Discrete Applied Mathematics 156 (2008) 2561–2572
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Discrete Applied Mathematics
journal homepage: www.elsevier.com/locate/dam
A general model for cyclic machine scheduling problems
, Thomas Kampmeyer
Universität Osnabrück, Fachbereich Mathematik/Informatik, 49069 Osnabrück, Germany
Bayer Technology Services, 51373 Leverkusen, Germany
a r t i c l e i n f o
Received 16 November 2006
Received in revised form 12 August 2007
Accepted 6 March 2008
Available online 21 May 2008
Cyclic scheduling problems
Single hoist scheduling problems
Mixed integer linear program
a b s t r a c t
A general framework for modeling and solving cyclic scheduling problems is presented. The
objective is to minimize the cycle time. The model covers different cyclic versions of the
job-shop problem found in the literature, robotic cell problems, the single hoist scheduling
problem and tool transportation between the machines.
It is shown that all these problems can be formulated as mixed integer linear programs
which have a common structure. Small instances are solved with CPLEX. For larger
instances tabu search procedures have been developed. The main ideas of these methods
© 2008 Elsevier B.V. All rights reserved.
In this paper we present a general mixed integer linear programming framework for modeling cyclic scheduling
problems. We show that the model covers some cyclic versions of the job-shop problem such as the robotic cell problem,
the single hoist scheduling problem, and cyclic scheduling with tool transportation.
The basis for our framework is a general model to describe cyclic machine scheduling problems without blocking
proposed by . Furthermore, Hanen shows that this problem can be described by a mixed integer formulation and
proposed a branch & bound procedure to solve cyclic job-shop-scheduling problems. In a cyclic machine scheduling problem
• operations (tasks) i = 1, . . . , n,
• a set M = M
, . . . , M
of machines (processors). i must be processed without preemption on a dedicated machine M(i).
A machine can process only one operation at a time,
• each operation must be repeated infinitely often. i; k is the kth occurrence of i. A schedule is defined by the starting
times t(i; k). A schedule is called periodic with cycle time α if
t(i; k) = t(i; 0) + αk for all i and k ∈ Z,
• generalized precedence constraints between i; k and j; k + H
t(i; k) + L
≤ t(j; k + H
can take any rational value and H
can take any integer value.
Corresponding author. Tel.: +49 2212981226.
E-mail addresses: Peter.Brucker@mathematik.uni-osnabrueck.de (P. Brucker), Thomas.Kampmeyer@bayertechnology.com (T. Kampmeyer).
0166-218X/$ – see front matter © 2008 Elsevier B.V. All rights reserved.