Stochastic Processes (300IGQ004)

Basic Information

  • Course code number and name: 300IGQ004, Stochastic Processes.
  • Credits and contact hours: 2 credit hours, 3 hours per week.
  • Course coordinator: Álvaro Figueroa
  • Type of course: Required.

Text book

  • Operations Research, H. Taha, 2012.

Supplemental materials

  • Introduction to Operations Research, H. Lieberman, 2012.
  • Operations Research: Applications and Algorithms, W.L. Winston, 2003.

Specific course information

The purpose of this course is to introduce the field of optimization under stochastic parameters. To that effect, the models of the Classical Theory of Decisions are presented with attention to the models under certainty, risk and uncertainty as well as the hierarchical analysis and the organizational problems that can be treated from that perspective. On the other hand, Dynamic Programming is used to present recurrent relationships, the analysis derived from the Bellman principle and to model realistic situations where decisions are taken sequentially. The Markov chains are studied as well as several models of finite-state chains and realistic systems that can be studied as markovian chains and their effect under equilibrium conditions. Finally, Queues Theory is studied to analyze, formulate and solve problems related to queues and waiting phenomena and their applications in organizations.

Specific goals of the course

Learning objectives:
  • To describe the principles of the theory of decisions.
  • To define the decision criteria under risk.
  • To analyze the sensitivity of a solution due to changes in the probabilities of the nature of the problem of interest.
  • To construct tables of analysis by criteria and alternatives, according to the AHP methodology.
  • To define the state variables, the steps, the decisions and the recursive equation corresponding to a problem that can be decomposed in steps.
  • To construct one-step transition matrices in markovian processes.
  • To calculate the steady-state probabilities of a Markov chain.
  • To identify the components and features of a system of waiting queues.
  • To formulate the balance equations of a waiting queues system with markovian distribution.
  • To calculate the expected costs of waiting, abandonment, and the use of attendants in systems of queues with markovian distributions.
Relationship with student outcomes
Student Outcomes
A B C D E F G H I J K
Relevance 3 2 2 3 2

1: low relevance; 2: medium relevance; 3: high relevance.

Topics of the course

  • Decision models under uncertainty.
  • Decision models under risk.
  • Decision trees.
  • Analytical Hierarchy Process – AHP.
  • Bellman principle.State variables, decisions, steps and recursive equation.
  • Finite-state Markov chains.
  • Transition probabilities.
  • Transition matrices. Limiting distribution in Markov chains.
  • Processes of arrival and service. Queues models. Kendall notation.
  • One-channel and multi-channel models with infinite capacity and population. Finite- queue models. Finite-population models.
  • Queues models with Erlang services. Models that do not follow the Poisson distribution. The Pollaczec-Khintchine formulae.
 
undergraduate/dptocivileindustrial/stochasticprocesses.txt · Última modificación: 2014/10/05 20:36 por lsosorio
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