20,226 research outputs found
Algebraic solution of project scheduling problems with temporal constraints
New solutions for problems in optimal scheduling of activities in a project
under temporal constraints are developed in the framework of tropical algebra,
which deals with the theory and application of algebraic systems with
idempotent operations. We start with a constrained tropical optimization
problem that has an objective function represented as a vector form given by an
arbitrary matrix, and that can be solved analytically in a closed but somewhat
complicated form. We examine a special case of the problem when the objective
function is given by a matrix of unit rank, and show that the solution can be
sufficiently refined in this case, which results in an essentially simplified
analytical form and reduced computational complexity of the solution. We
exploit the obtained result to find complete solutions of project scheduling
problems to minimize the project makespan and the maximum absolute deviation of
start times of activities under temporal constraints. The constraint under
consideration include ``start-start'', ``start-finish'' and ``finish-start''
precedence relations, release times, release deadlines and completion deadlines
for activities. As an application, we consider optimal scheduling problems of a
vaccination project in a medical centre.Comment: 20 page
Taming Numbers and Durations in the Model Checking Integrated Planning System
The Model Checking Integrated Planning System (MIPS) is a temporal least
commitment heuristic search planner based on a flexible object-oriented
workbench architecture. Its design clearly separates explicit and symbolic
directed exploration algorithms from the set of on-line and off-line computed
estimates and associated data structures. MIPS has shown distinguished
performance in the last two international planning competitions. In the last
event the description language was extended from pure propositional planning to
include numerical state variables, action durations, and plan quality objective
functions. Plans were no longer sequences of actions but time-stamped
schedules. As a participant of the fully automated track of the competition,
MIPS has proven to be a general system; in each track and every benchmark
domain it efficiently computed plans of remarkable quality. This article
introduces and analyzes the most important algorithmic novelties that were
necessary to tackle the new layers of expressiveness in the benchmark problems
and to achieve a high level of performance. The extensions include critical
path analysis of sequentially generated plans to generate corresponding optimal
parallel plans. The linear time algorithm to compute the parallel plan bypasses
known NP hardness results for partial ordering by scheduling plans with respect
to the set of actions and the imposed precedence relations. The efficiency of
this algorithm also allows us to improve the exploration guidance: for each
encountered planning state the corresponding approximate sequential plan is
scheduled. One major strength of MIPS is its static analysis phase that grounds
and simplifies parameterized predicates, functions and operators, that infers
knowledge to minimize the state description length, and that detects domain
object symmetries. The latter aspect is analyzed in detail. MIPS has been
developed to serve as a complete and optimal state space planner, with
admissible estimates, exploration engines and branching cuts. In the
competition version, however, certain performance compromises had to be made,
including floating point arithmetic, weighted heuristic search exploration
according to an inadmissible estimate and parameterized optimization
Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation
The technical report presents a generic exact solution approach for
minimizing the project duration of the resource-constrained project scheduling
problem with generalized precedences (Rcpsp/max). The approach uses lazy clause
generation, i.e., a hybrid of finite domain and Boolean satisfiability solving,
in order to apply nogood learning and conflict-driven search on the solution
generation. Our experiments show the benefit of lazy clause generation for
finding an optimal solutions and proving its optimality in comparison to other
state-of-the-art exact and non-exact methods. The method is highly robust: it
matched or bettered the best known results on all of the 2340 instances we
examined except 3, according to the currently available data on the PSPLib. Of
the 631 open instances in this set it closed 573 and improved the bounds of 51
of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table
A CSP model for simple non-reversible and parallel repair plans
Thiswork presents a constraint satisfaction problem
(CSP) model for the planning and scheduling of disassembly
and assembly tasks when repairing or substituting
faulty parts. The problem involves not only the ordering of
assembly and disassembly tasks, but also the selection of
them from a set of alternatives. The goal of the plan is the minimization
of the total repairing time, and the model considers,
apart from the durations and resources used for the assembly
and disassembly tasks, the necessary delays due to the change
of configuration in the machines, and to the transportation
of intermediate subassemblies between different machines.
The problem considers that sub-assemblies that do not contain
the faulty part are nor further disassembled, but allows
non-reversible and parallel repair plans. The set of all feasible
repair plans are represented by an extended And/Or graph.
This extended representation embodies all of the constraints
of the problem, such as temporal and resource constraints and
those related to the selection of tasks for obtaining a correct
plan.Ministerio de Educación y Ciencia DIP2006-15476-C02-0
Project scheduling under undertainty – survey and research potentials.
The vast majority of the research efforts in project scheduling assume complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. However, in the real world, project activities are subject to considerable uncertainty, that is gradually resolved during project execution. In this survey we review the fundamental approaches for scheduling under uncertainty: reactive scheduling, stochastic project scheduling, stochastic GERT network scheduling, fuzzy project scheduling, robust (proactive) scheduling and sensitivity analysis. We discuss the potentials of these approaches for scheduling projects under uncertainty.Management; Project management; Robustness; Scheduling; Stability;
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