Summary: 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 defined 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 in the design and implementative of 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.