《1993 A practical approach to job-shop scheduling problems》.pdfVIP

IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 9, NO. I , FEBRUARY 1993 1 A Practical Approach to Job-Shop Scheduling Problems Debra J. Hoitomt, Member, IEEE, Peter B. Luh, Senior Member, IEEE, and Krishna R. Pattipati, Senior Member, IEEE Abstract-Scheduling is one of the most important issues in the planning and operation of manufacturing systems, but the generation of consistently good schedules has proven to be ex- tremely difficult. The problem is that optimal scheduling solutions involve costly and impractical enumeration procedures, while the performance of most heuristic techniques is difficult to estimate and varies comiderably from one problem to the next. Recently, scheduling methodologies based on Lagrangian relaxation have proven to be computationally efficient and have provided near- optimal solutions to identical, parallel machine scheduling prob- lems. In tliispaper, we explore the use of Lagrangian relaxation to schedulejob shops, which include multiple machine types, generic precedence constraints, and simple routing considerations. Using an augmented Lagrangian formulation, the scheduling problem is decomposed into operation-level subproblems for the selection of operation beginning times and machine types, with given Mlhng multipliers and penalty coefficients. The multipliers and penalty (h coefficients are then updated at the high level. The solution forms the basis of a list-scheduling algorithm that generates a feasible schedule. A procedure is also developed to evaluate the quality of this feasible schedule by generating a lower bound on the optimal cost. Numerical examples are taken from a representative industrial