The shifting bottleneck procedure for job shop scheduling
Management Science
An algorithm for solving the job-shop problem
Management Science
Optimal and approximately optimal control policies for queues in heavy traffic
SIAM Journal on Control and Optimization
Sequencing in an assembly line with blocking to minimize cycle time
Operations Research
Routing and singular control for queueing networks in heavy traffic
SIAM Journal on Control and Optimization
Operations Research - Supplement to Operations Research: stochastic processes
Journal of the ACM (JACM)
Cyclic schedules for job shops with identical jobs
Mathematics of Operations Research
IEEE/ACM Transactions on Networking (TON)
Improved Approximation Algorithms for Shop Scheduling Problems
SIAM Journal on Computing
IEEE/ACM Transactions on Networking (TON)
On some geometric methods in scheduling theory: a survey
Discrete Applied Mathematics
Makespan minimization in job shops: a polynomial time approximation scheme
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The Complexity of Optimal Queuing Network Control
Mathematics of Operations Research
Asymptotically optimal algorithms for job shop scheduling and packet routing
Journal of Algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Sequencing and Routing in Multiclass Queueing Networks Part I: Feedback Regulation
SIAM Journal on Control and Optimization
Performance Evaluation and Policy Selection in Multiclass Networks
Discrete Event Dynamic Systems
A New Approach to Computing Optimal Schedules for the Job-Shop Scheduling Problem
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Fluid Heuristic for Minimizing Makespan in Job Shops
Operations Research
In Search of Sensitivity in Network Optimization
Queueing Systems: Theory and Applications
Maximum Pressure Policies in Stochastic Processing Networks
Operations Research
Data and Computer Communications (8th Edition)
Data and Computer Communications (8th Edition)
Mathematics of Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
Control Techniques for Complex Networks
Control Techniques for Complex Networks
Microchip Fabrication, 5th Ed.
Microchip Fabrication, 5th Ed.
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We consider large volume job shop scheduling problems, in which there is a fixed number of machines, a bounded number of activities per job, and a large number of jobs. In large volume job shops it makes sense to solve a fluid problem and to schedule the jobs in such a way as to track the fluid solution. There have been several papers which used this idea to propose approximate solutions which are asymptotically optimal as the volume increases. We survey some of these results here. In most of these papers it is assumed that the problem consists of many identical copies of a fixed set of jobs. Our contribution in this paper is to extend the results to the far more general situation in which the many jobs are all different. We propose a very simple heuristic which can schedule such problems. We discuss asymptotic optimality of this heuristic, under a wide range of previously unexplored situations. We provide a software package to explore the performance of our policy, and present extensive computational evidence for its effectiveness.