A survey of results for sequencing problems with controllable processing times
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Single machine scheduling with discretely controllable processing times
Operations Research Letters
Single-machine scheduling with trade-off between number of tardy jobs and resource allocation
Operations Research Letters
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
Throughput-constrained voltage and frequency scaling for real-time heterogeneous multiprocessors
Proceedings of the 28th Annual ACM Symposium on Applied Computing
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We consider a single-machine scheduling problem, in which the job processing times are controllable or compressible. The performance criteria are the compression cost and the number of tardy jobs. For the problem, where no tardy jobs are allowed and the objective is to minimize the total compression cost, we present a strongly polynomial time algorithm. For the problem to construct the trade-off curve between the number of tardy jobs and the maximum compression cost, we present a polynomial time algorithm. Furthermore, we extend the problem to the case of discrete controllable processing times, where the processing time of a job can only take one of several given discrete values. We show that even some special cases of the discrete controllable version with the objective of minimizing the total compression cost are NP-hard, but the general case is solvable in pseudo-polynomial time. Moreover, we present a strongly polynomial time algorithm to construct the trade-off curve between the number of tardy jobs and the maximum compression cost for the discrete controllable version.