Algebraic, mathematical programming, and network models of the deterministic job-shop scheduling problem

In the contemporary literature on deterministic machine scheduling, problems are formulated from three different, but equivalent, perspectives. Algebraic models provide a rigorous problem statement in the language of set theory and are typical of the more abstract development of scheduling theory in mathematics and computer science. Mathematical programming models rely on familiar concepts of nonlinear optimization and are generally the most accessible. Network models (disjunctive graphs) are best suited to the development of solution approaches and figure prominently in discussions of algorithm design and analysis. In this tutorial, it is shown how the minimum-makespan job-shop problem (n/m/G/C_max) is realized in each of these three model forms. A common notation is developed and how the underlying structure and fundamental difficulty of the problem are expressed in each model is demonstrated