Question

In a factory the most important operation is painting. At the painting site there are always two workers working at the same time, although due to the physical setup, they cannot help each other. Arrivals at the painting area occur according to a Poisson process with an average arrival rate of 100 per day. Each collaborator takes an average of 27 minutes to paint an article. Lately, the excess of ongoing work is a cause for concern, so management is considering expanding the painting area and hiring a third worker. (It is assumed that the 3rd worker, after a training period, will also take an average of 27 minutes per piece). After the advancement of technology, the other option would be to buy a robot to carry out the workers' task, since it is known that the average time it will take for each piece is 10 minutes.

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Answer to a math question In a factory the most important operation is painting. At the painting site there are always two workers working at the same time, although due to the physical setup, they cannot help each other. Arrivals at the painting area occur according to a Poisson process with an average arrival rate of 100 per day. Each collaborator takes an average of 27 minutes to paint an article. Lately, the excess of ongoing work is a cause for concern, so management is considering expanding the painting area and hiring a third worker. (It is assumed that the 3rd worker, after a training period, will also take an average of 27 minutes per piece). After the advancement of technology, the other option would be to buy a robot to carry out the workers' task, since it is known that the average time it will take for each piece is 10 minutes.

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La fábrica se enfrenta a un problema de exceso de trabajo en curso en el sitio de pintura, donde actualmente dos trabajadores trabajan de forma independiente. Para abordar esta preocupación, la fábrica está considerando dos opciones: contratar a un tercer trabajador o comprar un robot. Analicemos cuantitativamente ambas opciones. **Opción 1: Contratar a un tercer trabajador** - Con dos trabajadores, la capacidad actual del área de pintura en términos de artículos por día es el número de minutos por día dividido por el tiempo promedio que tarda cada trabajador en pintar un artículo. - Si cada trabajador dedica 27 minutos a cada artículo y hay 1440 minutos en un día, en teoría cada trabajador puede pintar hasta \( \frac{1440}{27} \) artículos por día. - Con dos trabajadores esta capacidad se duplica. La contratación de un tercer trabajador triplicaría la capacidad inicial de un solo trabajador. **Opción 2: Comprar un robot** - Si un robot tarda una media de 10 minutos en cada pieza, podría pintar \( \frac{1440}{10} \) artículos en un día. - Dependiendo de cuántos robots se compren, esto podría aumentar significativamente la capacidad. Por ejemplo, un robot ya proporcionaría una capacidad superior a la de un trabajador humano. Ahora calculemos estas capacidades para compararlas con la demanda de 100 artículos por día. También calcularemos las tasas de utilización tanto para la configuración actual como para las opciones que se están considerando. La tasa de utilización es la relación entre la tasa de demanda (\( \lambda \)) y la tasa de servicio (\( \mu \)), que es la capacidad de los trabajadores o del robot. Para un proceso de Poisson, \( \lambda = 100 \) artículos por día. Actualmente, cada trabajador tiene capacidad para pintar aproximadamente 53,33 artículos por día. Con dos trabajadores, la capacidad total es de 106,67 artículos por día. - La tasa de utilización con los dos trabajadores actuales es del 93,75%. Esto es bastante alto e indica que los trabajadores se utilizan casi al máximo, lo que se alinea con la preocupación por el exceso de trabajo en curso. - Si se contrata a un tercer trabajador, la tasa de utilización baja al 62,5%. Esta menor tasa de utilización sugiere que los trabajadores tendrán más tiempo libre y que debería aliviarse el problema del exceso de trabajo. - Para el robot, con una capacidad de 144 artículos por día, la tasa de utilización sería del 69,44%. Esto es más alto que la tasa de utilización con tres trabajadores, pero aún menos que la configuración actual. Teniendo en cuenta estos cálculos, contratar a un tercer trabajador llevaría la tasa de utilización a un nivel que generalmente se considera más eficiente y manejable en la gestión de operaciones. A menudo se apunta a una tasa de utilización de alrededor del 60-70% para equilibrar la eficiencia y la capacidad de manejar la variabilidad en las cargas de trabajo. Por otro lado, utilizar un robot también reduciría la tasa de utilización, pero no tanto como contratar a un tercer trabajador. Sin embargo, el robot puede ofrecer un rendimiento constante sin fatiga y, dependiendo del costo del robot en comparación con el salario y los beneficios de un nuevo trabajador, podría ser la opción económicamente más viable a largo plazo. La gerencia necesitaría considerar estas cifras a la luz de los costos totales involucrados, incluida la contratación y capacitación de un nuevo trabajador, la compra y mantenimiento de un robot y cualquier factor adicional como la calidad del trabajo, la confiabilidad y la flexibilidad de la fuerza laboral. frente a la automatización.

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