MA3605: Queueing Theory and Inventory Control
| School | Cardiff School of Mathematics |
| Department Code | MATHS |
| Module Code | MA3605 |
| External Subject Code | G200 |
| Number of Credits | 10 |
| Level | L6 |
| Language of Delivery | English |
| Module Leader | DR Timm Oertel |
| Semester | Spring Semester |
| Academic Year | 2016/7 |
Outline Description of Module
This module consists of two parts, queueing theory and stock control. The queueing theory section develops methodology introduced in MA0261 in order to analyze more realistic queueing systems. As a key concept in this course, we introduce Markov chains to model random presses. This allows us then to analyze more general, in particular more realistic, queueing systems. In the stock control section, we develop basic inventory stock models and introduce important management decision processes.
Prerequisite Modules: MA0261 Operational Research
On completion of the module a student should be able to
- understand the principle concept of Markov Chains.
- work with various distributions such as the negative exponential distribution and Erlang distribution.
- apply Markov Chains to general queues, such as M/G/1 and GI/M/1.
- set up differential-difference equations and use generating function techniques to find steady-state solutions.
- understand, model and analyze simple deterministic and stochastic inventory control systems.
- undertake simple cost analyses relating to the above models.
How the module will be delivered
22 fifty-minute lectures
5 fifty-minute exercise classes.
Students are also expected to undertake at least 50 hours private study including preparation of worked solutions for tutorial classes.
Skills that will be practised and developed
Problem solving, logical thinking and mathematical formulation of real-life situations
How the module will be assessed
Formative assessment is carried out by means of regular exercises. Feedback to students on their solutions and their progress towards learning outcomes is provided during classes.
Summative assessment is by means of the written examination at the end of the module. This gives students the opportunity to demonstrate their overall achievement of learning outcomes. It also allows them to give evidence of the higher levels of knowledge and understanding required for above average marks.
The examination paper has a choice of three from four equally weighted questions.
Assessment Breakdown
| Type | % | Title | Duration(hrs) |
|---|---|---|---|
| Exam - Spring Semester | 100 | Queueing Theory And Inventory Control | 2 |
Syllabus content
- Markov chains.
- Generating functions.
- Little’s law.
- Erlang distribution.
- M/G/1 and GI/M/1 queueing models.
- Deterministic inventory control models involving cyclical review and re-order level methods.
- Constrained systems.
- Simple stochastic inventory control models
Background Reading and Resource List
Gross,D. et al. 2008. Fundamentals of Queueing Theory, 4th ed. Wiley. eBook available at: http://bit.ly/2d3wK8s
Beyer, D. et al. 2009. Markovian Demand Inventory Models. Springer.