Generating Better Cyclic Fair Sequences Faster with Aggregation

Fair sequences allocate capacity to competing demands in a variety of manufacturing and computer systems. This paper considers three problems that motivate generating cyclic fair sequences: (1) the response time variability problem, (2) routing jobs to parallel servers (the waiting time problem), and (3) finding balanced words. This paper discusses the similarities among these three problems and presents a general aggregation approach. Computational results show that using aggregation with stride scheduling both generates solutions that are more fair and reduces computational effort. The paper concludes with some ideas for applying the approach to related problems.

[1]  Naoto Miyoshi,et al.  m-Balanced words: A generalization of balanced words , 2004, Theor. Comput. Sci..

[2]  Kyung S. Park,et al.  Optimal Scheduling of Periodic Activities , 1985 .

[3]  Wieslaw Kubiak,et al.  Proportional Optimization And Fairness , 2008 .

[4]  Jeffrey W. Herrmann,et al.  Constructing Perfect Aggregations to Eliminate Response Time Variability in Cyclic Fair Sequences , 2008 .

[5]  Albert Corominas,et al.  Solving the Response Time Variability Problem by means of metaheuristics , 2006, CCIA.

[6]  Boaz Patt-Shamir,et al.  Nearly optimal perfectly-periodic schedules , 2001, PODC '01.

[7]  Jeffrey W. Herrmann,et al.  Generating Cyclic Fair Sequences using Aggregation and Stride Scheduling , 2007 .

[8]  Jill R. Hardin,et al.  Vehicle minimization for periodic deliveries , 2005, Eur. J. Oper. Res..

[9]  Carl A. Waldspurger,et al.  Stride Scheduling: Deterministic Proportional- Share Resource Management , 1995 .

[10]  Dinard van der Laan Routing Jobs to Servers with Deterministic Service Times , 2005, Math. Oper. Res..

[11]  Jeffrey W. Herrmann,et al.  Aggregating Alphabets to Construct Balanced Words , 2009 .

[12]  Jeffrey W. Herrmann,et al.  Generating Cyclic Fair Sequences for Multiple Servers , 2009 .

[13]  Wieslaw Kubiak,et al.  Response time variability , 2007, J. Sched..

[14]  Jeffrey W. Herrmann,et al.  Using aggregation to reduce response time variability in cyclic fair sequences , 2011, J. Sched..

[15]  C. L. Liu,et al.  On a Periodic Maintenance Problem , 1983, Oper. Res. Lett..

[16]  J. Miltenberg,et al.  Level schedules for mixed-model assembly lines in just-in-time production systems , 1989 .

[17]  James R. Evans,et al.  Aggregation and Disaggregation Techniques and Methodology in Optimization , 1991, Oper. Res..

[18]  R. R. Inman,et al.  Sequencing JIT mixed-model assembly lines , 1991 .

[19]  Randeep Bhatia,et al.  Minimizing service and operation costs of periodic scheduling , 2002, SODA '98.

[20]  Jeffrey W. Herrmann,et al.  Using aggregation to construct periodic policies for routing jobs to parallel servers with deterministic service times , 2012, J. Sched..