We consider the problem of scheduling n independent jobs on m identical machines that operate in parallel. Each job has a controllable processing time. The fact that the jobs have a controllable processing time means that it is allowed to compress (a part of) the processing time of the job, in return for compression cost. We present the first known polynomial time approximation schemes for the ...

This article addresses resource allocation scheduling problems with slack due window on a single machine. Linear and convex are considered. Our goal is to determine the optimal schedule, window, allocation, minimizing various objective functions respect criteria (position-dependent weights number of early jobs, tardy starting time, size) consumption function. For linear problem, we study two ca...

This paper provides a review of recent results on scheduling with controllable processing times. The stress is on the methodological aspects that include parametric flow techniques and methods for solving mathematical programming problems with submodular constraints. We show that the use of these methodologies results into fast algorithms for solving problems on single machine or parallel machi...

The single machine scheduling problem with two types of controllable parameters, job processing times and release dates, is studied. It is assumed that the cost of compressing processing times and release dates from their initial values is a linear function of the compression amounts. The objective is to minimize the sum of the total completion time of the jobs and the total compression cost. F...