Explore linear integer programming and mixed integer programming in this comprehensive lecture by Professor Raphael Hauser from the Alan Turing Institute. Delve into supply chain management applications and learn about the branch and bound algorithm, including its use in solving the Traveling Salesman problem. Understand the mechanism of bounds, infeasibility, pruning by optimality, and LP relaxation. Examine fractional branching techniques and their implementation in optimization problems. Gain insights from a renowned expert with extensive experience in mathematics, theoretical physics, and operations research, whose work spans across numerical analysis, applied probability, and distributed computing.