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Mixed-Model Sequencing to Minimize Utility Work and the Risk of Conveyor Stoppage
Abstract
This paper investigates the problem of sequencing N products on an assembly line with two objectives: minimizing (1) the risk of conveyor stoppage and (2) the total utility work. For a single station with arbitrary processing times, this problem is proved NP-hard in the strong sense for each of the two objectives. For a single station with two product types, each of which has a constant processing time, a sequence minimizing both objectives can be found in O(log N) computation time.
... The MMS problem is NP-hard as the number of sequences grows exponentially with the number of jobs to be produced (Tsai, 1995). In addition, the sequences must be produced within a fixed cutoff time, e. g. 60 or 300 seconds (Boysen et al., 2011). ...
... Mixed model assembly lines have been studied for more than half a century (Thomopoulos, 1967) and the MMS problem has been shown to be NP-hard (Tsai, 1995). 1 ...
... As scheduling problems like the mixed model sequencing (MMS) problem are NPhard, researchers propose metaheuristics to provide solutions in a feasible time (Tsai, 1995;Boysen et al., 2009b). These approaches strongly depend on the initial solution, which is optimized by methods such as tabu search, local search, or simulated annealing. ...
Manufacturing fundamentally changed when, in the late 1980s, growing demand for product variants led to the manufacturing paradigm of mass customization. The goal was to develop products that had so much variety and customizability that nearly everyone could find a product that matched his or her requirements. Despite this development, low production costs remained an important factor. Advancements such as mixed model assembly lines in the automotive industry became useful tools for producing multiple car variants while keeping costs low. However, such systems must be well-defined and operated to handle the high number of variants and increasingly complex production processes.
This thesis presents a new machine learning-based approach to coping with product variety in real-world automotive scheduling problems. As the solution quality in scheduling is affected by the limited computation time, the idea of the presented method is to use reinforcement learning to train a scheduling policy before production. The real problem instance with real parameters is solved on production day by applying the trained scheduling policy.
The results of this study indicate that the presented method can lead to improved solution qualities, lower computation times and better incorporation of real-world characteristics. The study is structured into five chapters. In the first chapter, the motivation, basic concepts and thesis structure are introduced. Each of the following chapters II to IV presents an individual application of the developed method to one of three types of sequencing problems. In chapter V the results are summarized, implications are given, and paths for future research are presented.
... Tsai [8] extends the problem considering the displacement time the worker needs for going from one finished unit to the next. The author also establishes two objectives: 1) to minimize total worker displacement and 2) to minimize the unfinished work in the station. ...
... 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. ...
... The constraints (5), (6) and (7) control the jobs, so that they can be started only when the work is inside the station, whether the previous work has been completed or it has left the station unfinished. Non negative and binary restrictions are in (8). The size of the problem increases exponentially with the number of jobs and stations. ...
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.
... Bolat y Yano [ 4] extienden el trabajo anterior proponiendo tres métodos de resolución: (1) el primero determina un esquema regenerativo (la situación del operario al inicio y final del esquema es la misma) que se replica, para construir la solución; (2) el segundo es un algoritmo greedy que procura, paso a paso, evitar la trabajo perdido (sobrecarga) inevitable, combinando unidades; y (3) el tercer algoritmo, también greedy, intenta reducir el tiempo ocioso al evitar mientras es posible, asignar unidades con poca carga de trabajo. Tsai [5] extiende los trabajos anteriores al tener en consideración los tiempos de desplazamiento del operario, y establece dos objetivos: minimiza r el desplazamiento máximo del trabajador a partir del origen de la estación y minimizar el trabajo no completado. El procedimiento propuesto tiene una complejidad computacional O(logN) y ofrece la solución óptima en determinadas condiciones. ...
... En el presente texto nos centraremos en las aportaciones de Yano y Rachamadugu [3], de Bolat y Yano [2,4] y Tsai [5], extendiéndonos sobre ellas. Nuestras propuestas contemplan procedimientos para varios productos y varias estaciones . ...
... La mayor dificultad es el gran número de soluciones posibles y el esfuerzo computacional para evaluarlas. El problema es NP-hard [3], [5] o [6]. ...
Resumen—Se consideran una variante del problema de secuenciación de unidades en líneas de montaje en contexto JIT. El criterio es la minimización de la sobrecarga. Se proponen algunas heurísticas que buscan el orden en que se introducirán los diferentes variantes de un mismo producto en una estación. Se toma de la literatura un procedimiento para varias estaciones para probar las heurísticas greedy propuestas.
... To ease computation, Bolat and Yano (1992b) also introduce a surrogate objective for utility work. Tsai (1995) investigates the problem of sequencing two types of products on an assembly line with two objectives: minimizing (1) the risk of conveyor stoppage and (2) the total utility work. He developed an optimal algorithm minimizing both objectives for a single station with two product types, each of which has a constant processing time. ...
... Bolat (1997) compares a single pass deterministic (SPD) heuristic with the Yano and Rachamadugu (1991) algorithm. The problem of minimizing the total utility work in cases of multiple stations based on the Tsai's (1995) optimal algorithm is not studied further and compared also. ...
... First, we solve the sequencing problem for minimizing the total utility work at each station independent of each other. Here we apply Tsai's (1995) algorithm, which gives an optimal solution for a single station problem and get the minimum utility work for each station. Next, we add up the minimum utility work of each station and the sum is the lower bound on the total utility work for our problem. ...
This paper presents a fast sequencing algorithm for a mixed model assembly line with multiple workstations which minimize the total utility work and idle time. We compare the proposed algorithms with another heuristic, the Tsai-based heuristic, for a sequencing problem that minimizes the total utility works. Numerical experiments are used to evaluate the performance and effectiveness of the proposed algorithm. The Tsai-based heuristic performs best in terms of utility work, but the fast sequencing algorithm performs well for both utility work and idle time. However, the computational complexity of the fast sequencing algorithm is O (KN) while the Tsai-based algorithm is O (KNlogN). Actual computational time of the fast sequencing heuristic is 2-6 times faster than that of the Tsai-based heuristic.
... MMS, a problem known for its NP-hard nature (Tsai, 1995), becomes significantly more challenging to solve when faced with stochastic product (car) failures and integrated reinsertion process in a multiobjective setting. Therefore, it is essential to develop effective heuristic methods to tackle large-scale problems. ...
... We note that the traditional MMS problem is NP-hard Tsai (1995), hence, the problem proposed in this study is NP-hard since it is a more complicated version of the traditional MMS. Considering the stochastic failure of vehicles poses a significant complexity increase in the model. ...
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.
... With the advancement of computer technology, more and more heuristic algorithms and simulation software are gradually used in the improvement methods of production lines. Tisa, Li-Hui proposed that the balancing problem of an assembly line is a multi-objective optimization problem [9] . Hujunyi et al. added a heuristic task set filtering mechanism to the ant colony algorithm and proved through a case study that the algorithm has significant effects on the optimization of production lines [3] . ...
... Tab.3 Comparison of Effects of m=5,6,7,8,9 ...
... For example [10] incorporated into the CSP conditions from the level scheduling and [11] incorporated conditions such as the minimization of the total utility work and idle costs into the mixed model assembly line (MMAL). Focusing on mixed model sequencing [12] incorporated the minimization of the utility work into the mixed model sequencing problem (MMSP). There also exist more recent works: for example [13] and [14] proposed incorporating conditions from the PRV into the MMSP-W. ...
... Constraint (11) requires the assignment variables to be binary. Constraint (12) fixes the start of operations. Constraints (13) and (14) are those that incorporate the preservation property of the production mix desired in the JIT (Toyota) and Douki Seisan (Nissan) philosophies. ...
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.
... In this paper an extension of a procedure in [3] is proposed, which considers not only two different jobs/products (basic product and special product, differentiable by their poor and rich work content respectively), but also multiple products. Other literature related with the problem is [5], [6], [7] and recently [8]. Inspired on procedures from [4] and [9], in [10] constructive procedures in proposed, which consider multiple products and multiple stations. ...
... To elucidate the reader on the work overload problem, a single station illustrative example is shown. Four products are considered: A, B, C, and D, with the following processing times (0.82, 0.94, 1.19, 1.15), and demands (3,5,7,1). Station length L=1.2. Processing times and station length are expressed in cycle time units (c=1). ...
There are different approaches for the mixed-model assembly-lines sequencing problem. In this paper the goal of minimizing work overload is treated. This approach considers the existence of time windows in each work station. Different versions of a product are considered to be assembled in the line (e.g. car industry), which require different processing time according to the work required in each work station. Long sequences of rich-work products can lead to produce work overload when stations cannot fulfil all the assigned tasks. Since solve this problem optimally is difficult, we test local search and a hyper-heuristic procedure. A computational experiment is used to detect the performance of the proposed procedures.
... Ceci pourrait constituer un frein à l'optimisation et à la mise en place industrielle si de telles données sont difficiles à collecter. (Bautista et Cano, 2008) x x (Bautista et Cano, 2011) x x x Interruption conditionnée des opérations suite à un retard (Bolat, 1997) x x Temps de retour à la limite sup du poste non négligeables Bolat et Yano (1992) x x x Un poste de travail et deux modèles (Bolat et Yano, 1992b) x x x (Bolat et al., 1994) x x x Minimise les coûts de préparation en plus des retards x (Sarker et Pan, 1998 x x x Postes de travail ouverts (Scholl, 1999) x x x (Scholl et al., 1998) x x (Sumichrast et al., 2000) x x (Tavakkoli-Moghaddam et Rahimi-Vahed, 2006) x x Multi-objectifs (temps de préparation, retards, lissage consommation des pièces) (Thomopoulos, 1970) x x x x Postes de travail ouverts (Tsai, 1995) x x x Un seul poste de travail (Wester et Kilbridge, 1964) x x x Un seul poste de travail (Xiaobo et Ohno, 1994) x x La ligne est stoppée dès qu'un retard apparaît. (Xiaobo et Ohno, 1997) x x x La ligne est stoppée dès qu'un retard apparaît. ...
... Il est donc intéressant d'étudier les performances de méthodes exactes sur les instances réelles de notre cas d'étude. Le problème de séquencement des véhicules en prenant en compte les temps opératoires est prouvé NP-difficile même pour le cas mono-opérateur (Kotani * et al., 2004;Tsai, 1995;Yano et Rachamadugu, 1991). ...
In this thesis, the problem of sequencing mixed model assembly lines (MMAL) is considered. Our goal is to determine the sequence of products to minimize the work overload. This problem is known as the mixed model assembly line sequencing problem with work overload minimization (MMSP-W). This work is based on an industrial case study of a truck assembly line.Two approaches can be used to minimize the work overload: the use of task operation times or the respect of sequencing rules. Most of the earlier works applied in car industry use the latter approach. The originality of this work is to employ the task operation times for the generation of the product sequence in a MMAL.The literature review has highlighted two main gaps in previous works: most of the papers consider a single type of operators, and propose heuristics or metaheuristics to solve the problem. The originality of this work is to test exact methods for industrial case instances and to model three different types of operators.Two exact methods are developed: the mixed integer linear programming and dynamic programming. The models are tested on industrial case study instances. An experimental study is developed for both approaches in order to understand the complexity factors.Moreover, the problem is treated by two approximate methods: a heuristic based on dynamic programming and metaheuristics (genetic algorithm, simulated annealing and a hybrid method based on both genetic algorithm and simulated annealing). All approaches are tested on academic instances and on real data from the industrial case study.
... Considerando las trabajos anteriores como punto de partida, en el presente texto nos centraremos en las aportaciones de Yano y Rachamadugu [4], de Bolat y Yano [1,2] y Tsai [3], extendiéndonos sobre ellas. Nuestra propuesta incluye, para el caso de dos tipos de producto, dos familias de algoritmos para una sola estación y cuatro procedimientos para el caso de múltiples estaciones; y, para el caso de múltiples productos, se proponen extensiones de los algoritmos para dos tipos de producto. ...
... (2) si hay unidades especiales pendientes y hay unidades básicas pendientes, se secuencia una unidad básica si ésta no genera tiempo improductivo, o una unidad especial si aquella genera tiempo improductivo. (3) si no hay unidades básicas pendientes y hay unidades especiales pendientes, se secuencia una unidad especial. ...
... In this paper an extension of a procedure in [3] is proposed, which considers not only two different jobs/products (basic product and special product, differentiable by their poor and rich work content respectively), but also multiple products. Other literature related with the problem is [5], [6], [7] and recently [8]. ...
... To elucidate the reader on the work overload problem, a single station illustrative example is shown. Four products are considered: A, B, C, and D, with the following processing times (0.82, 0.94, 1.19, 1.15), and demands (3,5,7,1). Station length L=1.2. Processing times and station length are expressed in cycle time units (c=1). ...
There are different approaches for the mixed model sequencing problem on assembly lines. In this paper the goal of minimizing work overload is treated. Since solve this problem optimally is difficult, we test c onstructive procedures, local search and a new hiperheuristic procedure.
... Since MMSP with deterministic task times has been proven to be NP-hard (Tsai, 1995), the problem with interval task times is also NP-hard. In this paper, a discrete cuckoo search particle swarm optimization (DCSPSO) algorithm is proposed to solve MMSP with interval task times. ...
This paper addresses a sequencing problem with uncertain task times in mixed model assembly lines. In this problem, task times are not known exactly but are given by intervals of their possible values. A mixed integer non-linear programming model is developed to minimize the utility work time, which is converted into a mixed integer linear programming (MILP) model to deal with small-sized instances optimally. Due to the NP-hardness of the problem, a discrete cuckoo search particle swarm optimization (DCSPSO) algorithm is developed. In the proposed algorithm, a particle position is updated by crossover and mutation operators in the discrete domain and discrete Levy flight is used to improve the solution quality further. Numerical experiments are conducted on the designed instances. The results indicate that the DCSPSO algorithm outperforms the exact method and the other three meta-heuristic algorithms. A case study of engine cylinder heads sequencing problem shows the proposed approach can obtain multiple solutions for decision-makers to choose according to the actual situation.
... 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. Fattahi and Salehi (2009) minimize the total idle time in addition to utility work. ...
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.
... Considering practically relevant instance sizes and the nature of an online problem, an exact procedure which guarantees a solution cannot be found in a reasonable decision period (Gujjula et al., 2011). Tsai (1995) shows that the sequencing problem for mixed-model assembly lines to minimize overload situations is NP-hard. Table 1 contains a summary of the articles mentioned above. ...
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.
... Inefficient implementation of MMALSP leads to reduction production efficiency and line stoppage due to large variations in assembly lines for different types of products. In fact, when different types of products are produced in a mixed-model assembly line and the assembly time is significantly different between them, production efficiency is reduced due to consecutive line stops and variations, which eventually leads to failure in the implementation of JIT system [2,3]. Therefore, the use of bypass sub-line that performs a proportion of assembly activities reduces the variations. ...
Nowadays, mixed-model assembly lines (MMALs) are extensively applied to manufacture different products with no need for the changeover of the whole lines to satisfy the diversified preferences of consumers. In some assembly lines, there is a considerable variation in cycle times, which reduces production efficiency. However, a bypass sub-line that undertakes a portion of product assembly operations reduces the variation in the assembly times. In the present paper, the following three objective functions are considered simultaneously: (1) minimizing the variation in the actual and required production capacity, (2) minimizing total utility work, and (3) minimizing total variation in production rate. The formulated sequencing problem is solved by two different Multi-Objective Evolutionary Algorithm (MOEAs) including the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO). Then, some numerical examples are conducted, and the efficiency of the two proposed algorithms is measured based on some comparison metric.
... In the ideal case, there is a degree of freedom to optimise the sequence of the production by minimising the risk of conveyor stoppage and maximising the total utility/productivity of the production line. The proposed MPC has been developed for the same purpose, so it can maximise the benefits of the sequencing as it will be demonstrated in the case study (in Section 6) where the sequencing algorithm proposed in [37] was incorporated into the proposed framework. Based on this information, the model calculates which elementary activities should be performed at a given station. ...
The sequencing and line balancing of manual mixed-model assembly lines are challenging tasks due to the complexity and uncertainty of operator activities. The control of cycle time and the sequencing of production can mitigate the losses due to non-optimal line balancing in the case of open-station production where the operators can work ahead of schedule and try to reduce their backlog. The objective of this paper is to provide a cycle time control algorithm that can improve the efficiency of assembly lines in such situations based on a specially mixed sequencing strategy. To handle the uncertainty of activity times, a fuzzy model-based solution has been developed. As the production process is modular, the fuzzy sets represent the uncertainty of the elementary activity times related to the processing of the modules. The optimistic and pessimistic estimates of the completion of activity times extracted from the fuzzy model are incorporated into a model predictive control algorithm to ensure the constrained optimization of the cycle time. The applicability of the proposed method is demonstrated based on a wire-harness manufacturing process with a paced conveyor, but the proposed algorithm can handle continuous conveyors as well. The results confirm that the application of the proposed algorithm is widely applicable in cases where a production line of a supply chain is not well balanced and the activity times are uncertain.
... Worker movement diagrams are widely used to model the work of operators at conveyor belts [7]. Such models can be used to reduce the risk of conveyor stoppage [8] and optimize production sequence [9], since the optimal distribution of the products can also reduce the probability of critical backlogs [10]. * Correspondence: research@abonyilab.com ...
Human resources are still utilized in many manufacturing systems, so the development of these processes should also focus on the performance of the operators. The optimization of production systems requires accurate and reliable models. Due to the complexity and uncertainty of the human behavior, the modeling of the operators is a challenging task. Our goal is to develop a worker movement diagram based model that considers the stochastic nature of paced open conveyors. The problem is challenging as the simulator has to handle the open nature of the workstations, which means that the operators can work ahead or try to work off their backlog, and due to the increased flexibility of the moving patterns the possible crossings which could lead to the stopping of the conveyor should also be modeled. The risk of such micro-stoppings is calculated by Monte-Carlo simulation. The applicability of the simulator is demonstrated by a well-documented benchmark problem of a wire-harness production process.
... 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.
... In addition to multi-objective studies where utility work is one of the objectives, there are also studies that exclusively focus on utility workers (Tsai, 1995;Kotani et al., 2004;Kim and Jeong, 2007;Giard and Jeunet, 2010;Cevikcan and Durmusoglu, 2011). These studies use both heuristic and meta-heuristic methods. ...
Today’s manufacturing systems are undergoing significant changes in the aspects of planning, production execution, and delivery. It is imperative to stay up-to-date on the latest trends in optimization to efficiently create products for the market.
The Handbook of Research on Applied Optimization Methodologies in Manufacturing Systems is a pivotal reference source including the latest scholarly research on heuristic models for solving manufacturing and supply chain related problems. Featuring exhaustive coverage on a broad range of topics such as assembly ratio, car sequencing, and color constraints, this publication is ideally designed for practitioners seeking new comprehensive models for problem solving in manufacturing and supply chain management.
... A slightly different approach is taken when the operator moves along with the conveyor. For example, in Tsai (1995), the spacing of products on the conveyor is evaluated to minimise the risk of conveyor stoppage and the total utility work. The NP-hard algorithm, derived for a single station, can be used as a lower bound for analysis of multiple-station problems. ...
... A slightly different approach is taken when the operator moves along with the conveyor. For example, in Tsai (1995), the spacing of products on the conveyor is evaluated to minimise the risk of conveyor stoppage and the total utility work. The NP-hard algorithm, derived for a single station, can be used as a lower bound for analysis of multiple-station problems. ...
In line-cell reconfiguration, cycle time is adjusted whenever operators involve multiple tasks. One crucial factor frequently overlooked is changes in situational awareness, which relates to the comprehension on the task importance of operators. This paper presents a line-cell reconfiguration that considers changes in situational awareness. A mathematical model is developed and tested via simulation of a case study facility. The simulation model seeks to find the best operator assignment and obtain the number of cells needed to achieve the objective. The model also determines whether it performs better than the existing assembly line conveyor system. The cells marginally perform better than the original system but are subjected to constraints in the operator assignment method. Despite the close proximity of operators, the cycle time expansion of individual tasks contributes to the poor performance of the cells. This paper is the first to examine changes in situational awareness in the context of manufacturing.
... The utility work is defined as the uncompleted amount of work within the given length of workstation. The minimizing the utility works are the most important objective investigated by Kim et al. (2000), Boysen et al. (2009), Hyun et al. (1998), Tsai (1995, Tavakkoli-Moghaddam and Rahimi-Vahed (2006). The balancing and sequencing of the MMAL problem are the independently NP-hard (Gutjahr andNemhauser 1964, Tsai 1995), so the combination of them imposes an additional level of complexity. ...
... In this paper, two objective functions have also been presented. However, for large-sized problem instances, the use of heuristics becomes more appropriate as sequencing problems in MMAL fall into the NP-hard class of combinatorial optimization problems (Tsai, 1995). Hence, this paper introduces a Discrete Particle Swarm Optimization (DPSO) algorithm to solve a JIT sequencing problem. ...
This paper deals with the formulation of a sequencing problem with the dual goals of varying the parts
utilization at different workstations of the assembly line and varying the workload associated with
each workstation; these two objectives are typically inversely correlated with each other, and therefore
the simultaneous optimization of both is challenging. Owing to the NP-hardness of the problem, this
paper introduces a Discrete Particle Swarm Optimization (DPSO) algorithm, a Memetic Algorithm
(MA), a Weighted sum Multi-Objective Genetic Algorithm (MOGAW), and a Non-dominated Sorting
Genetic Algorithm (NSGA-II) to solve a just-in-time sequencing problem where these objectives are to
be optimized simultaneously. The performance of these algorithms is compared against each other on
small, medium, and large problems. According to statistical analysis, experimental results show that
discrete particle swarm optimization outperforms the other algorithms in respect of a comparison
metric.
... 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.
... En Tsai (1995) se extienden los trabajos anteriores al tener en consideración los tiempos de desplazamiento del operario. Uno de los objetivos es minimizar la distancia recorrida por el operario que equivale, en este caso, a minimizar la sobrecarga que la secuencia inflige. ...
... 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.
... 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.
... 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 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 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.
... Additionally, Fattahi and Salehi (2009) incorporated conditions such as the minimization of the total utility work and idle costs into the mixed model assembly line (MMAL). Focusing on mixed model sequencing, Tsai (1995) incorporated the minimization of the utility work into the mixed model sequencing problem (MMSP). There also exist more recent works: for example Bautista, Cano and Alfaro (2012a) and Manavizadeh, Tavakoli, Rabbani et al. (2013) proposed incorporating conditions from the PRV into the MMSP-W. ...
In this article, we propose a hybrid procedure based on bounded dynamic programming (BDP) assisted by linear programming to solve the mixed-model sequencing problem with workload minimization (MMSP-W) 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 the Gurobi solver and previous procedures. MSC: 90C39, 90B35
... Comme la ligne est tractée, l'ordre de passages des produits sera le même pour tous les postes. Le problème est considéré comme NP-difficile ( [23], [19], [18] et [14]). Les observations faites sur les caractéristiques de la solution optimale peuvent permettre de trouver des solutions approchées efficaces. ...
... To contextualize these discursive constructions, I first describe the production system the company had introduced in the early 2000s, based on just in time and total quality management (JIT/TQM). Widely utilized in the automobile industry, lean production is a way of substantially cutting costs by 'producing only the necessary products in the necessary quantities at the necessary times' (Miltenburg, 1989: 192;Thomopoulos, 1967;Tsai, 1995) and is notorious for its effectiveness in intensifying work (Barker, 1993;Delbridge, 1995;Graham, 1994;Sewell, 1998). ...
The paper investigates how diversity informs and is in turn informed by the dynamics of control and resistance. Drawing on an in-depth qualitative case study of CarCo, an automobile factory, I show that diversity is constructed in highly problematic terms, as a synonym of types of workers who fail to meet the productive demands of just-in-time production. Specifically, female, older, and disabled workers are constructed as ‘different’ because they hamper constant productivity gains and the flexible allocation of labour, two cornerstones of lean production. Yet paradoxically, such stigmatized construction of diversity opens up ways for these employees to effectively resist managerial control, as it legitimates their claims not to be fit for certain jobs. In as much as specific socio-demographic groups actually lack needed skills, are expected by management to lack them, or claim themselves to lack them, being ‘different’ becomes a powerful way to resist.
... El motivo fundamental para ello es que, de no respetar la limitación de Tiempo de Ciclo, la Línea podría parar o el trabajo podría no acabarse para un producto determinado [2]. Esta restricción es considerada un objetivo por algunos autores, como el propio Monden o Yano y Rachamadugu [3]. ...
RESUMEN La Secuenciación eslal última de las etapas a realizar en el Proceso de Negocio de Planificación y Programación de Producción en las Empresas de Montaje de Automóviles; al Programa Maestro de Montaje (PMM), que normalmente incluye un Horizonte de 1 o 2 semanas. Establece el orden de paso de los vehículos por la Línea de Montaje, para cada período en los que se divide el Horizonte del PMM. Es una etapa crítica, pues se establece en función de varios factores, como puedan ser: restricciones operativas de Planta (Equilibrado de la Línea de Montaje, cargas de operarios, etc.) o en cuanto al suministro y su regularidad desde algunos Proveedores (Secuenciados y/o Sincronizados). Se da a conocer prácticamente on-line a los Proveedores Secuenciados y/ o Sincronizados, de forma que puedan suministrar a Montaje los materiales exactamente en el orden en que se montarán sobre las carrocerías pintadas. Posterior a la Secuenciación, estaría la supervisión y en su caso modificación, en función de posibles incidencias (tanto de la Planta como de algún Proveedor, etc.). En definitiva la Re-secuenciación a la salida de determinados Almacenes reguladores.
... Hence, the mixed-model approach entails a high complexity, which makes the running time a critical factor for any practical application of a solution method. The minimisation of the utility work at a single station is an NP-hard problem (Tsai 1995) in this context. The same property holds for a different formulation featuring the same objective as in this paper (cf. ...
In this paper, we investigate a dynamic resequencing problem covering realistic properties of a mixed-model assembly line. To this end, we present a mathematical model that addresses dynamically supplied blocking information and viable due dates.We developed two different strategies that use a static resequencing algorithm as a subroutine. One strategy integrates each unblocked order immediately into the planned sequence, whereas the other strategy waits for good positions that do not conflict with the due dates. All algorithms construct guaranteed feasible sequences. Using industrial test data, we show that both strategies perform significantly better than a simple method derived from practice. A replanning procedure that
tries to improve the current planned sequence whenever computing time suffices yields an additional improvement for both
strategies.
... Many studies have been done around improving sequencing in mixed-model assembly lines. Tsai [1995] investigated the sequencing problem with the objective of simultaneously minimizing the risk of conveyor stoppage and total utility work. Fliedner and Boysen [2008] applied a branch and bound method for sequencing to minimize station overloads. ...
The analysis of overload conditions for each cell and the assembly operator is carried out based on micro modeling of operator movement patterns for the actual sequence of vehicles entering trim and final assembly. To achieve this, the system integrates the broadcast signal of the vehicle VIN number as the vehicles are released to final assembly with detailed information on the work elements from the direct labor management system and the workcell layout from the e-workcell system. This system gives advance warning to assembly line management and work group leaders of potential operator overload and/or interference, allowing time to dispatch auxiliary workers and eliminate potential line stoppages.
... En Tsai (1995) se extienden los trabajos anteriores al tener en consideración los tiempos de desplazamiento del operario. Uno de los objetivos es minimizar la distancia recorrida por el operario que equivale, en este caso, a minimizar la sobrecarga que la secuencia inflige. ...
RESUMEN Una variante del problema de secuenciación de productos mixtos en una línea de montaje es la propuesta por Yano y Rachamadugu. En ella se considera la existencia de ventanas temporales en las estaciones de trabajo y el concepto de trabajo perdido (suma de las diferencias entre los instantes reales de compleción de las unidades en las estaciones y sus fechas de finalización comprometidas dependientes del valor de la ventana temporal). En el presente trabajo se propone una serie de procedimientos para resolver el problema, y se comparan con los existentes en la literatura a través de una experiencia computacional.
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
A newly emerging mass-individualisation concept has attracted increasing attention in recent years. However, this concept increases the complexity of manufacturing systems within organisations. In such systems, one of the main challenges is the sequencing problem, especially in dynamic environments where unpredictable events demand new constraints. In this context, the ability to use real-time data to make efficient, quick decisions has become one of the main priorities of managers. In this paper, based on a real-world case from Fiat Powertrain Technologies, we define a dynamic mixed-model assembly line sequencing problem with walking workers. In this context, each worker is assigned to a product for all assembly operations and moves from one station to another. A mathematical model is proposed to minimise production time. Since the problem is NP-hard, a hyper-heuristic is also developed to solve the problem. Moreover, a simulation-optimisation model is developed using FlexSim software to solve a real-world problem in a dynamic environment. Comparison of the results illustrates the effectiveness of using the simulation approach to dynamically solve such problems, especially in real-world cases. Finally, a thorough description of managerial insights is provided to indicate the applicability of the proposed approach.
This study presents a reinforcement learning (RL) approach for the mixed model sequencing (MMS) problem with a minimization of work overload situations. The proposed approach generates the sequence in a constructive way, so that an action denotes the model to be sequenced next. The trained policy quickly creates an initial sequence, which allows us to use the cutoff time to further improve the solution quality with a metaheuristic. Our numerical evaluation based on an existing benchmark dataset shows that our approach is superior to established methods if the demand plan follows its expected distribution from the learning process.
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.
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.
Despite many pioneering efforts and works over the past decades, stochastic events have not been studied extensively in mixed-model assembly lines thus far. For a mixed-model sequencing problem with stochastic processing times, this paper aims to minimise expected total work overload. It also focuses on the most critical workstation of the line. In practice, this assumption is useful when the whole or a big portion of the assembly line is considered as a single station. In order to tackle the problem, a dynamic programming (DP) algorithm as well as two greedy heuristics from the literature is employed. However, it is realised that the DP cannot guarantee the optimal sequence neither for stochastic nor deterministic problems. It is because the calculation of work overload is involved in a recursive procedure that affects the states’ value functions. Therefore, by the use of network representation, the problem is modelled as a shortest path problem and a new heuristic, inspired by Dijkstra’s algorithm is developed to deal with it. Numerical results show that the proposed method outperforms other algorithms strongly. Finally, some discussion is provided about why one should consider stochastic parameters and why the proposed heuristic performs well in this regard.
The concept of Autonomation in the Toyota production system admits workers to stop the conveyor whenever they fail to complete the operations within their work stations in a mixed-model assembly line. Therefore, the conveyor stoppage becomes a crucial criterion in sequencing problems for mixed-model assembly lines in the Toyota production system. In this paper, we consider a goal of minimizing a total conveyor stoppage time. A sequencing problem with this goal is formulated. Several useful properties, such as, the computational complexity of the sequencing problem, necessary and sufficient conditions that a conveyor stoppage occurs, lower and upper bounds of the objective function, and sufficient conditions for the optimality of a solution, are characterized. Based on the properties, a heuristic algorithm is designed. A numerical example is given to illustrate the methodology.
A mixed-model, multi-level production facility operating under a JIT system is controlled by setting a production schedule for the final assembly line. The schedule depends on the goals of the production facility which are: (1) to keep a constant rate of usage of all parts used by the line, (2) to maintain a smooth production load, and (3) to minimize the sequence-dependent setup times (SDST) due to changeovers between different products. This paper presents a Simulated Annealing (SA) algorithm for sequencing the mixed-model final assembly line with three goals. Several test problems are experimented and analyzed. Computational results show that the proposed SA algorithm is efficient in finding near-optimal solutions.
This paper proposes a method to address a mixed-model sequencing problem that currently exists in automobile manufacturing. From the standpoint of supply chain management, we proposed a new sequencing method that aims at: 1) levelling the workloads for each process on an assembly line; 2) maintaining a constant rate of production for all the parts in the production process; 3) meeting delivery dates of distributors when the final products are delivered by specialised shipping vessels. In order to simultaneously satisfy these three goals, a two-stage approach is proposed. First, by dividing the production period into shorter periods, the production volume of each product is determined for each of these shorter periods to maintain a constant rate of parts usage and meet the delivery date to distributors. Next, a production schedule is established for each period to realise smoother production on the assembly line.
To improve the work efficiency of the mixed model assembly line, the products sequencing problem with the skip utility work strategy is addressed, where the idle cost and the utility cost are to be optimized simultaneously. Then, a necessary condition of skip utility work and a lower bound of utility work cost are given. The strong NP-hardness of the problem is proved. Since the problem is strongly NP-hard, a hybrid algorithm based on embeded VNS-EM (variable neighborhood search-electromagnetism-like mechanism) algorithm is developed. To escape from the local optima, the enhanced VNS algorithm is embedded in each iteration of EM. With the aid of the good local search ability of VNS algorithm, the fine neighhood search of the optimum individual can be made and the solution is improved. Simulation results confirm the feasibility and validity of this proposed method.
Medium-term sales and operations as well as medium to short-term production planning in customer order driven production processes are performed using a cascading planning process. A lack of coordination and feedback between different planning phases causes problems with a negative effect on costs in production that originate from unfeasible production programs. Based on a system for the classification of planning restrictions the planning process will be controlled utilizing a newly developed combination of the methods of Linear Programming and Constraint Programming. The result is a formal logic to combine the different planning horizons and the two sets of planning methods.
Nowadays, there are many production systems in which the manufacture of all or part of the production takes place in assembly lines. In addition, the current demand of the market, makes necessary that companies provide a wide range of products with different options. This situation can easily be found in the automobile sector, where different product types, despite belonging to the same family, have different characteristics and require, therefore, different component consumptions and resource use. Indeed, not all vehicles carry the same type of engine, and not all vehicles are equipped with the same components, both indoors and outdoors.
A clear example of this type of assembly lines with mixed products (MMAL, Mixed-Model Assembly Lines), is found in the engine lines or in assembly lines, where different components (seats, steering wheel and pedals) are incorporated into the body of the vehicle. This variety of the product range, leads to the need for the current production or assembly lines are flexible and , therefore, the lines can adapt to the diversity of product types that are manufactured in them, without incurring excessive costs.
Thus, with the aim of making flexible and reducing costs by labor, handling and storage, the mixed product lines have two basic problems: (1) the balancing assembly line and (2) the sequencing of units of mixed-products.
Among the latter problems, we find the study object of this thesis, known as MMSP (Mixed-Model Sequencing Problem) in the literature. This problem consist of establishing a manufacturing order of the products with the aim of: minimising the product and component stock levels; (2) minimising the work overload or the uncompleted work; or (3) minimising the sub-sequence number with special options.
Specifically, in this thesis we study the mixed-model sequencing problem, in assembly lines, with the minimisation of the uncompleted work or work overload (MMSP-W: Mixed-Model Sequencing Problem with Workload Minimisation). Indeed, with the focus of addressing the literature problem, not only to the improvement of productivity, but also to the improvement of the working conditions of the operators of the line, we study four variants, in which we incorporate aspects of the real-life situations that occur in the current production systems.
In the first studied variant, in addition to consider workstations arranged in series and, therefore, interlinked, we consider that in a same workstation may coincide different homogeneous processors, as well as the possibility that all stations can hold all product units a time longer than the cycle time, in order to complete the required work. This variant will result in two equivalent mathematical models, whose objectives will be based on the optimization of the work overload or the completed work and which will serve as the starting point of the following studied variants.
The second variant, incorporates concepts from the management ideology JIT (Just In Time), since, in addition to minimise the work overload or maximise the completed work, this extension considers the convenience of obtaining product sequences that distribute evenly over time the required work, the completed work or the work overload corresponding to all work stations in a workday. This study will give rise to new multi and mono-objectives mathematical models, whose purpose will be to minimize the workload avoiding undesirable excess efforts for human resources.
In the third variant, are considered variable processing times of operations according to the rhythm of activity of operators throughout their workday. Thus, based on the idea that the activity of operators is not maintained constant along the time, different profiles for the factor of activity or work pace are defined. These profiles will force an increase of the working speed of the operators, at certain times of the workday, thus completing more required work and, therefore, reducing the overall work overload.
At last, taking into account, also, the presence of human resources on workstations, we consider the working conditions agreed between the company and trade unions with respect to saturation or level of employment of the workers of the line. Thus, we formulate new mathematical models for the MMSP-W, which, in addition to minimise the amount of lost work, respect the maximum values, laid down by collective agreements, in terms of average and maximum saturation of workstation processors.
Finally, note that all studied extensions for the MMSP-W are evaluated through a case study linked to the plant of engines from Nissan in Barcelona. In this way, we can compare the results obtained with the reference models, with those obtained with the proposed models throughout this thesis, from a computational, economic, social and legal point of view.
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