176 research outputs found

    Exact and heuristic solution approaches for energy-efficient identical parallel machine scheduling with time-of-use costs

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    Nowadays, energy-efficient scheduling has assumed a key role in ensuring the sustainability of manufacturing processes. In this context, we focus on the bi-objective problem of scheduling a set of jobs on identical parallel machines to simultaneously minimize the maximum completion time and the total energy consumption over a time horizon partitioned into a set of discrete slots. The energy costs are determined by a time-of-use pricing scheme, which plays a crucial role in regulating energy demand and flattening its peaks. First, we uncover a symmetry-breaking property that characterizes the structure of the solution space of the problem. As a consequence, we provide a novel, compact mixed-integer linear programming formulation at the core of an efficient exact solution algorithm. A thorough experimental campaign shows that the use of the novel mathematical programming formulation enables the solution of larger-scale instances and entails a reduction in the computational times as compared to the formulation already available in the literature. Furthermore, we propose a new heuristic that improves the state-of-the-art in terms of required computational effort and quality of solutions. Such a heuristic outperforms the existing heuristics for the problem and is also capable of speeding up the exact solution algorithm when used for its initialization. Finally, we introduce a novel dynamic programming algorithm that is able to compute the optimal timing of the jobs scheduled on each machine to further improve the performance of the new heuristic

    Scheduling on Identical Parallel Machines with Time-of-Use Costs

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    In the latest years, energy-efficient scheduling has become an increasingly compelling and relevant matter due to both the rising global pollution levels and the growing interest of the industry towards sustainable manufacturing [1]. Specifically, many efforts have been devoted towards scheduling with the Time-of-Use (TOU) energy consumption model [2]. A scheduling horizon subject to a TOU policy is partitioned into different time slots, each one characterized by a different cost. The typical goal is to assign jobs to available machines in order to minimize the total energy consumption together with other possible objectives, such as the makespan or the total weighted tardiness. In this work, we consider the problem of scheduling a set of independent jobs on a set of identical, parallel machines with the objective of simultaneously minimizing the makespan and the total energy consumption. In more detail, we build upon [3] and provide an enhanced heuristic as well as a novel mixed-integer programming formulation. Finally, we show the effectiveness of the proposed solution approaches by reporting results from experimental tests performed on large size instances. [1 ] K. Gao, Y. Huang, Ali Sadollah, and L. Wang. A review of energy-efficient scheduling in intelligent production systems. Complex Intell. Syst., 6:237-249, 2020. [2 ] K. Train and G. Mehrez. Optional time-of-use prices for electricity: Econometric analysis of surplus and pareto impacts. RAND J. Econ., 25:263-283, 1994. [3 ] D. Anghinolfi, M. Paolucci, and R. Ronco. A bi-objective heuristic approach for green identical parallel machine scheduling. Eur. J. Oper. Res., 289(2):416-434, 2021

    L’identificazione dei personaggi nella Chronique di Ernoul e Bernard le Trésorier : strategie testuali e varianti

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    The Chronique that goes under the names of Ernoul and Bernard the Treasurer is a good example of the problems raised by the study of how characters are mentioned in a chronicle where, proper names refer to historical figures. The interplay between named and unnamed characters in the Chronique is not only due to the kind of historical information available to the author: it also reveals the author’s point of view on the narrative. The study of variant readings in the manuscript tradition shows how some tendencies in rewriting the text that are constant in some groups, and in some individual copies. Scribes mostly relied on the context to gather the information on the character’s names, and sometimes on a more extensive knowledge of the text. There is only small evidence pointing to the use of external sources
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