Multiprocessor Scheduling with Rejection
SIAM Journal on Discrete Mathematics
Preemptive multiprocessor scheduling with rejection
Theoretical Computer Science
Towards Stochastic Constraint Programming: A Study of Online Multi-choice Knapsack with Deadlines
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Batch processing with interval graph compatibilities between tasks
Discrete Applied Mathematics
Mutual exclusion scheduling with interval graphs or related classes, Part I
Discrete Applied Mathematics
Computers and Operations Research
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At regular times, a satellite launcher company has to plan the use of its launcher to get the maximum profit. In a more formal way, the problem consists of selecting and scheduling a subset of unit-length jobs constrained by capacitated time slots so that the overall cost is a minimum. The data associated with each job are its weight, its time-window and its expected gain when it is performed. With each time slot are associated a setup cost and a capacity. The setup cost of a time slot is due when this time-slot is used to perform at least one job. Moreover the total weight of all jobs scheduled within a time slot is at most the time slot capacity. We first show that the general problem is hard and provide some easy special cases. We then propose a first dynamic-programming polynomial-time algorithm for the special case with unit weights. A second and more efficient dynamic programming algorithm is also provided for the special case of unit weights and agreeable time windows. This last algorithm is finally improved for the special case of equal gains.