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The problem of sequencing mixed model assembly lines is characterized by a set of parameters whose values are dictated by the actual manufacturing environment. In some cases, it may be desirable to minimize the size of the facility, while in others, the throughput time is paramount. Important design considerations include operator schedules, the product mix, station boundaries, and the launching discipline. The intent of this paper is to present a common mathematical framework in which each possible variant can be addressed. By implication, a solution technique developed for one can be readily adopted for the others.Virtually all of the previous work on mixed model sequencing has focused on the development of heuristics. While these may work well in specific instances, it is difficult to assess their performance without a frame of reference. Moreover, they cannot be universally applied. In this paper, we show that it is possible to obtain optimal solutions at very little cost. The presentation is concerned with sequencing the minimum part set; however, experience indicates that much larger problems can be solved.

Content uploaded by Jonathan Bard

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All content in this area was uploaded by Jonathan Bard on Jun 07, 2016

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... Dar-El (1978) categorizes the MMAL into four categories based on their main characteristics of assembly lines: product transfer system, product mobility on the conveyor, accessibility among adjacent stations, and the attribute of the launching period. An analytic framework for the categorization of Dar-El (1978) is given by Bard et al. (1992). Later, a survey is presented by Boysen et al. (2009), where they define tuple notation for the sequencing problems based on more detailed characteristics of assembly lines, including work overload management, processing time, concurrent work, line layout, and objective in addition to the main characteristics. ...

... Formulating the MMS problem based on the vehicle configurations instead of vehicles is usual (Bolat and Yano, 1992;Bard et al., 1992;Scholl et al., 1998), however, automobile manufacturers offer billions of combinations of options (Pil and Holweg, 2004). When this high level of customization is combined with a short lead time promised to the customers, each vehicle produced in a planning horizon becomes unique. ...

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.

... Cette configuration est plus dense et considérée comme plus flexible que celle en ligne droite (Kucukkoc & Zhang, 2015;Miltenburg, 1998). Ces deux configurations sont illustrées dans la (Bard et al., 1992;Dar-El & Cother, 1975;Sarker & Pan, 2001). De plus raresétudes considèrent simultanément des postes de travail ouverts et fermés (Dar-El, 1978;Kim et al., 1996, par exemple). ...

... For example, Okamura & Yamashina (1979) suggest minimizing the movement of operators in their workstations. Bard et al. (1992) address the objective of minimizing the total makespan, i.e. the time difference between the start and the end of work for a given sequence of products. Later, Bard et al. (1994) focus on minimizing the length of the assembly line. ...

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.

... The introduction of variable takt time groups puts companies in a position to meet these challenges and improves their competitiveness by maintaining high efficiency levels when increasing the number of products on an assembly line and aligning the assembly sequence to customer demand. Dar-El (1978), Bard, Dar-El, and Shtub (1992), Bock, Rosenberg, and van Brackel (2006), and Fattahi and Salehi (2009) distinguish between fixed and variable launching intervals. Simulation studies show the benefit of increased operator efficiency when variable launching is introduced-that is, when the spacing between units (placed on the assembly conveyor) varies. ...

... The optimal line length for achieving zero idle time and utility work is found by defining the extreme operator movement locations as the station's upstream and downstream boundaries. Bard, Dar-El, and Shtub (1992) introduce a mathematical framework to assess the optimal line length or throughput time for the sequencing problem in mixedmodel assembly as a function of the following line parameters: operator schedules, product mix, station boundaries, and launching interval strategy. Bard et al. establish that, in terms of reducing line length and throughput time, variable rate launching yields higher benefits than does fixed rate launching. ...

Natural disasters, pandemics, and political nationalism force companies toward more responsive, flexible, and resilient assembly systems. For manufacturers, adaptability of the assembly process and local production ensure short product lead times even during supply chain disruptions. Yet one downside of regional production is that fixed takt time assembly lines become overburdened, especially when customisation is unlimited. In this context, variable takt time groups (VTGs) are a major competitive lever. We introduce the notion of a workload equilibrium balancing overload and underutilization. This preliminary stage of the assembly line balancing and sequencing problem significantly reduces the planning effort. Moreover, we present a model for minimising (i) the number of VTGs for a given maximum operator drift per unit or (ii) the maximum operator drift per unit for a given number of VTGs. We solve these dynamic problems by developing a heuristic approach: the variable takt time groups algorithm (VTGA). In our analysis of three real-world data sets from two German manufacturers—Fendt and Rolls-Royce Power Systems—we benchmark the VTGA against existing takt times. We find that VTGs result in higher labour efficiency than a fixed takt time and that the VTGs segmentation level plays an important role in reducing operator inefficiencies.

... The efficiency of an MMAL primarily relies on the management of two key decision problems (Bard et al., 1992). As a long-term decision problem, line balancing has a strategic role, as it involves allocating the workload across the workstations in the assembly line (Becker and Scholl, 2006;Boysen et al., 2007;Sivasankaran and Shahabudeen, 2014;Pearce et al., 2019;Yilmazlar et al., 2020). ...

In the automotive industry, some vehicles, failed vehicles, cannot be produced according to the planned schedule due to some reasons such as material shortage, paint failure, etc. These vehicles are pulled out of the sequence, potentially resulting in an increased work overload. On the other hand, the reinsertion of failed vehicles is executed dynamically as suitable positions occur. In case such positions do not occur enough, either the vehicles waiting for reinsertion accumulate or reinsertions are made to worse positions by sacrificing production efficiency. This study proposes a bi-objective two-stage stochastic program and formulation improvements for a mixed-model sequencing problem with stochastic product failures and integrated reinsertion process. Moreover, an evolutionary optimization algorithm, a two-stage local search algorithm, and a hybrid approach are developed. Numerical experiments over a case study show that while the hybrid algorithm better explores the Pareto front representation, the local search algorithm provides more reliable solutions regarding work overload objective. Finally, the results of the dynamic reinsertion simulations show that we can decrease the work overload by ~20\% while significantly decreasing the waiting time of the failed vehicles by considering vehicle failures and integrating the reinsertion process into the mixed-model sequencing problem.

... Set-up times between models are considered negligible. We adopt the Minimum Part Set (MPS) principle (Bard, Darel, & Shtub, 1992). Let Δm be the demand of model m during the planning horizon, and h be the greatest common divisor of Δ0, …, ΔM-1. ...

In the paper two popular techniques able to improve the efficiency of mixed model asynchronous assembly lines are compared: the allocation of buffers within work centers and the optimization of the sequence of models entering the line. The comparison has been performed on a set of benchmark instances related to the MALBP (Mixed-model Assembly Line Balancing Problem). In fact, the buffer allocation problem (BAP) and the sequencing problem (SP) are strictly connected to the MALBP, because balancing decisions, buffer allocation and sequencing optimization have a direct impact on the line throughput. The presented approach allows to simultaneously solve the BAP, the SP and the MALBP for asynchronous unpaced lines. In this way, by an opportune design of experiment, it is possible to compare the different solutions found for the benchmark instances and to quantify the impact of buffer allocation and sequencing optimization on the quality of the solutions.

... For example, Okamura and Yamashina (1979) suggest minimising the movement of operators in their workstations. Bard, Dar-Elj, and Shtub (1992) address the objective of minimising the total makespan, i.e. the time difference between the start and the end of work for a given sequence of products. Bautista and Cano (2011) and introduce MMS formulations that maximise the total work done. ...

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.

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

We come to the core of our book. In our Mixed-Model Assembly Design (MMAD, Sect. 1.4), it is our most important element from Assembly Design for Mixed-Model Assembly (AD for MMA). As in the other chapters, we try to stay close to the language of Operations Management practice in the form of presentation, but further see ourselves as mediators of current findings from scientific work. For motivation, we comment again in the first part on an increased need for mixed-model assembly for current and future production sites, which we had already touched on in the introduction to this book. This is followed by a brief explanation of the classic solution strategies for coping with variants in assemblies with fixed takts, because the disadvantages of these can be eliminated with variable takt. In Sect. 4.4, we explain in detail how variable takt works, with its effect on takt times and the sizing of assembly lines. In Sect. 4.5, we show the numerous advantages of variable takt, using many practical examples. We explain the necessary technical requirements for implementing variable takt in Sect. 4.6 and the possibilities for linking different assembly sections in Sect. 4.7. This chapter concludes with the experiences gained from more than 4 years of practical implementation of variable takt in tractor assembly at Fendt.

Scheduling decisions in mixed-model assembly lines are frequently multi-objective. No work till date has jointly examined the impact of the production sequence in unpaced manual mixed-model assembly lines operated as permutation flow shops concerning a set of objectives broad enough to capture the interests of its customers and suppliers as well as the manufacturer’s interests related to productivity, production flow and human aspects. This work sets up a simulation study based on a real unpaced mixed-model assembly line with seven products to analyse the impact of five different sequence types on objectives from all these interest fields while modelling human learning and deterioration effects explicitly. The results show that considerable trade-offs exist as different sequence types are preferred for the various scheduling objectives. For makespan and mean flow time as widely used productivity– and flow-related objectives, cases of conflicts and complementarity can be found depending on the actual operational conditions in terms of product and volume mix. A strong dilemma emerges between supplier– and human-related objectives favouring different sequence types. Concerning due date based customer-related objectives, the preferred sequence type varies with the operational conditions. The observed trade-offs confirm the multi-objective nature of the scheduling decision.

We consider an assembly line with m stations in series having finite capacity buffers. Blocking occurs when buffers are full. There are M different types of products to be assembled, each with its own processing requirements. There is a production target set for each type. The problem is to operate the line to maximize throughput. We propose heuristic approaches to this problem based on an equivalent maximum flow problem and on critical path techniques.

This research compares seven approaches from the literature to the selection of part types for simultaneous production over the next time horizon. A flexible approach to the selection of part types and the simultaneous determination of their mix ratios so as to balance aggregate machine workloads is presented. Constraints on tool magazine capacity are considered. Simulation studies are conducted on realistic, detailed models of flexible flow systems (FFSs) configured as pooled machines of equal sizes. The simulated settings are constructed to evaluate the impact of such factors as blocking, transportation, buffer utilizations, and fixture requirements and limitations of various types.
One of the goals of this study is to encourage industry to relax, for those FMS types for which the procedure is appropriate, what is essentially an artificial constraint: that tool changing be isolated in time, to a period between batches. For other types of FMSs, batching may be appropriate.
The results indicate that using the flexible approach enables the system to be more highly utilized. It is also observed that the batching approaches tend to require more fixtures of each type than the flexible approach. The system utilizations for the batching approaches seem to be more sensitive to restrictions on the number of fixtures of each type. Further research needs are also discussed.

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.

Many companies are converting their mixed-model multi-level production systems to just-in-time systems. This requires reducing set-up times so that small-lot production can be run. In this paper a theoretical basis is developed for scheduling these systems, and scheduling algorithms and heuristics are developed. The only other known scheduling method (the goal-chasing method), developed and used by Toyota, is shown to be a special case of these heuristics.

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 lines are used to produce many different products without carrying large inventories. The effective utilization of these lines requires that a schedule for assembling the different products be determined. For Just-In-Time (JIT) production systems, which require producing only the necessary products in the necessary quantities at the necessary times, the objective is to keep a constant rate of usage of all parts used by the line. This is called levelling or balancing the schedule. This paper develops a theoretical basis for scheduling these systems, and presents new scheduling algorithms and heuristics.

The general practice in mixed model assembly line balancing is to assign work to stations in a manner that each station has an equal amount of work on a daily or shift basis. This paper shows how a modification to mixed model line balancing algorithms can be used so that the stations are loaded more consistently on a model by model basis as well. In addition, the modification now allows mixed model line balancing to become a plausible tool for batched assembly line processes. The procedure is general in nature and is applicable to most line balancing algorithms.

This paper discusses scheduling algorithms for a certain kind of manufacturing environment, called the “flexible flow line.” Two scheduling problems are considered. “Loading” decides when each part should be loaded into the system. “Mix allocation” selects the daily part mix. The goals are to maximize throughput and reduce WIP. New heuristic algorithms specially suited to solve these problems in the context of a flexible flow line are described. The paper also discusses experience with the use of an experimental implementation of these algorithms to solve such problems arising in a real production line.

The paper develops a comprehensive classification of mixed-model assembly lines from which four categories of model sequencing are derived. Each category aims at satisfying one or both of two objective criteria, the one minimizing the overall line length, and the other minimizing the thruput time. Approaches for solving the sequencing problem in each category are presented. The paper suggests a design strategy that can be followed by designers of mixed-model assembly lines. Specific topics requiring further research are also defined.

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.