Mixed-Integer Linear Programming: Formulations and Applications

This lecture covers the motivation behind mixed-integer linear programming (MILP) by highlighting the need to model practical problems with discrete variables. It explains the concept of binary variables in LPs, the formulation of mixed-integer LPs, and their applications in decision-making problems such as the 0-1 knapsack problem and the assignment problem. The lecture also delves into the relationships between events, disjunctive constraints, and forcing constraints in MILPs. It concludes with a discussion on the strength of LP relaxations, the ideal formulation for an integer problem, and the importance of formulating MILPs effectively.