Workforce minimization for a mixed-model assembly line in the automotive industry

A paced assembly line consisting of several workstations is considered. This line is intended to assemble products of different types. The sequence of products is given. The sequence of technological tasks is common for all types of products. The assignment of tasks to the stations and task sequence on each station are known and cannot be modified, and they do not depend on the product type. Tasks assigned to the same station are performed sequentially. The processing time of a task depends on the number of workers performing this task. Workers are identical and versatile. If a worker is assigned to a task, he/she works on this task from its start till completion. Workers can switch between the stations at the end of each task and the time needed by any worker to move from one station to another one can be neglected. At the line design stage, it is necessary to know how many workers are necessary for the line. To know the response to this question we will consider each possible takt and assign workers to tasks so that the total number of workers is minimized, provided that a given takt time is satisfied. The maximum of minimal numbers of workers for all takts will be considered as the necessary number of workers for the line. Thus, the problem is to assign workers to tasks for a takt. We prove that this problem is NP-hard in the strong sense, we develop an integer linear programming formulation to solve it, and propose conventional and randomized heuristics

Algorithmes et logiciels pour aide à la décision dans la conception de lignes d'assemblage et des lignes de transfert

An overview of existing problems and methods for the design of assembly and transfer lines is given. A new workforce assignment problem for a paced multi-product assembly line with a goal of minimizing the number of workers is studied. Various precedence relations between operations and functions of operation processing times dependent on the number of workers areconsidered. A new problem of multi-objective optimization for a single product transfer line is solved. Several exact and heuristic methods and their computer implementations for both problems are developed by the author. An application of developed approaches to solving a real production problem relevant to the European project amePLM is demonstrated.Une vue d'ensemble des problèmes et des méthodes pour la conception des lignesd'assemblage et d'usinage est donnée. Un nouveau problème d'affectation de la main-d’œuvrepour une ligne d'assemblage multi-produit cadencée avec un objectif de minimiser lenombre d'opérateurs est étudié. Diverses relations de priorité entre les opérations et lesdifférentes fonctions définissant les temps d'opérations, en fonction du nombre d'opérateurssont considérés. Un nouveau problème d'optimisation multiobjectif pour une ligne d'usinagemono-produit est formulé. Plusieurs méthodes exactes et heuristiques et leursimplémentations informatiques pour les deux problèmes sont développées par l'auteur. Unmodule logiciel d'aide à la décision pour résoudre ces problèmes est développé et implémentédans un environnement d'un nouveau PLM d'IBM dans le cadre du projet européen amePLM.Ce module est testé sur un exemple réel de conception d'une ligne de montage des moteurschez Mercedes Benz en Allemagne

A multi-objective approach for design of reconfigurable transfer lines

International audienceThis paper studies a multi-objective line balancing problem for reconfigurable transfer lines. In nowaday industry, machining lines need to be highly reconfigurable in order to cope with market’s demand. However, the design of these reconfigurable lines implies more difficult optimisation problems to solve and new methods are required. Moreover, with the high level of uncertainty on demand, decision-makers now look to other criteria than the sole investment cost.A new heuristic, based on the GRASP (greedy randomized adaptive search procedure) framework and using mixed integer programming for solving sub-problems, is proposed to deal with the search of trade-offs between cost and productivity for such reconfigurable transfer lines. A case study is also described and tested in order to illustrate the interest of the proposed approach

A multi-objective algorithm for balancing reconfigurable transfer lines

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Optimal workforce assignment to operations of a paced assembly line

International audienceWe study a paced assembly line intended for manufacturing different products. Workers with identical skills perform non-preemptable operations whose assignment to stations is known. Operations assigned to the same station are executed sequentially, and they should follow the given precedence relations. Operations assigned to different stations can be performed in parallel. The operation's processing time depends on the number of workers performing this operation. The problem consists in assigning workers to operations such that the maximal number of workers employed simultaneously in the assembly line is minimized, the line cycle time is not exceeded and the box constraints specifying the possible number of workers for each operation are not violated. We show that the general problem is NP-hard in the strong sense, develop conventional and randomized heuristics, propose a reduction to a series of feasibility problems, present a MILP model for the feasibility problem, show relation of the feasibility problem to multi-mode project scheduling and multiprocessor scheduling, establish computational complexity of several special cases based on this relation and provide computer experiments with real and simulated data

Minimizing the number of workers for one cycle of a paced production line

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Optimal design of assembly lines with flexible workers

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Biocompatibility of Ceramic Materials in Ca₂P₂O_7–Ca(PO₃)₂ System Obtained via Heat Treatment of Cement-Salt Stone

Biocompatibility of ceramic materials in Ca2P2O7-Ca(PO3)2 system was investigated using different methods, including in vitro and in vivo tests. Ceramic materials in the Ca2P2O7-Ca(PO3)2 system were obtained by annealing cement-salt stone based on powder mixtures of calcium citrate tet-rahydrate Ca3(C6H5O7)2·4H2O and monocalcium phosphate monohydrate (MCPM) Ca(H2PO4)2·H2O. The phase composition of cement-salt stone included brushite, monetite as a result of chemical reaction of starting components after adding of water. The presence of citric acid as by-product of chemical reaction, leads to increase the setting time of the cement-salt stone. Highly concentrated aqueous suspensions based on calcium citrate and MCPM powders providing content of calcium polyphosphate Ca(PO3)2 up to 20 wt % in ceramics were used for designing bioresorbable materials. The presence of an excess of monocalcium phosphate monohydrate makes it possible to reduce the annealing temperature of ceramics, which is associated with the formation of a lower melting phase of Ca(PO3)2. In vivo tests shown that obtained ceramic materials can be recommended for regenerative treatments for bone defects

Solution study of novel diblock copolymers: Morphology and structural transition

The solution behavior and morphology of the nanostructures formed by novel block copolymers based on 1-cetyl[2-(acryloyloxy)ethyl]dimethylammonium bromide (ADHA) and 2-hydroxyethylacrylate (HEA) or N-isopropylacrylamide (NIPAM) have been studied using small angle X-ray scattering (SAXS), dynamic light scattering (DLS), and transmission electron microscopy (TEM). In these block copolymers the pADHA block consists of long hydrophobic C16 tails connected to a positively charged quaternary ammonium group, making it amphiphilic, while the second block is either fully hydrophilic (pHEA) or thermoresponsive (pNIPAM). Using SAXS, we demonstrate that the morphology of block copolymer nanostructures is dependent on the solute concentration and on the length and composition of the blocks. In the case of thermoresponsive pADHA-b-pNIPAM, two types of ordered structures are formed and their characteristics are also defined by the temperature. Complementary information is obtained from DLS, showing large particles with the size up to 280 nm, which is beyond the resolution of the SAXS data. Loss of ordering around the lower critical solution temperature followed by ordering restoration at the higher temperature was observed for the pADHA-b-pNIPAM block copolymers. The differences in the structural order in the block copolymer solutions are directly related to their ability to coat hydrophobic metal nanoparticles