238 research outputs found
The multi-item capacitated lot-sizing problem with setup times and shortage costs
International audienceWe address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities based on a generalization of Miller et al. [A.J. Miller, G.L. Nemhauser, M.W.P. Savelsbergh, On the polyhedral structure of a multi-item production planning model with setup times, Mathematical Programming 94 (2003) 375–405] and Marchand and Wolsey [H. Marchand, L.A. Wolsey, The 0–1 knapsack problem with a single continuous variable, Mathematical Programming 85 (1999) 15–33] results. We also describe fast combinatorial separation algorithms for these new inequalities. We use them in a branch-and-cut framework to solve the problem. Some experimental results showing the effectiveness of the approach are reported
Estrategias para el diseño de ayudas didácticas y pedagógicas que potencien el desarrollo de los procesos de lecto-escritura en niños y niñas de quinto de primaria
Es posible determinar en este ensayo los distintos componentes pedagógicos que optimicen el desarrollo de la intelectualidad del ser humano, como sujeto activo del aprendizaje que tiene verdaderamente un significado, donde el docente debe generar o proponer al estudiante las herramientas didácticas hábiles y útiles para incrementar desde su saber teórico-práctico la adquisición del conocimiento, explorando el entorno que lo rodea y desde allí presentar una propuesta que se funde o interprete en el progreso de las humanidades. Es por ello que la pedagogía tiene la finalidad de precisar los procesos adecuados de aprendizaje, potencializando ca vez más las habilidades en el educando en la lecto-escritura
Rol de la seguridad privada frente al lavado de activos en Colombia
Rol de la seguridad privada frente al lavado de activos.The roll of the private security in front of launderin
Mixed integer formulations using natural variables for single machine scheduling around a common due date
34 pages, 10 figuresWhile almost all existing works which optimally solve just-in-time scheduling problems propose dedicated algorithmic approaches, we propose in this work mixed integer formulations. We consider a single machine scheduling problem that aims at minimizing the weighted sum of earliness tardiness penalties around a common due-date. Using natural variables, we provide one compact formulation for the unrestrictive case and, for the general case, a non-compact formulation based on non-overlapping inequalities. We show that the separation problem related to the latter formulation is solved polynomially. In this formulation, solutions are only encoded by extreme points. We establish a theoretical framework to show the validity of such a formulation using non-overlapping inequalities, which could be used for other scheduling problems. A Branch-and-Cut algorithm together with an experimental analysis are proposed to assess the practical relevance of this mixed integer programming based methods
Lagrangean based lower bounds for a multi-plant lot-sizing problem with capacity constraints
2pInternational audienceThe paper addresses a multi-item, multi-plant lot-sizing problem with capacity restrictions. A set of facilities (plants) is available for producing some items. For each period of a discrete planning horizon, a demand is de ned for each pair of item and plant. The problem consists in producing all the demands such that the total production, inventory, setup and transfer costs is minimized. Setup production times are considered as well as capacity constraints on the production. Moreover, transfers between plants are allowed, however, the total transferred quantity between each pair of plants is upper bounded as well as the total inventory at each plant for a given period. The problem considered is NP-hard. We quote the work of Sambivasan and Yahya that describes some Lagrangean-based heuristics to solve a relaxed version of the problem where no transfer and storage capacities are considered. In the present work, we propose a Lagrangean lower bound on the optimal cost value of the problem based on the decomposition of the problem into Facility Location and Multi-Commodity Flow problems
Dominance inequalities for scheduling around an unrestrictive common due date
The problem considered in this work consists in scheduling a set of tasks on
a single machine, around an unrestrictive common due date to minimize the
weighted sum of earliness and tardiness. This problem can be formulated as a
compact mixed integer program (MIP). In this article, we focus on
neighborhood-based dominance properties, where the neighborhood is associated
to insert and swap operations. We derive from these properties a local search
procedure providing a very good heuristic solution. The main contribution of
this work stands in an exact solving context: we derive constraints eliminating
the non locally optimal solutions with respect to the insert and swap
operations. We propose linear inequalities translating these constraints to
strengthen the MIP compact formulation. These inequalities, called dominance
inequalities, are different from standard reinforcement inequalities. We
provide a numerical analysis which shows that adding these inequalities
significantly reduces the computation time required for solving the scheduling
problem using a standard solver.Comment: 30 pages, 7 figures and 4 table
Scheduling Independent Tasks on Multi-cores with GPU Accelerators
Best PaperInternational audienceMore and more computers use hybrid architectures combin-ing multi-core processors and hardware accelerators like GPUs (Graphics Processing Units). We present in this paper a new method for scheduling efficiently parallel applications with CPUs and GPUs, where each task of the application can be processed either on a core (CPU) or on a GPU. The objective is to minimize the makespan. The corresponding scheduling problem is NP-hard, we propose an efficient approximation algorithm which achieves an approximation ratio of . We first detail and analyze the method, based on a dual approximation scheme, that uses a dynamic programming scheme to balance evenly the load between the heterogeneous resources. Finally, we run some simulations based on realistic benchmarks and compare the solution obtained by a relaxed version of this method to the one provided by a classical greedy algorithm and to lower bounds on the value of the optimal makespan
Scheduling data flow program in xkaapi: A new affinity based Algorithm for Heterogeneous Architectures
Efficient implementations of parallel applications on heterogeneous hybrid
architectures require a careful balance between computations and communications
with accelerator devices. Even if most of the communication time can be
overlapped by computations, it is essential to reduce the total volume of
communicated data. The literature therefore abounds with ad-hoc methods to
reach that balance, but that are architecture and application dependent. We
propose here a generic mechanism to automatically optimize the scheduling
between CPUs and GPUs, and compare two strategies within this mechanism: the
classical Heterogeneous Earliest Finish Time (HEFT) algorithm and our new,
parametrized, Distributed Affinity Dual Approximation algorithm (DADA), which
consists in grouping the tasks by affinity before running a fast dual
approximation. We ran experiments on a heterogeneous parallel machine with six
CPU cores and eight NVIDIA Fermi GPUs. Three standard dense linear algebra
kernels from the PLASMA library have been ported on top of the Xkaapi runtime.
We report their performances. It results that HEFT and DADA perform well for
various experimental conditions, but that DADA performs better for larger
systems and number of GPUs, and, in most cases, generates much lower data
transfers than HEFT to achieve the same performance
New data on early blight of potato caused by a complex of large-spored Alternaria species in Algeria
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