# Scheduling Parallel Jobs with Time-Resource Tradeoff via Nonlinear Programming

A. Grigoriev, Marc Jochen Uetz

Research output: Book/ReportReportProfessional

## Abstract

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 timeresource 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 $(3 + \varepsilon)$ for any $\varepsilon > 0$. Our approach relies on a fully polynomial time approximation scheme to solve the mathematical programming relaxation. This result is interesting in itself, because we also show that the underlying mathematical program is NP-hard to solve. We also derive lower bounds for the approximation.
Original language Undefined Enschede University of Twente 18 Published - Apr 2008

### Publication series

Name CTIT Technical Report Series Centre for Telematics and Information Technology, University of Twente TR-CTIT-08-78 1381-3625

• EWI-15168
• IR-65415
• METIS-256465