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2006 ).
From the review above, it can be concluded that the study of processing time variability in both assembly and disas- sembly **line** **balancing** is limited to heuristic or metaheuristic approaches or to exact solution methods based on integer linear programmes with disjoint probabilistic constraints. In the case of disjoint probabilistic constraints, the decision- maker seeks an assignment of tasks to workstations where, for each station taken separately, the probability that the station time be smaller than cycle time should remain greater than a predetermined value. An important and more chal- lenging issue is to study the case where the cycle time constraints are satisﬁed jointly; i.e. the probability that all station times be smaller than cycle time should remain greater than a ﬁxed value. This case is considered in this paper which is organised as follows: a description and formulation of the studied stochastic DLBP are given in Section 2 . The proposed solution method using convex piecewise linear approximation is presented in Section 3 . The numerical experiments are given in Section 4 and Section 5 concludes the paper with future research directions.

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{bentaha,battaia,dolgui}@emse.fr
Abstract. The disassembly **line** **balancing** problem is studied under uncertainty. Disassembly task times are assumed random variables with known probability distributions. An AND/OR graph is used to model the precedence relations among tasks. The goal is to assign the disassembly tasks to workstations while respecting precedence and cycle time constraints. The objective is to minimize the total **line** cost including the incompletion cost arising from task incompletion within the cycle time. A stochastic linear mixed integer programming formulation is developed.

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ARTICLE HISTORY Compiled December 11, 2019 ABSTRACT
We consider the Reconfigurable Transfer **Line** **Balancing** Problem. This problem consists into allocating a set of operations (necessary to machine a single part) to different workstations placed into a serial **line**. Each workstation can contain multiple machines operating in parallel. The machines considered are mono-spindle head CNC machines which may imply sequence-dependent setup times between operations in order to perform tool changes. Therefore, the operations allocated to a workstation should be sequenced. Besides, accessibility, inclusion, exclusion and precedence constraints between operations are considered. In this article, we propose a polynomial exact algorithm that balances the transfer **line** provided the overall sequence of the operations (called "giant sequence") is given. We use this algorithm to solve the **balancing** problem when the overall sequence of operations is not fixed by embedding it in a metaheuristic framework. We perform experimentation on literature instances. The results obtained show the effectiveness of the proposed approach compared to literature.

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KEYWORDS: Transfer **line** **balancing**, Reconfigurability, Industry 4.0, Mixed integer programming, Hybrid algorithms, approximation algorithms
1 INTRODUCTION
New consuming trends, global competition and grow- ing variety in demand in the actual economical con- text raises an important issue in transfer **line** design. In fact, shortening life cycle times imposes the con- sideration of reconfigurabiliy in transfer **line** design. The modern transfer **line** should be easily and cost- effectively reconfigurable to address two different is- sues: the variability in production size and the vari- ability in the product specifications. While the first one imposes a variation in cycle time, the second one is linked to the set of tasks involved.

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Once all possible component and module EOL states are determined, including both the difference in disassembly task times and the probability of having a difference in certain task times[r]

In this paper, we present an overview of flow lines balancing problems recently appeared in the literature which try to expand the core optimization problem dealing with assigning tasks [r]

They dub the class of problems with ergonomic constraints or objectives as ERGO-SALBP and examine several possible objective functions: minimization of average ergonomic risks, minimizat[r]

The obligation of inclusion implies that technology assessment cannot be an issue advocate with regard to specific technologies, or to specific norms and values to be applied for asses[r]

The first part deals with mid-term decisions. It aims at computing lot-sizes and cover-sizes which are used in several Supply Chain processes as MRP (to decide the quantity of raw materials to order) or production planning (to decide the size of produced lots). At this level of decision, the objective for Argon Consulting is to reduce future inventory and the main constraint is the flexibility. Motivated by industrial considerations, we propose extensions of classical continuous- time inventory models by replacing setup costs by a bound on the maximal number of setups. We find closed-form formulas in the single-**line** cases and proposed efficient methods for multi- **line** cases. Argon Consulting was very enthusiastic about this formula because unlike the setups costs, the bound on the number of setups captures the interaction between items and is easy to estimate. Moreover, the closed-form formula makes it easier to use and is already used by practitioners.

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En effet, dans notre solution, nous utilisons simplement une combinaison linéaire pour modéliser le comportement des opérateurs de Tone mapping. Ce type de scène est difficile à modélise[r]

6. CONCLUSIONS
In this paper, the shaking force **balancing** of the DELTA robot has been discussed. The aim of this technique consists in the fact that the DELTA robot is controlled not by applying platform trajectories but by planning the displacements of the total mass centre of the moving links. The trajectory of the total mass centre of moving links is defined as a straight **line**. Then, it is parameterized with “bang-bang” profile. It allows the reduction of the maximum value of the centre of mass acceleration and, consequently, the reduction in the shaking force. It has also been shown that it is easy to take into account the varying payload with such **balancing** technique. Although such **balancing** does not lead to a complete cancellation of the shaking force, but it allows one to significantly reduce it without changing the basic design of the robot.

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The technique of using auxiliary tasks during learning have been popularized in the field of machine learning due to its great performance in practice: it can be used to increase gradien[r]

Statement of the problem
The aim of the suggested **balancing** approach consists of adding a two-link kinematic chain with prescribed geometrical parameters to an in-**line** four-bar linkage with arbitrary geometrical parameters. It is important to note that the added structure must be an Assur group, i.e. a group which does not add any supplementary degree of freedom into the mechanism [34]. This allows for the modification of the mass redistribution of the obtained six-bar mechanism without perturbation of the kinematic properties of the initial four-bar linkage. We would like to restate that this technique allows for the complete shaking force and shaking moment **balancing** without counter-rotating masses.

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© The Author(s) 2018
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article ’s Creative Commons license, unless indicated otherwise in a credit **line** to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ .

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work because workload scheduling among a large number of interconnected datacenters gives rise to computational problems (e.g., see the summary of the techniques used in geographical load **balancing** in [13]).
The works closest to ours are [11] and [10], where geographical load **balancing** is driven by time-varying energy prices, that can be due to a significant local production from renewable sources. While in these papers energy prices are considered to be known in advance over some future time- horizon, in our case renewable energy production is a stochastic process and scheduling is decided on the basis of the current state of the system.

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As the steady flow increases, transportation cost savings increase, cross-dock savings increase (until steady flow exceeds demand), but at the same time excess inventory costs also incre[r]

Software to run the robot was constructed using National Instruments LabVIEW; this software was based on the state feedback controller, and allowed users to select[r]

Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE` S NANCY Unite´ de recherche INRIA Rennes, Ir[r]

In this work we identify some natural additional conditions on deterministic **balancing** algorithms, resulting in a class of algorithms reaching a smaller discrepancy. This class contains well-known al- gorithms, e.g., the R OTOR -R OUTER . Specifically, we introduce the notion of cumulatively fair load- **balancing** algorithms where in any interval of consecutive time steps, the total number of tokens sent out over an edge by a node is the same (up to constants) for all adjacent edges. We prove that algorithms which are cumulatively fair and where every node retains a sufficient part of its load in each step, achieve a discrepancy of O(min{d p log n/µ, d √ n}) in time O(T ). We also show that in general neither of these assumptions may be omitted without increasing discrepancy. We then show by a combinatorial potential reduction argument that any cumulatively fair scheme satisfying some additional assumptions achieves a discrepancy of O(d) almost as quickly as the continuous diffusion process. This positive result applies to some of the simplest and most natural discrete load **balancing** schemes.

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