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International audienceIn this work, we are interested in scheduling dependent tasks for hybrid parallel multi-core machines, composed of CPUs with additional accelerators (GPUs). The objective is to minimize the make span, which is a crucial problem for reaching the potential of new platforms in High Performance Computing. We provide an approximation algorithm with a performance guarantee of 6 to solve this problem. The algorithm is a two-phase solving method: a first phase based on rounding the solution provided by solving a linear programming formulation for the assignment of the tasks to the resources. A second phase uses a classical list algorithm to schedule the tasks according to the assignment phase. The proposed approach is the first generic algorithm with a performance guarantee for scheduling tasks with precedence constraints on hybrid platforms with CPUs and GPUs resources

Abstract. More and more computers use hybrid architectures combining 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 m CPUs and k 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 maximum completion time (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 dynamic programming to balance evenly the load between the heterogeneous resources. Then, we present a faster approximation algorithm for a special case of the previous problem, where all the tasks are accelerated when affected to GPU, with a performance guarantee of 3 2 for any number of GPUs. We run some simulations based on realistic benchmarks and compare the solutions obtained by a relaxed version of the generic method to the one provided by a classical scheduling algorithm (HEFT). Finally, we present an implementation of the 4/3-approximation and its relaxed version on a classical linear algebra kernel into the scheduler of the xKaapi runtime system.

We consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and develop a branch-and-cut algorithm in order to solve the resulting mixed-integer linear program to optimality. This algorithm relies on a new set of tree inequalities obtained by combining valid inequalities previously known for each individual scenario of the scenario tree. These inequalities are used within a cutting-plane generation procedure based on a heuristic resolution of the corresponding separation problem. Computational experiments carried out on randomly generated instances show that the proposed branch-and-cut algorithm performs well as compared to the use of a stand-alone mathematical solver. Finally, rolling horizon simulations are carried out to assess the practical performance of the multi-stage stochastic planning model with respect to a deterministic model and a two-stage stochastic planning model.

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To cite this version:Nabil Absi, Safia Kedad-Sidhoum. The multi-item capacitated lot-sizing problem with setup times and shortage costs. European Journal of Operational Research, Elsevier, 2008, 185 (3) AbstractWe 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. [26] and Marchand and Wolsey [24] 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.

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International audienceWe address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over which a freezing or a relaxation strategy is applied. Some experimental results showing the effectiveness of the approach on real-world instances are presented. A sensitivity analysis on the parameters of the heuristics is reported