A generalized job shop scheduling problem is defined in detail. The proposed factory description is sufficiently realistic to model the routing and sequencing decisions made in a real manufacturing plant. An optimization problem is posed, permitting the use of very general cost functions. A variation of the method of simulated annealing is proposed as a tool for the solution of the optimization problem. A novel technique for embedding the space of feasible schedules into a permutation group is used to define a neighborhood structure for the simulated annealing process. This technique has algorithmic advantages over working directly in the space of schedules. These ideas were used to construct a scheduling software system which is in use at a Texas Instruments Custom Manufacturing Unit. We give a brief description of the software system, called ABES for Annealing Based Experiment in Scheduling, and comment on its effectiveness.