Online interval scheduling on a single machine with finite lookahead

Authors:
Feifeng Zheng;Yongxi Cheng;Ming Liu;Yinfeng Xu
Affiliations:
School of Management, Xi'an Jiaotong University, Xi'an 710049, China and Glorious Sun School of Business and Management, Donghua University, Shanghai 200051, China;School of Management, Xi'an Jiaotong University, Xi'an 710049, China;School of Economics & Management, Tongji University, Shanghai 200092, China;School of Management, Xi'an Jiaotong University, Xi'an 710049, China
Venue:
Computers and Operations Research
Year:
2013

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Abstract

We study an online weighted interval scheduling problem on a single machine, where all intervals have unit length and the objective is to maximize the total weight of all completed intervals. We investigate how the function of finite lookahead improves the competitivities of deterministic online heuristics, under both preemptive and non-preemptive models. The lookahead model studied in this paper is that an online heuristic is said to have a lookahead ability of LD if at any time point it is able to foresee all the intervals to be released within the next LD units of time. We investigate both competitive online heuristics and lower bounds on the competitive ratio, with lookahead 0@?LD@?1 under the preemptive model, and lookahead 0@?LD@?2 under the non-preemptive model. A method to transform a preemptive lookahead online algorithm to a non-preemptive online algorithm with enhanced lookahead ability is also given. Computational tests are performed to compare the practical competitivities of the online heuristics with different lookahead abilities.