Annals of Operations Research 96 (2000) 255–269 255
k-server problems with bulk requests:
an application to tool switching in manufacturing
Caroline Privault and Gerd Finke
Laboratoire Leibniz, Institut IMAG, 46 avenue Felix Viallet, F-38031 Grenoble, France
The classical k-server problem has been widely used to model two-level memory systems
(e.g., paging and caching). The problem is to plan the movements of k mobile servers on the
vertices of a graph under an on-line sequence of requests. We generalize this model in order
to process a sequence of bulk requests and formulate, in this way, a valid model for the usual
two-level tooling conﬁguration in automated production systems. A slight adaptation of the
so-called Partitioning Algorithm provides an on-line algorithm for this more general case,
preserving basically the same competitive properties as the classical model. This approach
yields a new tool management procedure in manufacturing which outperforms in its quality
the usual methods that are based on heuristics for the traveling salesman problem.
Keywords: paging, on-line tool switching, k-server problems, competitive analysis
AMS subject classiﬁcation: 90B30, 90B35
Within the classical operations research literature, the future is either assumed
to be known or is assumed to obey a probability law whose parameters are known.
Recently, within computer science, a literature has developed in which the future is
completely unknown. The goal is to ﬁnd a decision rule with the following property:
• For every realization of the future, the (possibly randomized) decision rule incurs
a cost whose expectation exceeds by a factor of not more than some constant c, the
cost of the cheapest rule for which the future is revealed before any decisions are
In computer science, the k-server problem has been widely studied to model such a
situation which occurs in memory allocation. In this paper, we slightly generalize
a famous algorithm of McGeogh and Sleator , initially dedicated to the uniform
k-server problem. We show that this generalization applies to an operations research
problem that arises in ﬂexible manufacturing systems.
In the next section, the k-server problems are extended to include bulk requests.
This model will describe, in addition to the classical memory allocation problem, also
the tool switching problem in manufacturing. We report brieﬂy, in section 3, the results
from the literature on optimal off-line strategies for these two cases, which are in fact
identical, but have been developed with a time difference of more than twenty years.
J.C. Baltzer AG, Science Publishers