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 OPERATIONAL RESEARCH: PROBABILISTIC MODELS
Code MATH268
Coordinator Dr R Tatar
Mathematical Sciences
Radu.Tatar@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2024-25 Level 5 FHEQ First Semester 15

Aims

To introduce a range of models and techniques for solving under uncertainty in Business, Industry, and Finance.

Learning Outcomes

(LO1) Compute probability distribution functions for a variety of probability densities relevant to queueing theories.

(LO2) Apply decision criteria, draw and use diagram trees, and apply dynamical programming procedures.

(LO3) Use queueing theory to compute waiting times, and the number of customers in the system and in the queue.

(LO4) Apply methods of simulation for discrete and continuous distributions, including to prove the inverse function theorem.

(LO5) Use time forecast series.

(S1) Problem solving skills

(S2) Numeracy

Syllabus
 

Decision analysis: strategies and decision trees. Markov Decision Processes. Forecasting: Queuing Theory: M/M/1, M/M/K and similar Markov models. Simulation: pseudo-random generators, universal and special algorithms (Polar, Von Neumann, etc). Simulation of stochastic processes including queues.

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

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

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:
 

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
final assessment  90    60       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework assignment 1 Standard UoL penalty applies for late submission. This is not an anonymous assessment.  0    10       
Homework assignment 2 Standard UoL penalty applies for late submission. This is not an anonymous assessment.  0    10       
Homework assignment 3 Standard UoL penalty applies for late submission. This is not an anonymous assessment.  0    10       
Homework 4 Standard UoL penalty applies for late submission. This is not an anonymous assessment.  0    10