Scheduling chain-structured tasks to minimize makespan and mean flow time
Information and Computation
Scheduling identical parallel machines to minimize total weighted completion time
CO89 Selected papers of the conference on Combinatorial Optimization
Approximating total flow time on parallel machines
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Minimizing mean flowtime in a two-machine flowshop with sequence-independent setup times
Computers and Operations Research
Scheduling Jobs that Arrive Over Time (Extended Abstract)
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
A note on scheduling multiprocessor tasks with identical processing times
Computers and Operations Research
Operations Research Letters
Parallel machine scheduling with precedence constraints and setup times
Computers and Operations Research
A multiobjective optimization approach to solve a parallel machines scheduling problem
Advances in Artificial Intelligence
Integrating parts design characteristics and scheduling on parallel machines
Expert Systems with Applications: An International Journal
| Hi-index | 0.01 |
This paper addresses an identical parallel machine scheduling problem, with sequence-dependent setup times and release dates to minimize total completion time. This problem is known to be strongly NP-hard. We prove a sufficient and necessary condition for local optimality which can also be considered as a priority rule. We then define a dominant subset based on this condition. We present efficient heuristic algorithms using this condition to build a schedule belonging to this subset. We also prove dominance theorem, and develop a lower bound that can be computed in polynomial time. We construct a branch-and-bound algorithm in which the heuristic, the lower bound and the dominance properties are incorporated. Computational experiments suggest that the algorithm can handle test problems with 40 jobs and 2 machines.