning
• Interactive class
• Research
• Tutorial

Assessment

Participation in lectures (mainly exercises): 30%
Final exam: multiple choice and open-ended questions: 70%

Recommended reading

• Hillier, F.S., M.S. Hillier (2008) Introduction to Management Science, 3rd Ed., Boston, Irwin/McGraw-Hill. -

• Williams, H.P. (2013) Model Building in Mathematical Programming, 5th Ed., New York, Wiley. -

Internet resources

• The intranet course website includes, among others, supplementary learning material, links to MP software and specific MP, OR and OM sites, etc. - Students are urged to consult this site on a regular basis!