Almost sure asymptotic optimality for online routing and machine scheduling problems

Authors

  • Patrick Jaillet,

    Corresponding author
    1. Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
    • Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
    Search for more papers by this author
  • Michael R. Wagner

    1. Department of Management, California State University East Bay, Hayward, California 94542
    Search for more papers by this author

Abstract

In this article, we study algorithms for online routing and machine scheduling problems. The problems are “online” because the problem instances are revealed incrementally. We first study algorithms for the online Traveling Repairman Problem (TRP), where a single server is to visit a set of locations in a network with the objective of minimizing the sum of weighted completion times. We then analyze well-known online algorithms for a variety of machine scheduling problems, which are appropriate models for many network optimization problems; in the scheduling notation of Graham et al. 18, we consider 1|rj,pmtn|∑jwjCj, 1|rj|∑jwjCj, Q|rj,pmtn|∑jCj, P|rj|∑jCj, Q|rj,pmtn|∑jwjCj and Q|rj|∑jwjCj. We introduce general probabilistic assumptions about the problem data as a tool to study the online algorithms for these online combinatorial problems. The algorithms do not utilize the underlying probabilistic assumptions in any way. We prove that these online algorithms are almost surely asymptotically optimal. © 2009 Wiley Periodicals, Inc. NETWORKS, 2010

Ancillary