Course syllabus - Operations Research

Objectives

Optimization, a subfield of operations research, is part of applied mathematics, i.e. mathematics dealing with mathematical models and algorithms to solve practical problems in the areas of computer science, economics, engineering, physics, chemistry, biology etc. The types of problems treated in the course are linear, nonlinear and discrete optimization problems. The course shall give a broad orientation of the field of optimization, with emphasis on basic theory and methods for continuous and discrete optimization problems in finite dimension, and it also gives some insight into its use for analyzing practical optimization problems.

Learning outcomes

At the end of the course the student is expected to be able to
- identify optimization problems and classify them according to their properties.
- construct mathematical models of elementary optimization problems.
- define and characterize common types of linear, nonlinear and discrete optimization problems.
- explain and apply the basic theory and understand the basic algorithms for the common types of linear, nonlinear and discrete optimization problems studied in the course.
- use standard optimization software to solve problems from the various areas studied.
- model and solve classical problems such as the shortest path problem: "Which route shall we choose between places A and B in order to find the shortest path?" and the fuel consumption problem: "Under the constraint that the travelling time should not exceed X minutes, how fast should we travel on the different sub-stretches in order to minimize the fuel consumption?"
- find practical applications, which could benefit from use of optimization methods.

Course content

Linear programming: the simplex algorithms, sensitivity analysis, duality, transportation problems, network optimization, dynamic programming, practical applications.
Nonlinear Programming: nonlinear optimization models with or without constraints, convex sets and functions, steepest descent and Newton type methods, quadratic programming with linear constraints, Karush-Kuhn-Tucker conditions, SQP methods, Lagrangean duality, practical applications.
Integer programming: Gomory's cutting plane methods for pure and mixed-integer linear programming, search methods, branch and bound algorithms, combinatorial programming, practical applications.
Practical solution of optimization problems in Matlab and/or other software for optimization.

Tuition

Lectures and exercises.

Specific requirements

At least totally 60 credits in the technical, natural sciences, business administration or economics areas including Basic Calculus Continuation Course, 7.5 credits, of which 2.5 credits must be completed at the beginning of the course, Numerical Methods, 7.5 credits, of which 3 credits must be completed at the beginning of the course, Basic Calculus, 7.5 credits, and Basic Vector Algebra, 7.5 credits, or equivalent.

Examination

Exercises (LAB1), 1.5 credits, marks Pass (G)
Written examination, (TEN1) 6 credits, marks 3, 4 or 5

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3