Proper organization, planning and design of production, storage locations, transportation and scheduling are vital to retain the competitive edge of companies in the global economy. Typical additional problems in the chemical industry suitable for optimization are process design, process synthesis and multi-component blended-flow problems leading to nonlinear or even mixed integer nonlinear models. Mixed integer optimization (MIP) determines optimal solutions of such complex problems; the development of new algorithms, software and hardware allow the solution of larger problems in acceptable times. This tutorial paper addresses two groups. The focus towards the first group (managers and senior executives) and readers who are not very familiar with mathematical programming is to create some awareness regarding the potential benefits of MIP, to transmit a sense of what kind of problems can be tackled, and to increase the acceptance of MIP. The second group (a more technical audience with some background in mathematical optimization), might rather appreciate the state-of-the-art view on good-modelling practice, algorithms and an outlook into global optimization. Some real-world MIP problems solved by BASF's mathematical consultants are briefly described, among them discrete blending and multi-stage production planning and distribution with several sites, products and periods. Finally, there is a focus on future perspectives and sources of MIP support are indicated from academia, software providers and consulting firms.