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We address the problem of sequencing jobs, each of which is characterized by one of a large number of possible combinations of customer-specified options, on a paced assembly line. These problems arise frequently in the automotive industry. One job must be launched into the system at equal time intervals, where the time interval (or cycle time) is prespecified. The problem is to sequence the jobs to maximize the total amount of work completed, or equivalently, to minimize the total amount of incomplete work (or work overload).
Since there is a large number of option combinations, each job is almost unique. This fact precludes the use of existing mixed model assembly line sequencing techniques. We first consider the sequencing problem for a single station which can perform two different sets of operations. We characterize the optimal solution for this problem and use the results as the basis for a heuristic procedure for multiple stations. Computational results with data from a major automobile company are reported.

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... Pour déterminer la séquence de véhicules garantissant le lissage de la charge de travail des opérateurs, le MMS prend en compte explicitement les temps de montage des véhicules et la configuration des différents postes de travail. Yano & Rachamadugu (1991) et Scholl et al. (1998) convergent vers une formulation similaire du MMS, avec un même objectif : minimiser la surcharge de travail totale. Boysen et al. (2009d) reprennent cette formulation et la considèrent comme le modèle de référence du MMS. ...

... Enfin, nous notons qu'une infime partie desétudes sur le CS discute de sa réelle capacité a minimiser des situations de surcharge de travail, alors qu'il s'agit de l'objectif sous-jacent de la minimisation des violations des règles de séquencement Yano & Rachamadugu, 1991). En effet, toute la performance du CS repose sur la bonne définition de ces règles de séquencement, pour lesquelles nous identifions seulement trois méthodes de calcul dans la littérature : -La méthode de Bolat & Yano (1992) qui génère un ratio H/N par poste de travail ; -La méthode de Golle et al. (2010) qui génère plusieurs ratios H/N par poste de travail ; -La méthode de Lesert et al. (2011) qui ne génère qu'un seul ratio H/N par groupe de véhicules lourds pour toute la ligne d'assemblage, afin de se conformerà l'usage des règles de séquencement par les constructeurs automobiles (qui n'en traitent en général qu'une dizaine). ...

... MMS is a sequencing model that explicitly considers manufacturing data such as processing times, workstation configurations, and operator movements to determine the best sequence of products to manufacture on an MMAL. Yano & Rachamadugu (1991) and Scholl et al. (1998) converge on a similar formulation of the MMS, with the same objective: minimizing total work overload. This formulation is taken up by Boysen et al. (2009d) and considered as the MMS reference model. ...

Pionnière dans la mise en place des lignes d’assemblage, l’industrie automobile demeure une référence en matière d’optimisation de ces équipements industriels incontournables. Initialement configurées pour la production de masse de produits standards, les lignes d’assemblage disposent aujourd'hui de la flexibilité nécessaire pour produire toute la diversité de véhicules proposée par les constructeurs, et réagir efficacement à l’évolution de la demande. Cependant, la diversité actuelle est telle que les véhicules produits sur la ligne d’assemblage sont distincts uns à uns, ce qui engendre une complexité sans précédent pour la gestion des approvisionnements en amont et en interne de l’usine, pour la planification et l’ordonnancement de la production dans tous les ateliers, ainsi que pour la distribution des véhicules dans le réseau commercial.Face à ce constat, nous étudions dans cette thèse l’intérêt et la faisabilité d’intégrer des stratégies de regroupement de véhicules similaires à l’ordonnancement de la production, afin de contribuer à la performance de la chaîne logistique au global.Pour cela, nous présentons une comparaison des espaces de solutions de deux modèles séquencement ayant pour objectif commun la minimisation de la surcharge de travail des opérateurs au montage : le Mixed-Model Sequencing et le Car Sequencing. A l’issue de cette comparaison, le premier modèle se distingue comme le plus adapté à intégrer de nouveaux critères d’optimisation.Par la suite, nous révélons les résultats de l’étude de terrain réalisée au sein de Renault Group qui nous a permis d’identifier et de qualifier des stratégies opportunes de regroupements des véhicules en production. Nous évaluons la pertinence de ces stratégies au regard de leur impact sur la qualité, les coûts et les délais. Nous établissons enfin une priorisation entre toutes ces stratégies qui nous permet d’en retenir deux majeures pour la dernière partie de cette thèse.Enfin, nous proposons deux nouvelles extensions au modèle du Mixed-Model Sequencing. La première intègre le besoin de l’atelier de peinture de regrouper les véhicules de même teinte afin de limiter les coûts liés aux purges des systèmes de peinture. Dans la seconde extension, nous considérons en plus le regroupement des véhicules de même destination afin d’optimiser la logistique aval.

... MMS is a sequencing model that explicitly considers manufacturing data such as processing times, workstation configurations, and operator movements to determine the best sequence of products to manufacture on an MMAL. Yano and Rachamadugu (1991) and Scholl, Klein, and Domschke (1998) converge on a similar formulation of the MMS, with the same objective: minimising total work overload. This formulation is taken up by Boysen, Fliedner, and Scholl (2009b) and considered as the MMS reference model. ...

... We review them below and present a comprehensive synthesis highlighting the originality of our study. Yano and Rachamadugu (1991) are the first authors to compare MMS and CS. They base their study on industrial data from a major automotive company using real-life sequencing rules and processing times. ...

... Regarding the identification of heavy variants, we stick in this paper to the 'one option-two temporisations' assumption which is commonly used in the CS literature (as in Yano and Rachamadugu 1991;Bolat and Yano 1992;Boysen, Kiel, and Scholl 2011, for instance). Hence we consider that every workstation k has only two variants and two processing times: a heavy one with T sup k > T cycle and a light one with T inf k < T cycle . ...

In the automotive industry, a great challenge of production scheduling is to sequence cars on assembly lines. Among a wide variety of scheduling approaches, academics and manufacturers pay close attention to two specific models: Mixed-Model Sequencing (MMS) and Car Sequencing (CS). Whereas MMS explicitly considers the assembly line balance, CS operates with sequencing rules to find the best car sequence fulfilling the assembly plant requirements, like minimising work overload for assembly workers. Meanwhile, automakers including Renault Group are increasingly willing to consider other requirements, like end-to-end supply chain matters, in production planning and scheduling. In this context, this study compares MMS- and CS-feasible solution spaces to determine which workload-oriented sequencing model would be the most appropriate to later integrate new optimisation. We introduce two exact methods based on Dynamic Programming to assess the gap between both models. Numerical experiments are carried out on real-life manufacturing features from a Renault Group assembly plant. They show that MMS generates more feasible sequences than CS regardless of the sequencing rule calculation method. Only the sequencing rules used by real-life production schedulers result in a higher number of distinct feasible sequences for CS, highlighting that the plant might select a sequence with work overload situations.

... In the context of line balancing problem of the two-sided assembly line (TSAL), comprehensive studies with various objective functions have been done in [2][3][4][5][6][7][8]. Lee et al. [3] studied TSAL to maximize work relatedness and slackness which they assigned a group of tasks at a time rather than a unit task. Kim et al. [4] was the first proposed that MILP model considering sequence dependent finishing time of tasks. ...

... For model sequencing problem, many researchers studied mixedmodel assembly line (MMAL) of traditional straight line and most of them focused on minimizing total utility work such as Yano and Rachamadugu [8]. The study by Fattahi and Salehi [9] focused on minimizing the cost of total utility work and idle time with variable launching interval. ...

... According to the study in [11], this objective contributes to reducing not only labor cost but the risk of stopping the conveyor and the required line length. Apart from the studies in [8][9][10], only Chutima and Naruemitwong [1] studied MMTSAL for solving the multiobjective of sequencing problems. Line balancing and model sequencing problems have also been studied in a hierarchical manner which solves one problem first and ...

This research explores two interrelated problems in Mixed-Model Two-Sided Assembly Line (MMTSAL), which are line balancing and model sequencing. These two problems are solved simultaneously using Mixed Integer Linear Programming (MILP) with the objectives of minimizing total utility work and idle time by considering various practical constraints. The problem is analyzed using small-size to large-sized test cases using General Algebraic Modelling System (GAMS) with the solver CPLEX. Experimental results indicate that integrating the problems help to minimize the proposed objective function. Also, it is found that the feasible solution for model sequence with the assignment of tasks to assembly line is optimal.

... In automotive assembly lines, work overload can lead to the work being unfinished and then having to be completed in the "nursing" area, to the assignment of more utility workers, or like in the worst case, to the halting of a line so that the work can be finished in the station, with the cost that it incurs. Yano and Rachamadugu [9] considered the aim of minimizing the work overload caused by the sequence and put forward a model of the problem. A case with a single station and two types of products is studied and a solution procedure is given. ...

... In this paper, we focus on the aforementioned procedures of Yano and Rachamadugu [9], Bolat and Yano [4][5], Tsai [8], and we extend procedures for the case of one station and two products, minimizing the work overload. It is organized as follows: In section §2, a formulation of Yano and Rachamadugu [9] for measuring work overload is mentioned. ...

... In this paper, we focus on the aforementioned procedures of Yano and Rachamadugu [9], Bolat and Yano [4][5], Tsai [8], and we extend procedures for the case of one station and two products, minimizing the work overload. It is organized as follows: In section §2, a formulation of Yano and Rachamadugu [9] for measuring work overload is mentioned. Section 3 deals with procedures for one station and two products, one taken from bibliography and a proposal inspired on Bolat greedy procedures. ...

A variant of the mixed-model sequencing problem on assembly lines is the one proposed by Yano and Rachamadugu. They consider time windows in workstations and the work overload concept (sum of differences between real completion time in the workstation and due dates, which depends on the time window value). This paper proposes some procedures for solving the problem, and compares them with others taken from literature using a computational experience.

... The greatest possible reduction of the levels of stocks in the system. For category A, in addition to a relative focus on maximising the total amount of work completed [2], the excess effort that must be applied over time for certain operations can be modulated [3]. ...

... Overload, or excess effort, is a measurement, in units of time, of work that cannot be completed at the standard rhythm of an established activity, within the time granted to the workstations (cycle). This overload may arise when the processing time of a unit at a workstation is greater than the cycle time [2], although there may be a certain amount of play associated with extended cycles, which is called the length of the workstation or the time window. ...

... Let the unit pass and finish the pending work in a final line at a later time. [2,6,7,8]. III. Increase productive activity above the standard, using the assistance of reinforcement operators or previously programmed robotised systems. ...

In this paper, we propose a procedure based on Bounded Dynamic Programming (BDP) to solve the Mixed-Model Sequencing Problem with Workload Minimisation (MMSP-W), with serial workstations and unrestricted (or free) interruption of the operations. We performed a computational experiment with 225 instances from the literature. The results of our proposal are compared with those obtained through the CPLEX solver.

... For category A, in addition to a relative focus on maximizing the total amount of work completed (Yano and Rachamadugu, 1991), the excess effort that must be applied over time for certain operations can be modulated. ...

... Overload, or excess effort, is a measurement, in units of time, of work that cannot be completed at the standard work pace established, within the time granted to the workstations (cycle). This overload may arise when the processing time of a unit at a workstation is greater than the cycle time (Yano and Rachamadugu, 1991), although there may be a certain amount of play associated with extended cycles, which is called the length of the workstation or the time window. ...

... When faced with a foreseeable workstation overload, at least three types of measures can be taken: (I) stop the line and complete the pending work using reinforcements (Okamura and Yamashina, 1979;Rabbani et al., 2011); (II) let the unit pass and finish the pending work in a final line at a later time. (Yano and Rachamadugu, 1991;Bolat, 2003;Tsai, 1995); and (III) increase productive activity above the standard, using the assistance of reinforcement operators (Cevikcan and Durmusoglu, 2011) or previously programmed robotized systems. The present study considered measures in categories II and III for handling work overloads. ...

In this paper, we propose a hybrid procedure based on Bounded Dynamic Programming (BDP) and linear programming to solve the Mixed-Model Sequencing Problem with Workload Minimization (MMSP-W), with serial workstations, free interruption of the operations and production mix restrictions. We performed a computational experiment with 225 instances from the literature. The results of our proposal are compared with those obtained through the Gurobi solver and previous procedures.

... One of these criteria is the minimization of the overload, which is a measurement, in units of time, of the remaining work on a product that is not done in a particular workstation. This overload may appear when the needed time to finish the work on given product is larger than the assigned cycle time [18], which is an average of the time needed by the different products manufactured in the line; thus, if several products with high processing time are consecutively fed in the line at some point one workstation will not have time enough to finish its expected work and, either the line is stopped to allow the workers finishing the product before it leaves the workstation (called conveyor stoppage [16]), or the product exits the workstation partially manufactured. The amount of work not done on a product in a workstation is called with different names: work overload [18] [2], remaining work [4], or utility work [15]. ...

... This overload may appear when the needed time to finish the work on given product is larger than the assigned cycle time [18], which is an average of the time needed by the different products manufactured in the line; thus, if several products with high processing time are consecutively fed in the line at some point one workstation will not have time enough to finish its expected work and, either the line is stopped to allow the workers finishing the product before it leaves the workstation (called conveyor stoppage [16]), or the product exits the workstation partially manufactured. The amount of work not done on a product in a workstation is called with different names: work overload [18] [2], remaining work [4], or utility work [15]. ...

... Minimizing the overload is a NP-hard problem [18], and different approaches have been proposed to solve it, like: exact procedures based on branch and bound [6] and dynamic programming [18]. Other procedures are based on a local search [17], greedy with priority rules [5], metaheuristics [13], or based on beam search [8]. ...

This paper reviews the formulation of the Mixed Model Sequencing Problem with Workload minimization (MMSP-W). Two significative models already presented in the literature are describe, showing that they are valid for the case of parallel workstations, but do not properly solve the case of serial workstations. After that, a new model is introduced that is valid for the case of serial workstations. An example is used to illustrate the performance of all the models, and a computational experience was done to verify the applicability of the proposed model using the solver CPLEX and a set of problem instances of small dimension adapted from the literature.

... In contrast, if we consider human resources (HR) as the relevant element of the manufacturing system, then a reasonable objective is to minimize the work overloads that can appear when the mixed-product units treated by the line require different processing times at each stage or, more concretely, at each workstation. To achieve this, we can minimize the total work overload or maximize the total work completed, as in the Mixed-model Sequencing Problem with Work-overload minimization (MMSP-W), which was proposed by [3]. A recent work regarding this problem is [4]. ...

... This paper examines a variant of the MMSP-W, the MMSP-W-pmr. The original problem, MMSP-W, is an NP-hard problem [3] for which several alternative procedures have been proposed. These solutions include exact procedures based on branchand-bound ( [16]), dynamic programming ( [3], [17], [18]), heuristic procedures based on local search ( [19]), greedy algorithms with priority rules ( [19], [20]), metaheuristics ( [21]) and beam search ( [22]). ...

... The original problem, MMSP-W, is an NP-hard problem [3] for which several alternative procedures have been proposed. These solutions include exact procedures based on branchand-bound ( [16]), dynamic programming ( [3], [17], [18]), heuristic procedures based on local search ( [19]), greedy algorithms with priority rules ( [19], [20]), metaheuristics ( [21]) and beam search ( [22]). Several studies have also considered the multi-criteria option (( [23], [24], [25], [26]). ...

In this article, we propose a hybrid procedure based on bounded dynamic programming assisted by linear programming to solve the mixed-model sequencing problem with workload minimization with serial workstations, free interruption of the operations and with production mix restrictions. We performed a computational experiment with 23 instances related to a case study of the Nissan powertrain plant located in Barcelona. The results of our proposal are compared with those obtained by mixed integer linear programming.

... The most common objective in the literature, also adopted in this study, is minimizing the total work overload duration, proposed by Yano and Rachamadugu (1991). Tsai (1995) describes hiring utility workers to execute tasks so that production delays are avoided, which leads to the objective of minimizing the total utility work duration. ...

In the automotive industry, the sequence of vehicles to be produced is determined ahead of the production day. However, there are some vehicles, failed vehicles, that cannot be produced due to some reasons such as material shortage or paint failure. These vehicles are pulled out of the sequence, and the vehicles in the succeeding positions are moved forward, potentially resulting in challenges for logistics or other scheduling concerns. This paper proposes a two-stage stochastic program for the mixed-model sequencing (MMS) problem with stochastic product failures, and provides improvements to the second-stage problem. To tackle the exponential number of scenarios, we employ the sample average approximation approach and two solution methodologies. On one hand, we develop an L-shaped decomposition-based algorithm, where the computational experiments show its superiority over solving the deterministic equivalent formulation with an off-the-shelf solver. Moreover, we provide a tabu search algorithm in addition to a greedy heuristic to tackle case study instances inspired by our car manufacturer partner. Numerical experiments show that the proposed solution methodologies generate high quality solutions by utilizing a sample of scenarios. Particularly, a robust sequence that is generated by considering car failures can decrease the expected work overload by more than 20\% for both small- and large-sized instances.

... The selected priority rules are described in table 2. The FiFo rule and the shortest PT rule can be found in Corsten (2016). The alternating rule is derived from the approach of Yano & Rachamadugu (1991) and the Min UW rule comes from the work of Thomopoulos (1967). In addition to the score values, a penalty term f j is introduced for each job, which comes into effect when the selected job does not meet the options' due date. ...

Mixed-model assembly lines are state of the art in automotive production systems. Because of the high number of customizable options which can be ordered in a vehicle, there is a huge variety of possible products. An important problem in this context is the sequencing of such products. Inevitably, there will be deviations from the intended production sequence in the course of production, as disruptions occur. The products must then be resequenced to ensure an optimal sequence. In this work, we consider the usage of a buffer (in form of an automated storage and retrieval system) between the paint shop and the final assembly to resequence the orders. We consider a high number of variants and, with this, a random input sequence for the buffer. Additionally to the physical resequencing in the buffer, the options get decoupled from the products. That allows virtual resequencing, in which parts and materials are interchanged. The dispatching selection must be made without full information in an online problem. To solve this problem, different heuristics and a lookahead algorithm are applied to minimize the amount of utility work in a paced automotive assembly line.

... Several previous studies have addressed many multi-item production systems. In the case of assembly production, it is necessary to allocate work to each process in consideration of the commonality and similarity of parts and work in the multi-item production, work-time difference between products, work-time variation, and so on [8] [9][10] [11][12] [13]. Conversely, as part of ongoing research on production systems similar to process production for multiple items, scheduling by lot sizes and on insertion order considering the setup time has been studied [14][15] [16] [17]. ...

... Here he positively supports the working of multiple assembly lines because they bring the best out of them by rationally scheduling them (Dong, Chen, & Lu, 2015). The author states that the, even if the number of models of the assembly line is limited it is better to use or affordable to use the assembly line to cope up with the ever-increasing demands of the customers (Yano & Rachamadugu, 1991). ...

Purpose: This paper shows the working of Supply Chain Management. Also, it gives the processes which happens in the supply chain industry. Methodology: This paper gives the hypothesis of process of supply chain management and gives whatever advanced changes made in the industry. Findings: This paper states, how time and transportation are basic pieces of SCM industry and how it is related to procedures inside. Also, this paper shows how raw material is also important in the process. Research implications: The research in the paper focus on the information about quality of the product, inventory management, and how to deliver the product to the end user in time. This all applications holds a lot of weightage in the supply chain industry. Practical implications: This model is utilized to do the item conveyance to the consumers everywhere throughout the world in excellent condition and in the stipulated time traverse. This model is used to imply for supply chain management all over the world. It gives guidelines to deliver product in time. Originality/value: This paper gives an idea of transferring the product to their exact location and it gives the process of supply chain.

... This problem is proven to be strongly NP-Hard ( McCormick & Rao, 1994 ) for unpaced lines of three or more stations. For paced lines, Yano and Rachamadugu (1991) developed an analytical solution for the case of a single station and two models. For more stations, the authors use a heuristic. ...

The quality of the balancing of mixed-model assembly lines is intimately related to the defined production sequence. The two problems are, however, incompatible in time, as balancing takes place when planning the line, while sequencing is an operational problem closely related to market demand fluctuations. In this paper, an exact procedure to solve the integrated balancing and sequencing problem with stochastic demand is presented. The searched balancing solution must be flexible enough to cope with different demand scenarios. A paced assembly line is considered and utility work is used as a recourse for station border violations. A Benders’ decomposition algorithm is developed along with valid inequalities and preprocessing as a solution procedure. Three datasets are proposed and used to test algorithm performance and the value of treating uncertainty in mixed-model assembly lines. The integration of the strategic balancing problem with the operational sequencing problem results in more robust assembly lines.

... Considering processing times to minimize work overload is very common in mixed-model sequencing of assembly lines [e.g. Scholl et al. (1998) or Yano and Rachamadugu (1991)]. We extend this idea to multi-level production systems. ...

Many manufactures are shifting from classical production environments with large batch sizes towards mixed-model assembly lines due to increasing product variations and highly individual customer requests. However, an assembly line should still be run with constant speed and cycle time. Clearly, the consecutive production of different models will cause a highly unbalanced temporal distribution of workload. This can be avoided by moving some assembly steps to pre-levels thus smoothing out the utilization of the main line. In the resulting multi-level assembly line the sequencing decision on the main line has to take into account the balancing of workload for all pre-levels. Otherwise, the modules or parts delivered from the pre-levels would cause congestion of the main line. One planning strategy aims at mixing the models on the main line to avoid blocks of identical units. In this contribution we compare two different realizations for this approach. On one hand we present a mixed-integer programming model (MIP), strengthen it by adding valid inequalities and enrich it with a number of relevant practical extensions. Also the actual objective of explicitly balancing pre-level workloads is considered. On the other hand, we illustrate how this strategy could be realized in an advanced planning system linked to an enterprise resource planning system, namely SAP APO. Finally, we perform a computational study to investigate the possibilities and limitations of MIP models and the realization in SAP APO. The experiments rely on a real-world production planning problem of a company producing engines and gearboxes.

... Among the objectives are the following: o1 Maximize the number of units completed in the production line. Hence, efforts are conducted to reduce the inert time of the workers, the unnecessary waiting, and the production losses caused by workload excess (overload) in the stations [Yano and Rachamadugu (1991), Cano-Belmán et al. (2010), Bautista et al. (2012)]. ...

The concept of partial demand uncertainty is introduced from the car sequencing problem (CSP) and incorporates special vehicle fleets in a demand plan. After establishing the working hypotheses with fleets, a mixed integer linear programming model, robust car sequencing problem (r-CSP), is proposed to satisfy the maximum number of CSP restrictions. Subsequently, multi-sequence production and metrics to evaluate its robustness are defined. The r-CSP considers various demand scenarios and functions to measure the excess of optional requirements in production programs. These functions are valid as objectives in optimization problems and as multi-sequence production robustness metrics.

... The coefficients k 1 , k 2 and k 3 convert the respective values in monetary equivalents. The further problem formulation is based on previous work regarding car sequencing (see [8], [9], [10], [12], [13]) and the following assumptions: ...

Mixed model assembly lines are state of the art for automotive mass production. In the context of mass customization and indi-vidualization the car sequencing recently became more and more challenging due to varying assembly tasks and processing times. Classical principles such as the vehicle pearl chain are thus reaching their limits. Therefore, planned changes in the vehicle sequence during final assembly, Proactive Resequencing, was proposed to optimize utilization segment by segment. The concept leads to a long-term buffer planning problem on a strategic level as well as to an adapted vehicle sequencing problem with enhanced flexibility on an operative level. This paper introduces a mathematical model for the combined buffer planning and order sequencing problem for automotive assembly lines. It also outlines a solution approach for the mentioned production planning challenges separated by their timing preferences.

... Kotani et al. [32] propose a new formulation of the sequencing problem for the Toyota production system aiming at the minimization of the line stoppage time as well as at ensuring a constant part usage rate [32]. While approaches such as those proposed by Bard et al. [10], Scholl [33] as well as Yano and Rachamadugu [34] use a weighted sum of these two objectives, Kotani et al. [32] consider the constant rate of part usage as a constraint in the optimization model [32]. With respect to the solution methodology, they suggest a two-phase approximation algorithm [32]. ...

Multi-variant products to be assembled on mixed-model assembly lines at locations within a production network need to be scheduled locally. Scheduling is a highly complex task especially if it simultaneously covers the assignment of orders, which are product variants to be assembled within a production period, to assembly lines as well as their sequencing on the lines. However, this is required if workers can flexibly fulfill tasks across stations of several lines and, thus, capacity of workers is shared among the lines. As this is the case for final assembly of the Airbus A320 Family, this paper introduces an optimization model for local order scheduling for mixed-model assembly lines covering both assignment to lines as well as sequencing. The model integrates the planning approaches mixed-model sequencing and level scheduling in order to minimize work overload in final assembly and to level material demand with regard to suppliers. The presented model is validated in the industrial application of the final assembly of the Airbus A320 Family. The results demonstrate significant improvement in terms of less work overload and a more even material demand compared to current planning.

... However, such flexibility supposes two main problems with respect to establishing the configuration of the line and product sequence. Indeed, these issues have been discussed at length in literature under the names assembly line balancing problems or ALBPs (Salveson 1955;Baybars 1986;Scholl and Becker 2006;Boysen et al. 2007Boysen et al. , 2008Battaïa and Dolgui 2013) and mixed-model sequencing problems or MMSP (Miltenburg 1989;Yano and Rachamadugu 1991;Bautista et al. 1996;Boysen et al. 2009;Bautista and Cano 2011;Dörmer et al. 2015;Bautista-Valhondo 2016;Bautista-Valhondo and Alfaro-Pozo 2018a). ...

We present a variant of the approach to the assembly line balancing problems, with the aim of reducing the ergonomic risk for operators of mixed-model assembly lines (MILP-3). Specifically, the MILP-3 model is focused on minimizing the average range between ergonomic risk values of workstations. Using a case study from Nissan's plant in Barcelona, not only are the differences between levels of ergonomic risk of stations reduced, but we attempt to reduce the average maximum ergonomic risk of the assembly line. The new model is compared with two others, MILP-1 and MILP-2, which minimize the average maximum ergonomic risk and the average absolute deviation of the risks, respectively.

... In studies of item process sequencing on a mixed-model assembly line, the objective function can be roughly divided into two types. The first aims at minimizing line stoppage time when processing cannot be completed within a station (Boysen et al., 2009;Shimizu et al., 2009;Xiaobo and Ohno, 1997;Yoo et al., 2004), whereas the second aims at minimizing the additional resources (i.e., total unfinished work time) needed to avoid stopping the line (Bard et al., 1992;Bautista and Cano, 2008;Bautista and Pereira, 2009;Bautista and Cano, 2011;Ishigaki and Miyashita;2016;Leu, 1997, Scholl et al., 1998Yano and Rachamadugu, 1991). ...

The diversification of customer needs and the shortening of product life cycle have increased the significance of small batch production. The growth of interest in environmental issues has generated a focus on methods such as recycling and reuse. Therefore, companies must pay attention to the environmental impact of their production cycle, discharge their social responsibility, and maintain their competitive advantage. In this research, we addressed the mixed-model assembly line, which is used to assemble or remanufacture multiple items simultaneously. Despite their versatility, these assembly lines carry a high risk of line stoppages, especially in dynamic environments. We describe the task assignment problem and item process sequencing problem of a mixed-model assembly line with multiple stations. A heuristic method for solving each of these problems was investigated.

... MMSP-W [1][2][3] (mixed-model sequencing problem with workload minimization) is a problem of sequences in assembly lines [4] that consists of establishing a bijection between the elements of a set T of manufacturing cycles (t = 1, . . . , T ) and those of a set Ψ of products (T elements). ...

PROGRESS IN ARTIFICIAL INTELLIGENCE 7(3): 197-211.
We present a GRASP algorithm to solve a problem that involves the sequencing of mixed products in an assembly line. The objective of the problem is to obtain a manufacturing sequence of models that generates a minimum work overload with a forced interruption of operations, which is regular in production, and in which, the production mix maintains the Quota property in the whole sequence. The implemented GRASP is compared with other procedures using instances of a case study of the Nissan engine manufacturing plant in Barcelona.

... ensuring smooth flow throughout the supply chain [13], smoothing out production peaks and troughs [11], reducing inventories [14], avoiding excessive work load [15], increasing manufacturing capacity [16], maximizing effectiveness of manufacturing resources [17], increasing competitiveness [18]. ...

... To keep a constant rate of feeding of every model insert to the line, see Kubiak [2] To level the load at each work stations, see Yano and Rachamadugu [3] To minimize the conveyor stoppage, as required by the machines times and number of products that must be produced, see Xiabo and Ohno [4,5] Designing appropriate configuration of the line assembly has some effects on decreasing of stoppages and cooperation of workers. In a U-type assembly line, the workers' moving is easier than the straight-type assembly line and workstations in opposite sides have a chance to get help from workers of both sides in a flexible manner, hence stoppages of the line reduce more than traditional straight-line formation. ...

Mixed-Model Assembly Line (MMAL) is a type of production line where a variety of products' models similar to products' characteristics are assembled in the same line. Many manufacturers tend to use mixed-model assembly line in their production lines, since this policy makes it possible to assemble various products in the Make-To-Order (MTO) environment. In this research, the sequence of U-type mixed-model assembly line is achieved through considering downstream help and storage of kits as effective help policies for reducing total line stoppages and tardiness in delivery time of products to customers. Since this problem is NP-hard, hybrid GA-Beam search algorithm is developed to solve the problem. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. To the best of our knowledge, this is the first study that considers getting help from downstream worker or using storehouse of kits, which has ready-toassemble parts in the conditions that workers cannot complete the remained task in the work horizon.

... In this article, we considered the same problem as in the work of Yano and Rachamadugu [38] for minimization of the total unfinished work or maximization of the total completed work which is the same as minimize work overload [8]. ...

Many assembly lines related optimization problems have been tackled by researchers in the last decades due to its relevance for the decision makers within manufacturing industry. Many of theses problems, more specifically Assembly Lines Balancing and Sequencing problems, are known to be NP-Hard. Therefore, Computational Intelligence solution approaches have been conceived in order to provide practical use decision making tools. In this work, we proposed a simultaneous solution approach in order to tackle both Balancing and Sequencing problems utilizing an effective meta-heuristic algorithm referred as Fish School Search. Three different test instances were solved with the original and two modified versions of this algorithm and the results were compared with Particle Swarm Optimization Algorithm.

... This work was funded by the Ministerio de Economía y Competitividad (Spanish Government) through the TIN2014-57497-P (FHI-SELM2) project. 2 sequence. Indeed, these issues have been discussed at length in literature under the name of Assembly Line Balancing Problems (ALBPs) (Salveson ME, 1955) and Mixed-Model Sequencing Problems (MMSP) (Yano and Rachamadugu, 1991). The first problems are focused on assigning the set of tasks or operations needed to manufacture the products to the set of workstations that make up the line in accordance with an optimization criterion. ...

This work presents a new variant for the Time and Space Balancing Problem whose objective is balancing the ergonomic risk of operators of mixed-model assembly line. Specifically, the model is focused on minimizing the range between ergonomic risk values of workstations. In this way, not only the differences between levels of ergonomic risk of workstations are reduced, but it is also attempted to reduce the maximum ergonomic risk of the assembly line. The model is compared to another one that minimizes the ergonomic risk dispersion of the line through the minimization of the standard deviation of the risks.

... El MMSP-W [1] (Mixed Model Sequencing Problem with Workload Minimisation) es un problema de secuencias en líneas de montaje [2] consistente en establecer una biyección entre los elementos de un conjunto Τ de ciclos de fabricación ! = 1, . . ...

Presentamos un algoritmo GRASP para resolver un problema de secuenciación de productos mixtos en una línea de montaje. El objeto del problema es obtener una secuencia de fabricación de modelos que genere la mínima sobrecarga con interrupción forzada de las operaciones, que sea regular en producción y que el mix de producción mantenga la propiedad quota en toda la secuencia. El GRASP implementado se compara con otros procedimientos usando instancias de un caso de estudio de la planta de fabricación de motores de Nissan en Barcelona.

... continuous flow throughout the entire supply chain [21] eliminating the production peaks [1] reducing the stock [10] avoiding work overload [24] improving the production capacity [33] maximizing efficiency [32] improving competitiveness [29]. ...

The article presents an extensive analysis of the literature on defining production leveling and the methodology for its implementation. The main aim of this article is to show how to change these factors after the implementation of production leveling. The article also presents an example of the implementation of leveling production at the department for the production of surgical instruments at a manufacturing enterprise. The current production scheme, including maps of material flow analysis, orders, and the flow from production are described. Finally, the article presents the successive steps in implementing the production leveling in the enterprise.

... Production levelling is construed as a method of determining product sequences to prevent from sudden changes in the quantity of manufactured products, which contributes to enhancing efficiency and flexibility, as well as to minimizing differences in workplace load [21]. The main objectives of levelled production include mostly: ─ continuous flow throughout the entire supply chain [22]; ─ eliminating peaks in production [23]; ─ reduction of stock levels [24]; ─ avoiding work overload [25]; ─ enhancing production capacity [26]; ─ maximizing efficiency of production resources [21]; ─ increasing company competitiveness [23]. ...

The article describes an original computer program developed by the authors to aid data analysis for the purposes of production levelling methodology. Individual stages of the methodology are connected with analysis of multiple types of data. The program AnaPro enables analysis of manufacturing process data to separate product families, specify the demand for products and implement production. Functions of the program are described along with examples of data analysis.

... Una variante sencilla del problema CLRV con solo dos tipos de unidades a secuenciar fue propuesta por Yano y Rachamadugu [14] y resuelta mediante un procedimiento heurístico por dichos autores. Nosotros hemos realizado una extensión al considerar ilimitado el número de tipos de unidades a secuenciar, resolviendo el problema por procedimientos heurísticos y exactos basados en la BDP [15]. ...

... Es fácil ver que la entrada sucesiva a línea de unidades con tiempo de proceso superior al ciclo puede generar sobrecarga o, por disponibilidad de tiempo, dejar parte del trabajo sin completar. Entre los trabajos que abordan este tipo de problema están: (1) Yano y Rachamadugu [4], con dos variantes de producto y una o varias estaciones de trabajo, con el propósito de minimizar la sobrecarga total generada por la secuencia; (2) Bolat y Yano [1] [2] que extienden el trabajo anterior, proponiendo tres métodos de resolución e introduciendo el concepto de tiempo ocioso; (3) Tsai [3] que extiende los trabajos anteriores al tener en consideración los tiempos de desplazamiento del operario, y establece dos objetivos: minimizar el desplazamiento máximo del trabajador a partir del origen de la estación y minimizar el trabajo no completado. Partiendo de trabajos anteriores [5], aquí nos centraremos en el caso múltiples estaciones y múltiples productos. ...

La secuenciación de unidades en líneas de montaje de productos mixtos puede atender a diversos criterios; uno de ellos es el que consiste en minimizar la sobrecarga o trabajo perdido. En el presente trabajo proponemos heurísticas para el caso general con n variantes de un producto y m estaciones de trabajo y probamos la eficiencia de dichos procedimientos a través de una experiencia computacional.

... El texto que inmediatamente sigue responde al siguiente orden: en la sección dos se describe la propuesta de Yano y Rachamadugu (1991) -medida de la sobrecarga-; en la sección tres se incluyen modelos para minimizar el trabajo perdido; en la sección cuatro se describe un conjunto de procedimientos de resolución para el caso de una estación -Yano y Rachamadugu (1991), Bolat y Yano (1992), y nuestra propuesta-; en la sección cinco realizan extensiones al procedimiento de Yano y Rachamadugu (1991) para varias estaciones, empleando, para el cálculo de cotas y predictores, los procedimientos descritos en la sección cuatro; en la sección seis se muestra los resultados de la experiencia computacional realizada; y, finalmente, la sección siete se dedica a conclusiones. Yano y Rachamadugu (1991) proponen una formalización general para medir la sobrecarga de trabajo considerando: una sola estación, una plantilla fija y la posibilidad de que haya más de un operario en la estación. La unidad de tiempo empleada se refiere al ciclo de fabricación (tiempo de ciclo). ...

... In the production system JIT, the sequence problems have diverse functions objective, among them we find those outlined by authors like Yano [5] in 1991 who looks for the minimization of total time of work, or the one outlined by Bard [1], to minimize the total cost of lot change or product, or the one outlined for Monden [2] which looks for to maintain a constant use of the consumption of components. ...

the system FMS-100 is a flexible manufacturing system used by the Militar Nueva Granada University for the teaching of modern systems of production and its integration with the industrial automation in the programs of industrial engineering and mecatronics engineering. It is a tool used for the integration of an automated system with tools for the administration of the production like MRP, JIT, TOC, among other. The following paper presents the application of a model of production programming in the system FMS, using tools of the production system JIT, since this it is characterized to be a tool that is applied in production environments in which the flexibility and the production of small lots are two of the main characteristics, that which allows the clients to receive the merchandise in short times of time and first floor inventory levels are managed.

... In the PRV problem the objective is to minimise the rate variation for different products in any segment of a sequence, i.e. regularity in manufacturing products. PRV was first presented in [3], and then, several works dealing with heuristic procedures [3,4,5,6,7,8,9,10 Moreover, load balancing is the main objective in the LRV (Load Rate Variation) problem, treated in [20,21]. ...

Sequencing units on assembly lines in order to attenuate rate variations in resource consumption is a problem that has received growing attention in recent years. In this work, we deal with a particular case, the constrained output rate variation (CORV) problem, that seems to be better adapted than other views to real industry problems, especially in car production systems. After giving a general introduction and formulation, a procedure is described to obtain the searched sequence.

Industry trends such as product customization, radical innovation, and local production, accelerate the adoption of mixed‐model assembly lines that can cope with a widening gap between model processing times and true build to order capabilitiy. The existing high work content deviations on such assembly lines stress production planning, especially the assembly line sequencing. Most manufacturers set the launching rate for all assembly line products to a fixed launching rate resulting in rising utility work and idle time when system load increases. We present an “ideal” variable rate launching case resulting in minimal computation and achieving 100 percent productivity (full elimination of ilde time and utility work) for balanced assembly times and homogenous station lengths. Managers should foster the ideal circumstances where operators need not wait for a preceding task to be completed and product sequence restrictions are eliminated. Thus, enabling un‐matched production flexibility. Furthermore, we present a mixed‐integer model to analyze both closed and open workstations on a mixed‐model assembly line for fixed and variable rate launching. This model incorporates costs not only for labor inefficiencies but also for extending the line length. We present a heuristic solution method when process times and station lengths are heterogeneous and demonstrate that the variable takt dominates the fixed takt. In a numerical, industrial benchmark study, we illustrate, that a variable rate launching strategy with open stations has significantly lower labor costs as well as a substantially reduced total line length and thus lower throughput time. This article is protected by copyright. All rights reserved

In mixed-model production, it is important to determine a proper production sequence which minimizes deterioration of production efficiency caused by variation of required processing times among the models. Properness of a production sequence depends on part delivery planning also, because it may be impossible to deliver a required part to its destination by the starting time of the process which requires the part. For this reason, integration of sequencing and part delivery planning has been discussed. This paper provides an efficient method for solving the integrated planning problem in which the problem is formulated as a 0-1 mixed integer programming and solved using both genetic algorithm and linear programming. The proposed method was applied to some numerical examples and it was possible to find a solution which is almost optimum for a small size problem and a reasonable solution for a large size problem.

The article presents the results of research on the comparison of the variants of the production planning and control on the example of the production department (department 1), active in the production of polyurethane products. The article contains an analysis of literature, which focuses on the presentation of concepts and methods related to the planning and control of production, including the aspect of leveling production. The article presents the current state of the production planning and control in the analyzed production department. Three concepts of the planning and control system were presented and compared based on accepted criteria. The tests were carried out using a simulation experiment. Simulation results were presented and changes for the department were proposed.

Purpose
In accordance with Bagozzi’s self-regulation theory, the aim of this paper is to explore the enablers and inhibitors of continuance intention from the perspective of bullet curtain, a new form of commentary on online video websites.
Design/methodology/approach
A total of 350 questionnaires were collected for the final analysis (covering 101 questionnaires for the pilot test) from China’s bullet curtain website. To analyze the model, the authors adopted SmartPLS 3.2, a structural equation modeling software.
Findings
As the results suggest, there is a positive correlation between satisfaction and continuance intention and a negative association between social network fatigue and continuance intention. In addition, synchronicity between the comments and video content, a dimension of synchronicity proposed in this study, improves the satisfaction. Furthermore, information overload significantly intensify social network fatigue.
Practical implications
The results help bullet curtain providers offer better interactive environment and improve websites’ functions to stimulate users.
Originality/value
By combining positive effect and negative effect of commentary, this study investigates Bagozzi’s theory in a context of bullet curtain. Besides, combinations of these factors help to gain insights in how the bullet curtain works in online video websites. These offer useful guidelines for managers to optimize a better system.

The aim of the article is to analyse the literature from the scope of the health costs for low emissions. Inthe article as the test method will be used to review the theoretical economic models. The added value of thearticle to be critical analysis of these models in connection with the match to the specificity of the conditionsof the Polish economy

We present a GRASP algorithm to solve a problem that involves the sequencing of mixed products in an assembly line. The objective of the problem is to obtain a manufacturing sequence of models that generates a minimum operational cost with a forced interruption of operations and that is regular in production. The implemented GRASP is compared with other procedures using instances of a case study of the Nissan engine manufacturing plant in Barcelona.

We propose a mathematical model to solve an extension to the mixed-model sequencing problem with work overload minimization (MMSP-W) for production lines with serial workstations and parallel homogeneous processors and regularizing the required workload. We performed a computational experience with a case study of the Nissan engine plant in Barcelona.

This book presents a selection of papers from the 2017 World Conference on Information Systems and Technologies (WorldCIST'17), held between the 11st and 13th of April 2017 at Porto Santo Island, Madeira, Portugal. WorldCIST is a global forum for researchers and practitioners to present and discuss recent results and innovations, current trends, professional experiences and challenges involved in modern Information Systems and Technologies research, together with technological developments and applications.
The main topics covered are: Information and Knowledge Management; Organizational Models and Information Systems; Software and Systems Modeling; Software Systems, Architectures, Applications and Tools; Multimedia Systems and Applications; Computer Networks, Mobility and Pervasive Systems; Intelligent and Decision Support Systems; Big Data Analytics and Applications; Human–Computer Interaction; Ethics, Computers & Security; Health Informatics; Information Technologies in Education; and Information Technologies in Radiocommunications.

Mixed-model assembly lines (MMALs) are a type of production lines where a variety of product models similar to product characteristics are assembled in a just-in-time production system. Usually, MMAL consists of a number of stations linked by a conveyor belt and each station has a work zone limited by upstream and downstream boundaries. To avoid improper interference between operators in the adjacent stations and excess of machine moving range, operators are forced to complete their operations within their predetermined work zone. There is a set of criteria on which to judge sequences of product models in terms of the effective utilisation of these lines. In this paper, the sequence of models for minimising the total unfinished work within their work zone is discussed. A novel imperialist competitive algorithm (ICA) is developed for solving this problem in small-, medium- and large-scale problems. The solutions obtained via ICA are compared against solutions obtained via B&B, a heuristic procedure, GRASP and BDP-2 in small problems, and also against a proposed genetic algorithm and a simulated annealing in small, medium and large problems. Experimental results show that this algorithm provides reasonably good solutions with low computational costs.

Mixed-model assembly lines present two issues due to differences in processing times from product types; these issues are the work overload or unfinished work and the useless time or unproductive time. Within this context, we present, in this paper, a new mathematical model for the mixed-model sequencing problem. This model minimizes the costs by lost production and idle productive time. The model also allows processors carry out their workload with a factor activity greater than the normal, in order to reduce the work overload if it is necessary. Obviously it is also considered to provide economic compensation to workers based on their level of activation. Finally, the model is evaluated by a computational experience linked to a real case from the automotive industry.

Now-a-days shorter product life cycles and increased demands for customization make it difficult to produce some products on traditional production lines. Often the best that can be done is to produce them in batch flow systems that have been improved through the incorporation of line flow principles. This is one-piece flow manufacturing. Traditional cells with irregular material flows are replaced by U-shaped production lines within which flow is regular and paced by a cycle time and between which flow is controlled by pull signals. This tutorial examines the research literature on one-piece flow manufacturing. It begins with the decisions rules that determine when one-piece flow is appropriate. Next the unique elements of one-piece flow (takt time, standard work, flow manufacturing on U-shaped lines, pull production, and jidoka) are reviewed. Then the mathematical models that are used to design one-piece flow systems are examined. Finally areas where more research is needed are discussed.

We propose a new line balancing approach for mixed-model assembly lines with an emphasis on how the assignment of tasks to stations affects the ability to construct daily sequences of jobs (customer orders) that provide stable workloads (in a minute-to-minute sense) on the assembly line, while also achieving reasonable workload balance among the stations. The issue of short-term workload stability has received little attention in the assembly line balancing literature. Such stability allows assembly workers to complete their tasks without being rushed and thereby contributes to product quality. We propose a new objective for assembly line balancing that helps to achieve better short-term workload stability and develop a heuristic solution procedure based on filtered beam search for this new objective. Computational results show that for small problems (which can be solved optimally), this approach provides near optimal solutions, and for larger problems, it provides significantly better results than traditional assembly line balancing methods.

This paper considers the problem of sequencing mixed-model assembly lines (MMALs). Our goal is to determine the sequence of products to minimise work overload. This problem is known as the MMAL sequencing problem with work overload minimisation: we explicitly use task operation times to find the product sequence. This paper is based on an industrial case study of a truck assembly line. In this industrial context, as a reaction to work overloads, operators at the workstations finish their tasks before the product reaches the next workstation, but at the expense of fatigue. Furthermore, there are different types of operators, each with different task responsibilities. The originality of this work is to model this new way of reacting against work overloads, to integrate three operator types in the sequencing model and to apply the developed methods in a real industrial context. To solve this problem, we propose three meta-heuristic procedures: genetic algorithm, simulated annealing and a combination of these two meta-heuristics. All the methods proposed are tested on industrial data and compared to the solutions obtained using a mixed-integer linear programme. The results show that the proposed methods considerably improve the results of the current procedure used in the case study.

DIRECCIÓN Y ORGANIZACIÓN 60 (Diciembre 2016): 57-65.
http://www.revistadyo.com/index.php/dyo/issue/view/45 ·
ABSTRACT: Partiendo del Car Sequencing Problem (CSP), introducimos el concepto de demanda parcial incierta, incorporando Flotas de vehículos especiales en un plan de demanda. Tras establecer las hipótesis de trabajo con Flotas, proponemos un modelo de programación lineal entera mixta (r-CSP) para satisfacer el máximo número de restric-ciones del CSP. Posteriormente, definimos multi-secuencia de producción y algunas métricas para evaluar su robustez. El r-CSP considera diversos escenarios de demanda y funciones para medir el requerimiento excesivo de opciones en programas de produc-ción. Dichas funciones son válidas como objetivo en problemas de optimización y como métricas de robustez de multi-secuencias de producción.

The objective of this chapter is to generalize the simple line-balancing problems handled in the previous chapter. Cases with several products in variable proportions or/and stochastic operation times are analyzed. Numerical solutions based on a triangular density of probability are presented. This part of the chapter ends with an assembly-line-balancing algorithm in the most general case of probability distribution. Three models are proposed to rectify when the actual loads of stations exceed the cycle time. Another section is devoted to the introduction of parallel stations and equipment-selection problems. Some additional constraints, which arise frequently in real-life situations, are examined. Finally, two specific models are introduced: the bucket-brigade assembly line, which is a self-balancing model, and the U-shaped assembly line able to adapt to frequent changes in demand. Numerous numerical examples illustrate and explain the approaches developed in this chapter.

A mixed model production plan may use a schedule that will consecutively produce a small batch of each product model on a production line. However, it may be necessary to deviate from this schedule and produce the models in larger batches at a manufacturing cell in the production line if the manufacturing cell cannot support many setups. A potential problem with large batches is that products that are produced early must wait for its turn at the next step of the production process. When additional operations are performed on products that wait in order to restore its quality, it is imperative to schedule production such that the total time products wait is minimized. We model the problem as scheduling jobs on a single machine with setups and deadlines such that the total waiting time is minimized. We develop a tabu search based heuristic and branch-and-bound algorithm to solve the model. Results show that the heuristic solution to 30-product–3-product model problems is within 3% of its optimal solution.

The push in the automotive industry towards lightweighting to meet new stricter fuel efficiency standards has driven the need to research lightweight material forming. This requires research into forming high strength materials, as well as lower strength lightweight materials that may typically have poor formability characteristics. 7075-T6 aluminum suffers from limited elongation during tensile forming; electrically-assisted forming, which uses direct current to improve formability, is a viable candidate process to improve formability. In past electrical tension testing by various authors, two types of wave forms have been examined: continuous current and square waveforms. For tension it was shown that applying current using square waveforms was able to extend formability beyond what continuous current could produce, due to reducing the overheating in the necking region. This paper examines the effect of a non-decaying and linearly globally decaying saw tooth wave on the formability and flow stress of 7075-T6 aluminum in tension. It is shown that EAM using a sawtooth waveform can result in further elongation than cold forming, with similar elongation to previously-investigated square waves. An existing temperature model is adapted to the saw tooth waveform and used to calculate the change in material properties to find the flow stress using a theoretical strength equation.
Copyright © 2016 by ASME Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature
Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

The purpose of this paper is to describe a new formulation of the mixed-model sequencing model in such a way as to minimize the risk of stopping the conveyor under the circumstances of system variability and to develop an efficient heuristic method for large-scale, mixed-model assembly lines. The proposed method always produced optimal solutions for. randomly constructed small-scale, mixed-model sequencing problems for which the optimal solutions were available through the application of the improved branch and bound method. The method should produce excellent (and almost always optimal) results for actual large-scale, mixedi-model sequencing problems.

This paper describes a model sequencing algorithm for model-mix assembly lines. A new formulation of the sequencing problem is proposed, the objective function of which is to minimize the overall assembly line-length for no operator interference. Lower bounds for the overall line-length are developed.Two types of work station interfaces are considered; ‘closed’, where boundaries cannot be violated, and ‘open’ where defined boundaries do not exist—adjacent operators being allowed to enter each others apparent work areas without causing any interference.A complete factorial experiment was made on five factors to determine their influence on the overall assembly line length. These are, the number of models, the model cycle time deviation, the production demand deviation for each model, the operator time deviation, and the number of stations in the assembly line. The main conclusions of this experiment are discussed and recommendations made for the selection of parameters used in the design of model-mix assembly lines.Also discussed is an approach for accommodating small changes in production demand for existing assembly lines.

Mixed-model assembly occurs when more than one model of the same general product are intermixed on one assembly line. The amount of work required to assemble units can vary from model to model, creating an uneven flow of work along the line. This paper describes a procedure of adapting single-model line balancing techniques to mixed-model schedules. The paper also introduces a sequencing procedure for determining the order in which models are to flow down the line. Because the line balancing and sequencing procedures consider a wide variety of factors, they are applicable to many types of assembly lines.

This paper describes an algorithm for solving optimally, the mixed-model sequencing problem when assembly line stations are balanced for each model. An optimal sequence is obtained with the minimization of the overall assembly line length for zero station idle time. The algorithm incorporates two basic steps. The first involves a search procedure that generates all cycle sequences; i.e. sequences having identical 'start' and 'finish' positions and whose work content can be executed within a defined station length. The second step uses integer programming (IP) to determine the number and combination of the various cycle sequences, such that the production demand is satisfied.