First semester

This module on Linear Programming offers a thorough study of fundamental and advanced methods in the field. It starts with modelling, where students learn to formulate linear programming problems by defining variables, constraints, and an objective function. Next, it introduces the graphical solution technique, particularly for solving two-variable problems. The course progresses to the simplex method, providing a detailed understanding of its application in larger problem sets. Advanced topics, such as the two-phase simplex and Big-M method, are then covered to manage more complex cases involving artificial variables and additional constraints. The concept of duality is explored, helping students interpret results and enhance solution optimisation. A section on sensitivity analysis examines the effects of parameter changes on the optimal solution, focusing on solution stability. Lastly, the module introduces transportation models, outlining their formulation and specific techniques for solving them. This structured course ensures a solid grasp of linear programming, from basic problem formulation to more intricate solution methods.