Mathematical Programming with Julia
An open-source approach to Linear & Mixed Integer Programming Version 1.0 Julia 1.7.2/JuMP 1.0
Richard Lusby & Thomas Stidsen
Introduction
Models of many kinds, both physical and mathematical, have been used for centuries, mainly to gain an understanding of the larger system that is modelled. Mathematical models have been applied in natural sciences and technical sciences at least since Galileo Galilei and Isaac Newton. With the advent of the computer, even models that cannot be solved analytically may produce results. In this book, we only consider two specific types of mathematical models: Linear Programming (LP) and Mixed Integer Programming (MIP). Since the world war II, these two types of models have been crucial for planning, and they have been applied widely in many areas. Both model types require model constructors to define decision variables, an objective function, and one or more constraints defining feasibility. Building LP and MIP models, thus builds understanding of the problem. Having an LP or a MIP model enables optimization, which can provide an optimal solution to the model. Recent technological developments have made the two standard techniques of LP and MIP even more powerful and much more accessible. Optimization software, e.g., Gurobi, Cplex and HiGHS, has not only improved dramatically, but computer hardware has also become much faster, not to mention cheaper. Modern open-source programming languages and some of the solvers, HiGHS, have made the price right; they are free. With this book, we hope to make open-source modelling and solver software for mathematical programming more accessible to a wider audience. Therefore, this book is freely available.
link to material: https://www.ifors.org/wp-content/uploads/2022/08/Mathematical-Programming-with-Julia.pdf
