Mathematical Optimisation

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs). Subjects: The scope of integer and combinatorial optimization, Linear programming, Network flow problems, Integer Programming, Combinatorial optimization, Heuristic algorithms, Relaxation techniques, Dynamic programming, Introducing python and Gurobi for optimisation. Goals: capability of formulating a discrete optimization model to maximize or minimize a function of many variables subject to (i) equality and inequality constraints, and (ii) integrality restrictions on some or all of the variables, capability of solving optimization models relying either on ad-hoc (e.g., Gurobi) or open-source (e.g., python) software in different application areas, such as production planning and scheduling, logistics and transportation, health care, and telecommunications. understanding how to translate a verbal description of a real-life optimization problem into a solvable mathematical formulation. capability of explaining to a wide audience, both in verbal and graphical terms, in a formally precise albeit simple way the meaning of the various results that are usually obtained from a linear programming optimization model (e.g., dual and slack variables, optimality gap, branch-and-bound search criterion, etc.). Capability of autonomously integrating different sources (textbooks, literature papers, optimization softwares, programming codes and libraries) to replicate and enhance existing formulations or designing new ones for real-life optimization problems.