Operational Research I and Mathematical Computing

Learning Outcomes

Learning Outcomes

Having successfully completed this module you will be able to:

• Code simple mathematical algorithm in a programming language (Python), to analyze the computational behavior of such algorithms, and to describe them in writing.
• Formulate a mathematical model for certain types of practical problem
• Implement simple mathematical modeling and algorithms for to computational solutions of decision making problems.
• Demonstrate knowledge and understanding of selected OR techniques
• Appreciate the capabilities and limitations of OR techniques.

Operational Research

• Linear programming (LP): assumptions, applications, geometry of LPs, graphical solution method, simplex method (single-phase and two-phase).
• Elements of integer programming modeling.
• Introduction to algorithms: definition and specification of algorithms; asymptotic estimates of their running times.
• Sorting algorithms.
• Shortest path algorithms for graphs with nonegative arc lengths.

Mathematical Computing

• Python: introduction, basic usage of the software used (either Jupyter notebooks or Spyder)
• Variables: Definition, naming conventions and using sensible names. Integer, float, strings, printing.
• Loops: Concept of iteration, using for and while loops, range function. Semantic whitespace in Python.
• Control flow: Logical statements and boolean variables. if/elif/else.
• Functions: Concept and procedural programming. Definition in Python: def and return keywords. Docstrings and help. Script files, import, packages.
• Data structures: Lists, tuples, dictionaries and sets. Vectors and arrays through numpy.
• LaTeX: Basic environments and sections. Packages such as amsmath. BibTeX and reference managers. Creating long documents.
• Excel: advanced data analysis and presentation. Linking to other packages (eg Python via xlrd and xlwt).

Teaching and learning methods

Lectures, problem classes, computer workshops, private study.

Resources & Reading list

Textbooks

S.Dasgupta, C.H. Papadimirriou, U. Vazirani (2006). Algorithms. McGraw-Hill.

W.L. Winston (2004). Operations Research: Applications and Algorithms. Thomson Brooks/Cole.

A.Saha (2015). Doing Math with Python. No Starch Press.

H.P. Langtangen (2016). A Primer on Scientific Programming with Python. Springer.

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External