2,813 research outputs found
Energy-efficient algorithms for non-preemptive speed-scaling
We improve complexity bounds for energy-efficient speed scheduling problems
for both the single processor and multi-processor cases. Energy conservation
has become a major concern, so revisiting traditional scheduling problems to
take into account the energy consumption has been part of the agenda of the
scheduling community for the past few years.
We consider the energy minimizing speed scaling problem introduced by Yao et
al. where we wish to schedule a set of jobs, each with a release date, deadline
and work volume, on a set of identical processors. The processors may change
speed as a function of time and the energy they consume is the th power
of its speed. The objective is then to find a feasible schedule which minimizes
the total energy used.
We show that in the setting with an arbitrary number of processors where all
work volumes are equal, there is a approximation algorithm, where
is the generalized Bell number. This is the first constant
factor algorithm for this problem. This algorithm extends to general unequal
processor-dependent work volumes, up to losing a factor of
in the approximation, where is the maximum
ratio between two work volumes. We then show this latter problem is APX-hard,
even in the special case when all release dates and deadlines are equal and
is 4.
In the single processor case, we introduce a new linear programming
formulation of speed scaling and prove that its integrality gap is at most
. As a corollary, we obtain a
approximation algorithm where there is a single processor, improving on the
previous best bound of
when
Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines
This paper deals with a realistic cyclic scheduling problem in the food industry environment in which
parallel machines are considered to process perishable jobs with given release dates, due dates and
deadlines. Jobs are subject to post-production shelf life limitation and must be delivered to retailers
during the corresponding time window bounded by due dates and deadlines. Both early and tardy jobs
are penalized by partial weighted earliness/tardiness functions and the overall problem is to provide
a cyclic schedule of minimum cost. A mixed integer programming model is proposed and a heuristic
solution beside an iterated greedy algorithm is developed to generate good and feasible solutions for the
problem. The proposed MIP, heuristic and iterated greedy produce a series of solutions covering a wide
range of cases from slow optimal solutions to quick and approximated schedules.Ruben Ruiz is partially supported by the Spanish Ministry of Economy and Competitiveness, under the project "RESULT - Realistic Extended Scheduling Using Light Techniques" with reference DPI2012-36243-C02-01 co-financed by the European Union and FEDER funds and by the Universitat Politecnica de Valencia, for the project MRPIV with reference PAID/2012/202.Shirvani, N.; Ruiz GarcĂa, R.; Shadrokh, S. (2014). Cyclic scheduling of perishable products in parallel machine with release dates, due dates and deadlines. International Journal of Production Economics. 156:1-12. https://doi.org/10.1016/j.ijpe.2014.04.013S11215
Weighted tardiness minimization for unrelated machines with sequence-dependent and resource-constrained setups
Motivated by the need of quick job (re-)scheduling, we examine an elaborate
scheduling environment under the objective of total weighted tardiness
minimization. The examined problem variant moves well beyond existing
literature, as it considers unrelated machines, sequence-dependent and
machine-dependent setup times and a renewable resource constraint on the number
of simultaneous setups. For this variant, we provide a relaxed MILP to
calculate lower bounds, thus estimating a worst-case optimality gap. As a fast
exact approach appears not plausible for instances of practical importance, we
extend known (meta-)heuristics to deal with the problem at hand, coupling them
with a Constraint Programming (CP) component - vital to guarantee the
non-violation of the problem's constraints - which optimally allocates
resources with respect to tardiness minimization. The validity and versatility
of employing different (meta-)heuristics exploiting a relaxed MILP as a quality
measure is revealed by our extensive experimental study, which shows that the
methods deployed have complementary strengths depending on the instance
parameters. Since the problem description has been obtained from a textile
manufacturer where jobs of diverse size arrive continuously under tight
deadlines, we also discuss the practical impact of our approach in terms of
both tardiness decrease and broader managerial insights
On Idle Energy Consumption Minimization in Production: Industrial Example and Mathematical Model
This paper, inspired by a real production process of steel hardening,
investigates a scheduling problem to minimize the idle energy consumption of
machines. The energy minimization is achieved by switching a machine to some
power-saving mode when it is idle. For the steel hardening process, the mode of
the machine (i.e., furnace) can be associated with its inner temperature.
Contrary to the recent methods, which consider only a small number of machine
modes, the temperature in the furnace can be changed continuously, and so an
infinite number of the power-saving modes must be considered to achieve the
highest possible savings. To model the machine modes efficiently, we use the
concept of the energy function, which was originally introduced in the domain
of embedded systems but has yet to take roots in the domain of production
research. The energy function is illustrated with several application examples
from the literature. Afterward, it is integrated into a mathematical model of a
scheduling problem with parallel identical machines and jobs characterized by
release times, deadlines, and processing times. Numerical experiments show that
the proposed model outperforms a reference model adapted from the literature.Comment: Accepted to 9th International Conference on Operations Research and
Enterprise Systems (ICORES 2020
Maintenance activities scheduling under competencies constraints.
International audienceCompetencies management in the industry is one of the most important keys in order to obtain good performance with production means. Especially in maintenance services field where the different practical knowledges or skills are their working tools. We propose here a methodology, which compares the human resource with parallel machine. As human resource competence levels of each are all differents, they are considered like unrelated parallel machines. Our aim is to assign tasks to the adequate resources by minimizing time treatment for each task and the makespan
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