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# Workers assignment in straight and U-line

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Workers assignment problems (WAPs) are found in several types of manufacturing systems. Typically, WAPs are known to greatly impact the system performance. Numerous research works related to WAPs have been published. In this work, we analyze this literature according to several types of criteria. We first take into account such important features o...

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... WS is one of the major problems that manufacturing companies have to face, in which workers can be assigned to one or several tasks within a certain period of time (Ammar & Elkosantin, 2013). The WS problem occurs when the number of available workers is less than the number of operations, as in dual resources constrained (DRC) systems where workers can be relocated across various workstations (Xu et al., 2015). ...

This work is focused on workforce scheduling for assembly lines with the additional constraint of workforce distancing. The aim is to warrant the necessary safety and health requirements due to COVID-19. The research stems within an industrial case in which a methodology has been developed with the objectives of i) developing a constraint optimization model considering the social distancing of workers as part of the workforce scheduling requirements and ii) investigating how the workforce distancing can affect certain production performances. Through an empirical investigation the impact of distancing on workforce allocation is appraised in terms of daily production capacity. Then, different distancing thresholds are assessed to seek the optimal balance among production performances and safety requirements. The research resulted in a tool able to adapt the scheduling sequence to those health/safetysituations where the production manager needs to minimize losses in terms of production capacity, warranting the safest working conditions.

... Most of the other studies were done in the context of production scheduling problems. Several articles provided the states of the art on the existing advances in workforce planning research [Ammar et al., 2013, De Bruecker et al., 2015]. ...

Mass customization and frequent market fluctuations push industrial companies to employ flexible and reconfigurable multi/mixed-model assembly lines instead of dedicated ones. This thesis focuses on this problem. It concentrates mainly on mixed-model assembly line design and balancing problems. The questions concerning the efficiency of such lines, the importance of optimal task assignment and use of walking workers are asked and studied. To increase the flexibility of the line, we account for different types of task assignments: fixed, model-dependent,and dynamic. We aim to design a line that can handle various entering product models. We use combinatorial optimization methods, and,in particular, robust optimization approaches. We present an extensive literature review on line balancing, workforce planning, and workforce reconfiguration strategies in different production systems. The first problem addresses a configuration selection problem between a single multi-model line and multiple dedicated lines. The second problem consists in designing and balancing a mixed-model assembly line with walking workers. We propose fixed and model-dependent task assignments for a given set of product mixes. The goal is to minimize the total cost of workers and equipment for the worst case. The third problem extends the second one. It considers the dynamic task assignment. In the last problem, we extend the third problem for the case where the sequence of products unfolds takt by takt. In this context, we minimize both the expected total cost and the worst-case cost. In order to solve the considered problems, we develop several exact methods and heuristics: mixed-integer linear programming models, greedy algorithm, local search,matheuristic and fixed-and-optimize heuristics among others. We also apply a Markov Decision Process to the proposed line balancing problem in the last chapter. It is the first study applying this method to a line balancing problem. Computational experiments evaluate the performance of the proposed approaches in terms of solution quality and time consumption. We draw managerial insights in each chapter. Our results show the superiority of the dynamic task assignment compared to model-dependent and fixed ones in different production situations.

... These types of problems have been widely studied in the literature about manufacturing systems and it is well known that the way how workers are assigned in the system greatly affects the system performances. Reviews of research works related to workers assignment in manufacturing systems are presented in (Ammar, Pierreval, & Elkosantini, 2013;Ernst, Jiang, Krishnamoorthy, & Sier, 2004;Van den Bergh, Beliën, De Bruecker, Demeulemeester, & De Boeck, 2013;Xu, Xu, & Xie, 2011). According to these literature reviews, there exist various definitions, assumptions, contexts and methods related to the workers assignment problems, which are known for their complexity and for their NP-Hardness (Mahdavi, Paydar, Kia, & Khonakdari, 2010;Sirovetnukul & Chutima, 2010). ...

... According to Ammar et al. (2013) and Xu et al. (2011), the majority of existing publications are concerned with problems where the set of jobs to be processed is defined in advance, with deterministic processing times. As a consequence, the task durations are known a priori, with enough certainty, and the completion dates of jobs can be computed. ...

... Given the lack of precision about the production plan to be performed, it is well known that usual optimization approaches can generally not be applied. As a consequence, several researchers, such as Ammar et al. (2013), Cesani and Steudel (2005) and Zavadlav, McClain, and Thomas (1996), have pointed out, from their literature analyses, that determining online, in real time, where the operators should be assigned can represent an alternative to react quickly to these changes. The assignment decisions are made, online, according to the current system state, with respect to a set of constraints (e.g. ...

It is known that the workers’ fatigue can greatly affect both industrial performances and the workers’ wellbeing at work. Consequently, when designing a manufacturing system, managers are interested in facility layouts that favor performance objectives, while avoiding excessive fatigue. Unfortunately, most existing studies related to layout design
focus on technical aspects of the considered system (e.g. flow costs, distance between machines, etc.) so that human factors, in particular fatigue, are insufficiently taken into
consideration. Therefore, we are interested in how the workers’ fatigue can be taken into account when evaluating possible layout designs. We analyze the factors that induce
fatigue, which are mainly concerned with the work arduousness, and depend on the layout. We explain how they can be considered in order to compare possible solutions of a layout problem. In such a context, emphasis is put on the role of simulation. We illustrate our purpose and highlight the importance of taking fatigue into consideration through a comparison, using simulation, of two different layouts of a jobshop system. The comparison is based both on the mean flowtime of jobs and how the workers’ fatigue evolves over time.

... These types of problems have been widely studied in the literature about manufacturing systems and it is well known that the way how workers are assigned in the system greatly affects the system performances. Reviews of research works related to workers assignment in manufacturing systems are presented in (Ammar, Pierreval, & Elkosantini, 2013;Ernst, Jiang, Krishnamoorthy, & Sier, 2004;Van den Bergh, Beliën, De Bruecker, Demeulemeester, & De Boeck, 2013;Xu, Xu, & Xie, 2011). According to these literature reviews, there exist various definitions, assumptions, contexts and methods related to the workers assignment problems, which are known for their complexity and for their NP-Hardness (Mahdavi, Paydar, Kia, & Khonakdari, 2010;Sirovetnukul & Chutima, 2010). ...

... According to Ammar et al. (2013) and Xu et al. (2011), the majority of existing publications are concerned with problems where the set of jobs to be processed is defined in advance, with deterministic processing times. As a consequence, the task durations are known a priori, with enough certainty, and the completion dates of jobs can be computed. ...

... Given the lack of precision about the production plan to be performed, it is well known that usual optimization approaches can generally not be applied. As a consequence, several researchers, such as Ammar et al. (2013), Cesani and Steudel (2005) and Zavadlav, McClain, and Thomas (1996), have pointed out, from their literature analyses, that determining online, in real time, where the operators should be assigned can represent an alternative to react quickly to these changes. The assignment decisions are made, online, according to the current system state, with respect to a set of constraints (e.g. ...

Facility layout problems (FLP) in manufacturing systems are widely addressed in the literature. FLP generally consist in finding the variables indicating the positions of the facilities, in order to favor (a) given objective(s), while respecting some constraints. They are known to have a significant impact on the performances of manufacturing systems. For instance, they can greatly impact the cost, productivity, works in process, and lead times of jobs in the system. Therefore, numerous studies have been conducted in the scientific literature to deal with this kind of problems and many approaches are proposed to solve it.
In most approaches, researchers focus on classical production objectives of the manufacturing systems such as transportation and material handling costs. I, they mainly use technical measures to evaluate the performances associated with a given layout (e. g. distance between machines, adjacency score and material handling device utilization). However, the way, in which the facilities are arranged, does not only affect this type of measures: it can also impact human productivity, behaviors and even health, which can also affect the system efficiency. Unfortunately, it seems that human factors, such as workers’ fatigue, are insufficiently taken into account in FLP.
In this study, we are particularly interested to the workers’ fatigue because it can lead to negative effects on workers (e.g. performances and musculo-skeletal troubles) and efficiency of production systems (e.g. deterioration of processing times and an increase in the flowtime). We are more particularly interested in taking into account the workers’ fatigue in the evaluation of layout designs. In this respect, we need to understand how a layout can contribute to the workers’ fatigue, in view of trying to avoid or to reduce its negative effects. For that, it is important to identify the fatigue factors related to FLP. Indeed, the factors that lead to the workers’ fatigue and can affect the design of layouts, particularly when workers are multi-skilled, are mainly related to the work arduousness such as noise, uncomfortable postures, vibrations and heavy loads. When workers are exposed to arduousness, task duration can also greatly impact the workers’ fatigue.
In order to understand the consequences of how manufacturing facilities are arranged in terms of efficiency and to understand how fatigue emerges and evolves along time if a given layout is chosen, we need to be able to evaluate possible layout solutions in order to define an appropriate design. In this respect, simulation turns out to be an interesting approach. Since the evolution of fatigue is dynamic and continuous, static criterion may be not suited. We need to dynamically describe the evolution of the workers’ fatigue (accumulation and recovery) so as to analyze the evolution trends of fatigue. This implies the use of a combined simulation model (discrete and continuous simulation) and to be able to specify how fatigue evolves along time.
In order to quantify the workers’ fatigue, we can use one of the few fatigue mathematical models, which are proposed in the ergonomic literature. In this study, we use the fatigue model (Eq (1) and (2)), which is widely used in the literature. Eq (1) represents the fatigue
accumulation function and Eq(2) represents recovery, where 𝐹𝑖(𝑡) indicates the fatigue of the worker i at time t.
Fi(t) = 1 ‒ e-λt (1)
R(θ) = Fi(t) e-μt (2)
The variables 𝜆 and µ indicate, respectively, the speed of accumulation and recovery. They depend on the fatigue factors, which are mentioned in the previous paragraph, and recovery factors (i.e. rest period and the physical characteristics of each worker for recovery (e.g. sex and age)). However, it is often difficult to have accurate information about how these factors can be considered so to determine 𝜆 and µ. Thus, fuzzy logic concepts could be used to deal with the problem of inaccuracy. We suggest representing the accumulation and recovery factors, in our simulation model, by linguistic variables and how they can impact the evolution of fatigue can be defined by fuzzy rules. For instance,
IF noise is high and load is heavy THEN the accumulation speed is high.
Regarding the evaluation of the layout efficiency, several criteria can be used such as the flowtime of jobs in the system and the work in process. In this study, we focus on the mean flowtime of jobs (MFT) because it is known as an interesting global performance measure and because operating times of tasks can increase due to the workers’ fatigue, so that they can take longer than expected. Let Tkj be the “theoretical” (expected) processing time of the task waiting the product k to be processed on machine j. In order to take into consideration the impact of fatigue on Tkj, we correct it as suggested in another previous work, such that T’kj(t) in (3) is the actual processing time and δ is a parameter used to tune the effect of fatigue.
T’kj(t) = Tkj (1+λ δ (1+Fi(t))) (3)
In order to illustrate our purpose and highlight the impact of the layout on the system performances and on the workers’ fatigue, we propose to compare two different layout designs of a job-shop system. To select the most appropriate design, we use a simulation model of a job-shop system and we are interested in choosing the design that reduces system efficiency while avoiding the excessive fatigue of the workers. Simulation results show the importance of taking fatigue into consideration to make better decisions about layouts so to improve system efficiency (MFT) and workers’ well-being at work

... These types of problems have been widely studied in the literature about manufacturing systems and it is well known that the way how workers are assigned in the system greatly affects the system performances. Reviews of research works related to workers assignment in manufacturing systems are presented in (Ammar, Pierreval, & Elkosantini, 2013;Ernst, Jiang, Krishnamoorthy, & Sier, 2004;Van den Bergh, Beliën, De Bruecker, Demeulemeester, & De Boeck, 2013;Xu, Xu, & Xie, 2011). According to these literature reviews, there exist various definitions, assumptions, contexts and methods related to the workers assignment problems, which are known for their complexity and for their NP-Hardness (Mahdavi, Paydar, Kia, & Khonakdari, 2010;Sirovetnukul & Chutima, 2010). ...

... According to Ammar et al. (2013) and Xu et al. (2011), the majority of existing publications are concerned with problems where the set of jobs to be processed is defined in advance, with deterministic processing times. As a consequence, the task durations are known a priori, with enough certainty, and the completion dates of jobs can be computed. ...

... Given the lack of precision about the production plan to be performed, it is well known that usual optimization approaches can generally not be applied. As a consequence, several researchers, such as Ammar et al. (2013), Cesani and Steudel (2005) and Zavadlav, McClain, and Thomas (1996), have pointed out, from their literature analyses, that determining online, in real time, where the operators should be assigned can represent an alternative to react quickly to these changes. The assignment decisions are made, online, according to the current system state, with respect to a set of constraints (e.g. ...

Manufacturing systems are often characterized by a stochastic and uncertain behavior in which frequent changes and unpredictable events may occur over time. Moreover, the customers’ demands can sometime evolve drastically along time. In order to cope with such changes in the manufacturing system state, and to optimize given performance criteria, the assignment of multi-skilled workers to the machines in the system can be decided online, in a dynamic manner, whenever workers become available and need to be assigned. Indeed, the starting and completion times of jobs in such systems cannot be predicted, so that static optimization approaches turn out not to be relevant. Several studies, in the ergonomics literature, have outlined that the operators' performances often decline because of their fatigue in work. In particular, in manufacturing contexts, fatigue can increase the processing times of jobs. Several online heuristic have been published, but to the best of our knowledge, they do not cope with this consequence of fatigue. We propose to solve this dynamic multi-skilled workers assignment problem using a new methodology, which aims to provide an adaptable dynamic assignment heuristic, which is used online. Our approach takes the impact of fatigue into consideration, in order to minimize the mean flowtime of jobs in the system. We suggest computing more realistic task durations, in accordance with the worker's fatigue. The heuristic uses a multi-criteria analysis, in order to find a compromise that favors short processing times and avoids congestions. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used to select the machine where to assign the worker. Since in our case no expertise is available, an offline adaptation process, based on simulation optimization, is used to identify the weights needed by TOPSIS, so as to better fit with the system specificities. A Job-Shop systems are simulated to illustrate the proposed approach. The performance of the suggested heuristic is assessed and compared to two other workers assignment rules, which are widely used in the scientific literature because of their efficiency on the mean flowtime: SPT and LNQ. The comparisons are made under different conditions (staffing level, operators’ flexibility). A sensitivity analysis is also performed to analyze the impact of the way how fatigue affects the task duration. Our experimental results show that our heuristic provides better results in every case studied. Several important research directions are finally pointed out.

... • Human factors and ergonomics need to be considered at configuration design stage in order to take into account operator skills, preferences and motivation in 2017 International Conference on Advanced Systems and Electric Technologies (IC_ASET) the assignment of operators to tasks within configurations [32]; ...

In reconfigurable manufacturing systems (RMS), the evaluation of configurations is usually based exclusively on technical performance indicators for an efficient and effective manufacturing. Ergonomics and human factors related aspects are rarely considered in the evaluation of reconfiguration opportunities, which leads to less realistic and pragmatic reconfiguration decisions. This article suggests both technical and ergonomics indicators to achieve a more realistic evaluation of reconfiguration decisions. A case study is introduced, and a TOPSIS based method is used to achieve multi-criteria evaluation and selection of an alternative configuration when reconfiguring an RMS. We particularly compare reconfiguration decisions with and without ergonomics indicators, and therefore establish the worthiness of considering both aspects simultaneously.

... Many manufacturing systems are characterized by a predefined arrival time of orders and constant operating times. In such cases, static assignment is used, so that workers could be assigned, for a single period, to the different machines in the system [3]. According to Ammar et al. [3] and Xu et al. [4], which have analysed the existing literature on the workforce assignment problems, classical optimization methods (i.e. ...

... In such cases, static assignment is used, so that workers could be assigned, for a single period, to the different machines in the system [3]. According to Ammar et al. [3] and Xu et al. [4], which have analysed the existing literature on the workforce assignment problems, classical optimization methods (i.e. exact, heuristics and metaheuristics approaches) have been extensively used to solve the static assignment of workers. ...

... In order to react quickly to these changes, workers can be assigned dynamically, online and according to the current system state. For such types of workers assignment problems, Ammar et al. [3] point out that the assignment rules When and Where are the most used in the literature. The When-rule specifies when the worker is eligible for transfer and the Where-rule specifies the machine to which the worker is going to move once he/she is released [7]. ...

In order to cope with the frequent unpredictable changes that may occur in manufacturing systems, and to optimize given performance criteria, the assignment of workers can be decided online in a dynamic manner, whenever the worker is released. Several studies, in the ergonomics literature, have shown that individuals' performances decrease because of their fatigue in work. In manufacturing context, the workers' fatigue impacts the task durations. Therefore, we propose to solve the online workers assignment problem through a heuristic, which takes this workers' fatigue into consideration, so as to minimize the mean flowtime of jobs. This approach suggests computing more realistic task duration in accordance with the worker's fatigue and it uses multi-criteria analysis in order to find a compromise to favor short durations and to avoid congestions. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method is used to select where to assign the worker. A learning process through simulation optimization is used to adapt the weights, in TOPSIS, to better fit with the system characteristics. The approach is illustrated with a simulated Job-Shop system. Experimental results comparing our approach with the rule Shortest Processing Time (SPT), which is known as efficient on the mean flowtime, show the effectiveness of the heuristic.

... En cohérence avec (Ammar et al. 2013), nous n'avons pas identifié de travaux utilisant des méthodes multicritères de choix, ni d'optimisation via simulation pour définir des méthodes d'affectation. Ces deux approches sont à la base de l'heuristique présentée dans le paragraphe suivant. ...

Colloque avec actes et comité de lecture. internationale.

... A recent survey of existing research about workers assignment shows that most works address static problems where tasks or machines are known and fixed for a given time period. Unfortunately, in many real situations, the frequent changes in the production, the unexpected disturbances and the arrival of urgent orders can make static approaches irrelevant [1]. For example, when the system has a stochastic behavior, the bottleneck can move from one work center to another, which implies the change of workers assignment. ...

... According to [1], most articles dealing with workers assignment address static cases where the production system features are defined by a fixed number of workers, each machine capacity being known and constant, workers are generally assigned for a single time period with deterministic and constant product mix and demand so that unexpected events are not considered. As a consequence, such problems are generally solved using classical optimization methods (either exact, such as branch and bound, or inexact such as heuristic methods). ...

Assigning workers to machines dynamically, so as to achieve production objectives, is known as a difficult problem which must be addressed in several manufacturing systems. In fact, production managers must determine when and where to assign workers, which is a very difficult task because of the complexity induced by the dynamic changes and the stochastic behavior of these systems. The current scientific literature is mainly oriented towards static assignments problems (only few dynamic heuristics are published). We propose a new approach whose aim is to help the managers in improving their knowledge about how to assign workers in real time. It is based on Serious Games built using Visual Interactive Simulation (discrete event). Our experiments show that an appropriate training using the proposed game can improve the users' ability to make good decisions about dynamic workers assignment and that human decisions can become more efficient than existing workers assignment rules found in the literature.

In this paper, we introduce a mixed-integer linear program for a shift scheduling problem in a German potash mine. In particular, we consider a short-term (work shift) production scheduling problem, where drill-and-blast mining operations have to be assigned to machines and workers simultaneously. Since we deal with several sequence-dependent setup, changeover, and removal times, TSP-variables are used in the mathematical program to determine the processing-sequence of the operations on each worker and each machine, respectively. In addition, several mining-specific requirements are taken into account to obtain a solution that can be put into practice. Computational experiments are conducted on problem instances of realistic size derived from real-world data. The results show that our new mixed-integer linear formulation outperforms both existing solution procedures for the problem at hand.