Math. Meth. Oper. Res (2005) 62: 99–122
DOI 10.1007/s00186-005-0443-4
ORIGINAL ARTICLE
Eugene A. Feinberg
·
Michael T. Curry
Generalized Pinwheel Problem
Received: November 2004 / Revised: April 2005
© Springer-Verlag 2005
Abstract
Thispaperstudiesanon-preemptiveinfnite-horizonschedulingproblem
with a single server and a fxed set oF recurring jobs. Each job is characterized by
two given positive numbers: job duration and maximum allowable time between
the job completion and its next start. We show that For a Feasible problem there
exists a periodic schedule. We also provide necessary conditions For the Feasibility,
Formulate an algorithm based on dynamic programming, and, since this problem is
NP-hard, Formulate and study heuristic algorithms. In particular, by applying the
theory oF Markov Decision Process, we establish natural necessary conditions For
Feasibility and develop heuristics, called Frequency based algorithms, that outper-
Form standard scheduling heuristics.
1 Introduction
Suppose there are
n
∈
N
={
1
,
2
,...
}
recurring jobs. Each job
i
=
1
,... ,n
is
characterized by two positive numbers:
τ
i
,
the duration oF job
i
, and
u
i
,
the maxi-
mum amount oF the time that can transpire between epochs when job
i
is completed
and is started again. We call them the duration and revisit time respectively. These
jobs are to be completed by a single server. There is no preemption and setups are
instantaneous. A schedule is a sequence in which the jobs should be perFormed. A
schedule is Feasible iF each time job
i
is completed, it will be started again within
E.A. ±einberg (
B
)
Department oF Applied Mathematics and Statistics,
State University oF New York,
Stony Brook, NY 11794-3600, USA
E-mail: eFeinberg@notes.cc.sunysb.edu
M.T. Curry
Department oF Applied Mathematics and Statistics,
State University oF New York,
Stony Brook, NY 11794-3600, USA
E-mail: curry@ams.sunysb.edu