| CODE | SOR1320 | ||||||||
| TITLE | Linear Programming | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| EQF/MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | - Problem Formulation and Graphical Solution; - Convex and Polyhedral Sets; - Extreme Points and Extreme Directions; - Fundamental Theorems of Linear Programming; - Simplex Method: - Derivation and Matrix Form; - Simplex Table and its Interpretation; - Initial Solution Search Methods; - Sensitivity Analysis. - Duality Theory: - Formulation of Dual Models; - Duality Theorems; - Dual Simplex Method; - Interpretation of Dual Models. - Network Flow Problems (Transportation, Assignment): - Designated Algorithms for Network Problems; - Conversion of Nonlinear Programs to Linear Programs; - Software Packages. Study-unit Aims: - Define and describe what an LP problem is - from real life examples to the mathematical formulation; - Introduce fundamental theoretical concepts underpinning LP, including linear independence, convexity of sets and functions, extreme points and directions, convex hull, etc. - Equip students with analytical and algorithmic solution methods, including graphical techniques and the Simplex Method; - Develop the ability to analyse and interpret LP solutions through sensitivity analysis; - Introduce concepts from Duality Theory and the relation between the primal and the dual problems, accompanied by the introduction and description of the Dual Simplex Algorithm; - Provide experience in applying LP techniques to practical problems, including network flow models and real-life applications using appropriate software tools. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - Formulate real-world problems as Linear Programming models, identifying decision variables, objective functions, and constraints; - Explain key theoretical concepts of LP, including convex sets, extreme points, and fundamental optimality results; - Describe and compare solution methods, including graphical methods, the Simplex Method, and the Dual Simplex Method; - Explain the concept of duality and interpret the relationship between primal and dual problems; - Interpret optimal solutions and sensitivity analysis results in practical decision-making contexts. 2. Skills By the end of the study-unit the student will be able to: - Solve Linear Programming problems graphically for two-variable cases; - Apply the Simplex Method and Dual Simplex Method to solve LP problems in standard form; - Perform sensitivity analysis and evaluate the impact of parameter changes on optimal solutions; - Formulate and solve dual problems and interpret their physical meaning; - Model and solve network flow problems such as transportation and assignment problems; - Use appropriate software tools (e.g. MATLAB, LINGO, or equivalent) to implement and solve LP models; - Communicate solutions clearly, including formulation, computational steps, and interpretation of results. Main Text/s and any supplementary readings: - Bazaraa, M.S., Jarvis, J.J. and Sherali, H.D. (2010) Linear Programming and Network Flows, Wiley, 4th ed. - Luenberger, D.G. (2005) Linear and Nonlinear Programming, Springer, 2nd ed. - Williams, H.P. (1999) Model Building in Mathematical Programming, Wiley, 4th ed. - Ahuja, R.K., Magnanti T.L. and Orlin, J.B. (1993) Network Flows: Theory, Algorithms and Applications, Prentice Hall Inc. - Taha, H.A. (2011) Operations Research: An Introduction, Pearson, 9th ed. - Winston,W.I. (2004) Operations Research: Applications and Algorithms, Thomson, 4th ed. - Luenberger, D.G. and Ye, Y. (2016) Linear and Nonlinear Programming, Springer, 4th ed. |
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| ADDITIONAL NOTES | Pre-requisite Qualification: Advanced Level in Pure Mathematics | ||||||||
| STUDY-UNIT TYPE | Lecture and Practical | ||||||||
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2026/7. It may be subject to change in subsequent years. |
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