Makespan Minimization via Posted Prices

Michal Feldman, Amos Fiat, Alan Roytman

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider job scheduling settings, with multiple machines, where jobs arrive online and choose a machine selfishly so as to minimize their cost. Our objective is the classic makespan minimization objective, which corresponds to the completion time of the last job to complete. The incentives of the selfish jobs may lead to poor performance. To reconcile the differing objectives, we introduce posted machine prices. The selfish job seeks to minimize the sum of its completion time on the machine and the posted price for the machine. Prices may be static (i.e., set once and for all before any arrival) or dynamic (i.e., change over time), but they are determined only by the past, assuming nothing about upcoming events. Obviously, such schemes are inherently truthful. We consider the competitive ratio: The ratio between the makespan achievable by the pricing scheme and that of the optimal algorithm.We give tight bounds on the competitive ratio for both dynamic and static pricing schemes for identical, restricted, related, and unrelated machine settings. Our main result is a dynamic pricing scheme for related machines that gives a constant competitive ratio, essentially matching the competitive ratio of online algorithms for this setting. In contrast, dynamic pricing gives poor performance for unrelated machines. This lower bound also exhibits a gap between what can be achieved by pricing versus what can be achieved by online algorithms.

Original languageEnglish
Title of host publicationEC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation
Number of pages18
ISBN (Electronic)9781450345279
StatePublished - 20 Jun 2017
Event18th ACM Conference on Economics and Computation, EC 2017 - Cambridge, United States
Duration: 26 Jun 201730 Jun 2017

Publication series

NameEC 2017 - Proceedings of the 2017 ACM Conference on Economics and Computation


Conference18th ACM Conference on Economics and Computation, EC 2017
Country/TerritoryUnited States


  • Job scheduling
  • Load balancing
  • Makespan
  • Pricing schemes

All Science Journal Classification (ASJC) codes

  • Computer Science (miscellaneous)
  • Statistics and Probability
  • Computational Mathematics
  • Economics and Econometrics


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