Over the last two decades, the globalization trend has brought about vibrant supply, demand and engineering chains of production. These systems are dynamic in their evolution, configuration and operation. At the same time, large scale, complex factories have been developed. In this course, we will discuss mathematical tools for analysis and optimization of production by factory and collaborative enterprise chain. This course will cover linear programming, unconstrained optimization, stochastic linear programming, non-linear programming, integer programming, and dynamic system optimization. We will use example problems in production systems engineering and industrial economics to develop in-depth understanding of the theory.