Module Specifications.
Current Academic Year 2024 - 2025
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Date posted: September 2024
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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 | |||||||||||||||||||||||||||||||||||||||||
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 |
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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. | |||||||||||||||||||||||||||||||||||||||||
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Indicative Reading List
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