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