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Stochastic Modelling

DATE: 4th - 8th April 2011
LOCATION: Lancaster University

Stochastic modelling is concerned with uncertainty. Many of the real-life systems and processes to which OR methods are applied are not deterministic in nature, but are characterised by significant degrees of uncertainty. Meaningful analyses of such systems must take serious account of this feature. The Operational Research literature abounds with applications of stochastic modelling. Healthcare, Transport, Communications, and Finance are areas which are replete with opportunities for the stochastic modeller. This course will present some of the theory. Important features of the course will be the use of case studies to illustrate and discuss applications and the deployment of numerical approaches.

Main contributors: Professor Jeff Griffiths (course leader, Cardiff), Professor Steve Gallivan (University College, London), Professor Kevin Glazebrook (Lancaster), Dr Tony Lewins (Ernst & Young), Dr Phil Scarf (Salford), Dr Dave Worthington (Lancaster).

PRE-REQUISITES

Much of the material needed as background reading for this course will be provided on-line. Topics included will be elements of probability and stochastic processes together with some introductory material on application areas, including queuing systems, inventory control and maintenance and reliability.

AIMS

The course aims to provide an appreciation of the theory which has been developed to model real-life situations which feature uncertainty. On completion of the course, participants should be better prepared to understand the more sophisticated models that appear in the literature.

LEARNING OUTCOMES

On completion of the block, students will be expected to:

  • understand the basics of stochastic processes, with particular relevance to queuing theory, inventory control and maintenance and reliability
  • be aware of the rich diversity of applications of stochastic modelling,
  • be conscious of the relationships and complementarities between analytic/numerical approaches and simulation modelling (Block E).

PRINCIPAL TOPICS OF STUDY

  1. Introductory material. Finite state Markov chains, both discrete and continuous time. Numerical issues. Examples will be chosen to support understanding of the later application-focussed material.
  2. Case studies. The following topics will be extensively illustrated by case studies taken from fields such as finance, telecommunications, epidemics, transport, healthcare.
  3. Queueing Systems and Networks. Queues with general arrival and service patterns, including batch arrivals and services and phase-type service distributions, queues in series and in parallel. Numerical approaches to transient behaviour.
  4. Maintenance, reliability and renewal processes. Replacement decisions (age, preventative, block, etc), inspection criteria, stochastic comparison of system reliabilities and maintenance policies, scheduling and sequencing decisions, continuous and discrete renewal and repair processes. Computational issues.
  5. Stochastic models of inventory control. Review of deterministic models as approximations to stochastic situations, Newsboy-type problems, time-varying demands, stochastic demand with constant lead-times, stochastic lead-times.
  6. Brownian motion. An introduction to Brownian motion and its application to finance.
  7. Assessment Assessments, which will be formative in nature, will be held each day. They will take a variety of formats, and will typically last about half-an-hour. Feedback will be provided before the end of the course.