A survey of results for sequencing problems with controllable processing times
Discrete Applied Mathematics - Southampton conference on combinatorial optimization, April 1987
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Coordination complexity of parallel price-directive decomposition
Mathematics of Operations Research
Linear Programming in O([n3/ln n]L) Operations
SIAM Journal on Optimization
A Linear Time Approximation Scheme for the Job Shop Scheduling Problem
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Fast approximation algorithms for knapsack problems
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Single machine scheduling with discretely controllable processing times
Operations Research Letters
Approximation schemes for parallel machine scheduling problems with controllable processing times
Computers and Operations Research
A framework for designing approximation algorithms for scheduling problems
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
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Most scheduling models assume that the jobs have fixed processing times. However, in real-life applications the processing time of a job often depends on the amount of resources such as facilities, manpower, funds, etc. allocated to it, and so its processing time can be reduced when additional resources are assigned to the job. A scheduling problem in which the processing times of the jobs can be reduced at some expense is called a scheduling problem with controllable processing times. In this paper we study the job shop scheduling problem under the assumption that the jobs have controllable processing times. We consider two models of controllable processing times: continuous and discrete. For both models we present polynomial time approximation schemes when the number of machines and the number of operations per job are fixed.