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Procedimientos heurísticos y exactos para la secuenciación en sistemas productivos de unidades homogéneas (contexto JIT)
Abstract
Las líneas de fabricación de productos mixtos, muy frecuentes en los entornos JIT (Just-in-Time) y DS (Douki Seisan), permiten tratar diversas variantes de uno o más productos. Esta flexibilidad condiciona el orden en que se han de tratar las unidades, al que llamaremos secuencia, para conseguir una reducción drástica de inventarios intermedios y para aprovechar al máximo el tiempo destinado a la fabricación.
En estos entornos podemos encontrar dos categorías de objetivos básicos: (A) Reducir el sobreesfuerzo o el trabajo perdido y (B) Reducir al mínimo los niveles de inventario.
También se distinguen en este contexto tres tipos de problemas de secuencias:
(1) Mixed-Model Sequencing Problem (MMSP): Secuencias que implican completar el máximo trabajo requerido por el programa de producción
(2) Car sequencing problem (CSP): Secuencias condicionadas por la limitación sobre la frecuencia con que pueden aparecer en éstas algunas opciones especiales.
(3) Level Scheduling (LS): Secuencias que implican trabajar con unas tasas de producción y de consumo de materiales lo más regulares a lo largo del tiempo.
La presente tesis se enmarca en la categoría B de objetivos y en la tipología 3 de problemas, y está estructurada en 7 capítulos.
- Tras una breve introducción a la planificación y programación de operaciones, en §1 se establece un marco general sobre la secuenciación de unidades de productos mixtos en contexto JIT.
- En §2 se formula un modelo general de secuenciación de productos con un solo nivel de componentes en la lista de materiales.
- Los criterios de valoración de dichas secuencias se establecen en §3, donde se propone una taxonomía de modelos, en función del objetivo, que permite clasificar los modelos presentes en la literatura.
- En §4 se explica el método Goal chasing, empleado por Toyota y propuesto por Monden, para resolver el problema ORV (Output Rate Variation).
- En el capítulo §5 se mejora el método Goal chasing con una drástica reducción de los tiempos de computación (usando la matriz de afinidad secuencial) y con la propuesta de 7 procedimientos heurísticos, cuyas eficiencias se contrastan mediante dos experiencia computacionales.
- El capítulo §6 está dedicado a la descripción y formalización de un procedimiento exacto basado en la programación dinámica, BDP (Bounded Dynamic Programming), para resolver el problema ORV. Aquí también se realizan dos experiencias computacionales que permiten estudiar el comportamiento de la BDP en función de sus parámetros algorítmicos.
- El capítulo §7 se centra en nuevas extensiones a los problemas de secuencias en contexto JIT. Se proponen modelos y procedimientos: (1) incorporando al problema ORV las restricciones del CSP relativas a la frecuencia de aparición de opciones especiales en la secuencia, (2) ponderando la regularidad en el consumo de componentes, (3) regularizando la producción y el consumo de componentes en sistemas con múltiples etapas productivas (caso multinivel), y (4) unificando las extensiones anteriores a través de la matriz de afinidad secuencial.
- La tesis finaliza con la síntesis y las conclusiones.
... This procedure combines features of dynamic programming with features of branch and bound algorithms. The principles of BDP have been described by [16] and [17]. Previous work on similar approaches has been done by [10] and [18]. ...
... This procedure combines features of dynamic programming (determination of extreme paths in graphs) with features of branch and bound algorithms. The principles of BDP have been described by [16,17]. The procedure is described below (see details on [10]): π (t, j))) ), and removing those vertices in which their lower bound is greater than Z 0 (known initial solution) • End_stage (): consolidates the most promising vertices in stage t (H vertices as maximum). ...
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.
... Bautista, Companys y Corominas (1996) proponen una clasificación más detallada de los problemas de secuenciación en función de dos aspectos: el objetivo al que está enfocada la regularización (productos o recursos) y el medio para definir la regularidad. Como ya indicábamos más arriba, esta problemática ha sido tratada desde hace algunas décadas, desde los trabajos pioneros de Kilbridge (1964), Thomopoulus (1867), Dar-El (1975) o Okamura (1979); un conjunto de trabajos en los que la regularidad se centra en los productos; Miltenburg (1989), Kubiak y Sethi (1991), Inman y Bulfin (1991), Ding y Cheng (1993a,1993b, Steiner y Yeomans (1993) o Smith, Palaniswami y Krishnamoorthy (1996; o el conjunto de trabajo en los que el objeto de la regularidad es el consumo de componentes: Monden (1987), Miltenburg y Sinnamon (1989), Sumichrast y Rusell (1990), Bautista (1993), Aigbedoy y Monden, Y. (1997) , Poler, et. al. (1999) , Xiaobo et. ...
... Para la resolución del problema se han propuesto diversas heurísticas: Miltenburg y Sinnamon (1989), Bautista (1993), Bautista, Companys y Corominas (1996b) y Duplaga, Hahn y Hur (1996), entre otros; así como métodos exactos: Bautista (1993) y Bautista, Companys y Corominas (1996b). ...
Se propone una generalización de los algoritmos GRASP (Greedy Randomized Adaptative Search Procedure). Se realiza una aplicación al problema de secuenciación de productos mixtos en una línea de montaje para regularizar el consumo de componentes ORVP (Output Rate Variation Problem). Mediante una experiencia computacional se analiza la eficacia de la propuesta con distintos valores de los parámetros asociados al algoritmo y se comparan los resultados con los ofrecidos por otros procedimientos heurísticos y exactos.
RESUMEN: El problema de secuenciación de unidades mixtas en una única línea de producción con el objetivo de atenuar las variaciones de las tasas de consumo y/o utilización de recursos (componentes, equipos y personal) ha recibido atención creciente durante los últimos años. En el presente trabajo se considera la variante del problema que denominamos CORV (Constrained Output Rate Variation) comparando los resultados obtenidos mediante dos procedimientos: Programación por restricciones (CP) y Programación Dinámica Acotada (BDP).
Palabras clave : Constraint Programming, Bounded Dynamic Programming, Líneas de producción, JIT, CORV.
El análisis de un Sistema Productivo de Fabricación de Automóviles lleva a considerar la Secuenciación para la Línea de Montaje como un proceso eminentemente Dinámico. De un almacén posterior a la Etapa de Pintado se extraen una a una las diferentes unidades que van a ser montadas. La Regularidad en la aparición de opciones y el cumplimiento de las Restricciones son al igual que en el planteamiento Estático del problema, los principales objetivos perseguidos. El carácter dinámico viene dado por la disponibilidad variable de los productos a secuenciar. Se proponen en primer lugar diferentes criterios de valoración para un modelo que considera el antedicho problema Dinámico. Además se propone un método heurístico paramétrico para la resolución práctica del problema.
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.
Sequencing units on an assembly line in order to obtain a regular requirement of resources is a problem that can be modelled in a variety of ways. One of the most popular is known as the Monden problem, and the heuristic proposed to obtain a 'satisfactory' solution is called 'goal-chasing' method. In the paper the myopic behaviour of this heuristic is shown, and some improvements are proposed. An exact procedure, based on BDP, is also proposed. By relaxing the assumptions, the BDP procedure becomes a new, powerful heuristic. A sample of computational results is included.
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.
Resumen: Se presenta un procedimiento de propósito general para resolver problemas de optimización combinatoria bajo un esquema de programación dinámica con uso de cotas para reducir el espacio de estados en la exploración de soluciones.
Abstract: We present a general-purpose method for solving combinatorial optimization problems under a scheme of dynamic programming with the use of bounds to reduce the state space that configures solutions.
The system we present is an application of the optimum programming methodology of modular unities for the production line in computer assisted planning and scheduling: ARTEMISA.
We provide a new formulation and solution procedure to sequence a mixed model just-in-time (JIT) assembly system. Mixed model JIT assembly systems are a fundamental part of the well-known "Toyota Production System." The underlying idea in sequencing these systems is to maintain a constant usage rate of all parts on the line. We give a polynomial algorithm to determine the optimal sequence for an objective function that is mathematically different, but intuitively similar to the objective functions of previous researchers. Furthermore, a computational study indicates that the new algorithm is robust in that its sequences are as good as those generated by other algorithms when evaluated with respect to traditional objectives, but are found 200 times faster.
This note formulates an assignment problem for obtaining optimal level schedules for mixed-model assembly lines in JIT production systems. The problem was formulated as a quadratic integer programming problem in a recent paper by J. Miltenburg [ibid. 35, No.2, 192-207 (1989; Zbl 0666.90040)] where, however, only enumerative algorithms and heuristics were proposed for its solution. Our assignment formulation can also be extended to more general objective functions than the one used by Miltenburg.
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.