Empowering the configuration-IP: new PTAS results for scheduling with setup times

• 成果类型: Article
• 署名作者: Jansen, Klaus; Klein, Kim-Manuel; Maack, Marten; Rau, Malin
• 署名单位: University of Kiel; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-021-01694-3
• 发表日期: 2022
• 页码: 367-401

摘要

Integer linear programs of configurations, or configuration IPs, are a classical tool in the design of algorithms for scheduling and packing problems where a set of items has to be placed in multiple target locations. Herein, a configuration describes a possible placement on one of the target locations, and the IP is used to choose suitable configurations covering the items. We give an augmented IP formulation, which we call the module configuration IP. It can be described within the framework of n-fold integer programming and, therefore, be solved efficiently. As an application, we consider scheduling problems with setup times in which a set of jobs has to be scheduled on a set of identical machines with the objective of minimizing the makespan. For instance, we investigate the case that jobs can be split and scheduled on multiple machines. However, before a part of a job can be processed, an uninterrupted setup depending on the job has to be paid. For both of the variants that jobs can be executed in parallel or not, we obtain an efficient polynomial time approximation scheme (EPTAS) of running time f(1/epsilon) . poly(vertical bar I vertical bar). Previously, only constant factor approximations of 5/3 and 4/3 + epsilon, respectively, were known. Furthermore, we present an EPTAS for a problem where classes of (non-splittable) jobs are given, and a setup has to be paid for each class of jobs being executed on one machine.