| dc.description |
In project scheduling, a set of precedence-constrained jobs has to be scheduled so as
to minimize a given objective. In resource-constrained project scheduling, the jobs
additionally compete for scarce resources. Due to its universality, the latter problem
has a variety of applications in manufacturing, production planning, project
management, and elsewhere. It is one of the most intractable problems in operations
research, and has therefore become a popular playground for the latest optimization
techniques, including virtually all local search paradigms. We show that a somewhat
more classical mathematical programming approach leads to both competitive feasible
solutions and strong lower bounds, within quite reasonable computation times. The
basic ingredients of our approach are the Lagrangian relaxation of a time-indexed
integer programming formulation and relaxation-based list scheduling, enriched with a
useful idea from recent approximation algorithms for machine scheduling problems.
The efficiency of the algorithm results from the insight that the relaxed problem can be
solved by computing a minimum cut in an appropriately defined directed graph. Our
computational study covers different types of resource-constrained project scheduling
problems, based on several, notoriously hard test sets, including practical problem
instances from chemical production planning. |
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