Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title INTRODUCTION TO METHODS OF OPERATIONAL RESEARCH
Code MATH261
Coordinator Dr JA Haddley
Mathematical Sciences
J.A.Haddley@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 5 FHEQ First Semester 15

Aims
After completing the module students should:
  • Appreciate the operational research approach.
  • Be able to apply standard methods to a wide range of real-world problems as well as applications in other areas of mathematics.
  • Appreciate the advantages and disadvantages of particular methods.
  • Be able to derive methods and modify them to model real-world problems.
  • Understand and be able to derive and apply the methods of sensitivity analysis. 

Learning Outcomes
Appreciate the operational research approach.
Be able to apply standard methods to a wide range of real-world problems as well as
applications in other areas of mathematics.
Appreciate the advantages and disadvantages of particular methods.
Be able to derive methods and modify them to model real-world problems.

Understand and be able to derive and apply the methods of sensitivity analysis.  Appreciate the importance of sensitivity analysis.


Syllabus
1 

Operational research methodology.

Linear programming:  solvability, simplex method, artificial variables, duality, degeneracy, elementary sensitivity analysis.

Transportation Problem: NWCR, Least-cost method, MODI methods, degeneracy, unbalanced problems.

Convex programming:  Lagrange multipliers, duality, numerical techniques (gradient methods, penalty functions, etc.).

Multiobjective problems:  dominance, non-inferior set, weighting method, other approaches.

Inventory theory:  fixed-order-quantity models, sensitivity analysis, production-inventory systems.

Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
MATH101; MATH102; MATH103  

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
Programme:G1N3 Year:2 Programme:NG31 Year:2 Programme:G101 Year:2 Programme:G110 Year:2 Programme:G1R9 Year:2 Programme:GG13 Year:2 Programme:GL11 Year:2,Programme:GL1Z Year:2 Programme:GN11 Year:2 Programme:GR11 Year:2 Programme:GG14 Year:2 Programme:GV15 Year:2 Programme:G1F7 Year:2 Programme:G100 Year:2

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Unseen Written Exam  2.5 hours  First semester  90  Yes  Standard UoL penalty applies  Main Exam Notes (applying to all assessments) Final exam rubric: Full marks can be obtained by fully answering all questions in Section A and THREE questions from Section B. Section A carries 55% of the total marks. Only the best THREE solutions to Section B will be counted. 
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework  12 weeks  First semester  10  No reassessment opportunity  Standard UoL penalty applies  Problem Sheets There is no reassessment opportunity,