  A mathematical programming model for a class of single machine family
scheduling problem is described in this technical report, with the aim of
comparing the performance in solving the scheduling problem by means of
mathematical programming with the performance obtained when using optimal
control strategies, that can be derived from the application of a dynamic
programming-based methodology proposed by the Author. The scheduling problem is
characterized by the presence of sequence-dependent batch setup and
controllable processing times; moreover, the generalized due-date model is
adopted in the problem. Three mixed-integer linear programming (MILP) models
are proposed. The best one, from the performance point of view, is a model
which makes use of two sets of binary variables: the former to define the
relative position of jobs and the latter to define the exact sequence of jobs.
In addition, one of the model exploits a stage-based state space representation
which can be adopted to define the dynamics of the system.
