Module: Operations Research Methods

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Operations Research Methods
Module Code	MM485 (ITS) / MEC1045 (Banner)
Faculty	Engineering & Computing	School	Mechanical & Manufacturing Eng
Module Co-ordinator	John Geraghty
Module Teachers	-
NFQ level	8	Credit Rating	7.5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

None
Array

Description

The purpose of this module is to introduce the fundamentals of the field of engineering and scientific practice of Operations Research. In this module students will develop knowledge and skills in formulating and analysing mathematical models for deterministic and stochastic optimisation problems subject to a set of constraints with particular emphasis on manufacturing planning problems. Students will participate in the following learning activities: they will attend weekly lectures and tutorials, participate in a group assignment and present for end of semester examination

Learning Outcomes

1. Formulate a mathematical model consisting of an objective function and a set of constraints to represent an optimisation problem
2. Solve deterministic Operations Research problems such as linear programming, integer programming, dynamic programming and inventory control problems using appropriate algorithms
3. Conduct sensitivity analysis of the solutions derived from solving linear progamming problems
4. Solve stochastic Operations Research problems such as stochastic inventory control, markovian analysis and queuing theory problems using appropriate algorithms
5. Develop and solve optimisation models using MS Excel Solver

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Formal timetabled lectures
Laboratory	24	Timetabled labs to support lecture series
Assignment Completion	36	Model development and testing and report preparation
Independent Study	91.5	including examination time and preparation
Total Workload: 187.5

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Problem Definition
Defining the problem, formulating a mathematical model, deriving solutions from the model, testing the model, and implementing the model.

Introduction to Linear Programming
LP assumptions, the Graphical solution method, the Simplex Method, Post-optimality analysis, duality and sensitivity analysis, the dual simplex method.

Transportation and Assignment Problems
Solution techniques for the transportation problem, the assignment problem, and the transhipment model. Using the Transportation problem to solve aggregated planning problems

Network Optimisation Models
Shortest-Path problem, Minimum Spanning Tree problem, Maximum Flow problem, Minimum Cost Flow problem, the Network Simplex Method.

Dynamic Programming
Introduction to dynamic programming, deterministic dynamic programming, probabilistic dynamic programming, formulation and application of DP.

Integer Programming
Binary Integer Programming and model formulation, Branch and Bound Technique for BIP, Mixed Integer Programming and Branch and Bound Algorithm for MIP.

Inventory Theory
Deterministic and Stochastic models, Periodic Review, Continuous Review and Single Period models.

Markov Chains
Introduction to Markov Chains and the Chapman-Kolmogorov Equations, Classification of States of a Markov Chain, Long run properties of a Markov Chain, Continuous Time Markov Chains

Queuing Theory
Structure of Queuing Models, Examples of Queuing systems, Role of the exponential distribution, the Birth-Death process, Queues with combined arrivals and departures, Queuing models based on the Birth-Death process, Queuing Models with non-exponential distributions, Priority-discipline queuing models, Queuing Networks. Queuing Theory in practice.

Markov Decision Process
Scope of the Markovian Decision Problem, Finite Stage Dynamic Programming Model, Infinite Stage Model, LP solution of the Markovian Decision Process

Introduction to Nonlinear Programming
Classical optimisation theory, unconstrained optima, constrained methods (Jacobian and Lagrangean), Khun-Tucker conditions for constrained nonlinear problems, Computation aspects of optimising unconstrained and constrained functions.

Assessment Breakdown
Continuous Assessment	30%	Examination Weight	70%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Group assignment	Formulate and solve mathematical models using technquies studied in this module and report and interpret results	30%

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 1

Indicative Reading List

Taha, Hamdy A: 2007, Operations Research - An Introduction,
Hillier, F.S. and Lieberman, G.J.: 2010, Introduction to Operations Researc, Ninth Ed, McGraw-Hill,

Other Resources

None