On the solution of concave knapsack problems
Mathematical Programming: Series A and B
An approximation algorithm for the generalized assignment problem
Mathematical Programming: Series A and B
Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem
Mathematics of Operations Research
Approximation algorithms
Scheduling problems for parallel dedicated machines under multiple resource constraints
Discrete Applied Mathematics - International symposium on combinatorial optimisation
Approximation schemes for parallel machine scheduling problems with controllable processing times
Computers and Operations Research
Machine scheduling with resource dependent processing times
Mathematical Programming: Series A and B
A survey of scheduling with controllable processing times
Discrete Applied Mathematics
Scheduling parallel jobs with linear speedup
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Operations Research Letters
Parallel machine scheduling with flexible resources
Computers and Industrial Engineering
| Hi-index | 0.00 |
We consider a scheduling problem where the processing time of any job is dependent on the usage of a discrete renewable resource, e.g. personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The objective is to find a resource allocation and a schedule that minimizes the makespan. We explicitly allow for succinctly encodable time-resource tradeoff functions, which calls for mathematical programming techniques other than those that have been used before. Utilizing a (nonlinear) integer mathematical program, we obtain the first polynomial time approximation algorithm for the scheduling problem, with performance bound (3+@e) for any @e0. Our approach relies on a fully polynomial time approximation scheme to solve the nonlinear mathematical programming relaxation. We also derive lower bounds for the approximation.