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Effects of stochastic and heterogeneous worker learning on the performance of a two-workstation production system

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Abstract

Production systems in industries are undergoing transformative changes, with the rise of Industry 4.0 technologies amplifying the complexity of manual and semi-automated workstations, necessitating advanced training and adaptability from human workers. Human workers, due to their unique blend of cognitive and motor skills, thus flexibility, are indispensable and will continue to play a pivotal role. Because of their unique experiences and attributes, they inherently exhibit variability in their processing times and learning rates, which complicates frequent production ramp-ups. Recognizing the lack of comprehensive models that simultaneously account for stochastic processing times and heterogeneous learning during production ramp-ups, this study aims to bridge this gap. We developed an analytical model of a two-worker production system with an intermediate buffer by focusing on worker learning curves, stochastic processing times, and learning heterogeneity. Through an illustrative case, we derived insights into the performance of such systems, specifically in terms of measures including the mean throughput time of a batch, mean waiting time of a part in the buffer, mean idle time of workers, work-in-progress distribution, and buffer usage during the production run. We found that deterministic learning models can significantly underestimate the throughput times, and even consistent average learning rates can lead to variable throughput times based on the learning patterns. Our findings emphasize the need for production managers to consider these factors for realistic and effective production planning, underscoring the novelty of our approach in addressing these intricate dynamics to improve not only system performance, but also worker well-being.

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... In recent years, cellular production has continuously penetrated and influenced various manufacturing modes (e.g., intelligent manufacturing, reconfigurable manufacturing, mass customization), showing an increasingly obvious trend of flexibility, collaboration and intelligence. To cope with the fluctuating production environment, the production cell also emphasizes the active role of humans, regarding high-quality workers and flexible cooperative production teams as important factors to improve the flexibility of the system (Bouaziz et al. 2022;Ranasinghe et al. 2024). Therefore, research on the cooperative behavior of production cell workers under a fluctuating environment is helpful to realize the best match between humans, machines and the environment to improve the manufacturing flexibility from the perspective of the organization. ...
... The manufacturing process of the production cell contains many discrete events, and the workers are active, autonomous and adaptable individuals; therefore, simulation technology based on complex system theory is considered to be a more effective way to study such complex production systems (Barbosa et al. 2015;Wang et al. 2016;Zhao et al. 2017). Current simulation studies on worker behavior show that organizational collaboration can significantly improve the performance of manufacturing systems (Liu et al. 2023;Mendez-Vazquez and Nembhard 2019;Ranasinghe et al. 2024;Zhang et al. 2015). However, in the actual production process, excessive collaboration also affects the system's smoothness, increasing labor training costs and communication costs, and reducing the overall system performance. ...
... Bouaziz et al. (2022) simulate the randomness of different workers' behaviors through Markov chains, testing the effects of different random behaviors on the performance of production systems. Ranasinghe et al. (2024) focus on workers' learning behavior, random behavior and learning heterogeneity, establishing a simulation model of a two-workstation production system with intermediate buffers to evaluate the effects of different learning models on the production system. Bokhorst et al. (2006) propose load-oriented collaboration and resource-oriented collaboration modes, analyzing the impact of these modes on system performance using the discrete event modeling method. ...
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In this paper, we consider a product manufacturer that seeks to leverage the potential of human learning to develop the capacity of its workforce and to reduce its costs. Unlike much of the literature in this area, we do not assume that the rate at which individuals learn is known with certainty. We present a two-stage stochastic programming model of the related production planning problem that quantifies the impact of worker assignment decisions to produce through an exponential learning curve which we linearize to yield a mixed integer linear program that can be solved efficiently. With this stochastic program, we perform a rigorously designed computational study and statistical analysis to derive tactics and managerial insights for how an organization should plan its production operations about assignment, cross-training and practicing. Results suggest that explicitly recognizing uncertainty in learning rates would reduce costs and that when dealing with assignment decisions, the leading factor to consider is the mean learning rate. On the other hand, when dealing with cross-training and practicing decisions, the learning rate variance is more predictive. We also assess the impact of explicitly considering stochastic forgetting rates in the productivity curve, finding that in the optimal assignment schedule, workers practice more and always specialize.
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Mass Customization (MC) implies in large product variety and reduced production batch sizes. Tasks that rely on human ability are especially affected in this context as workers must quickly adapt to the requirements of new models. That adaptation process takes place differently in each worker, justifying the development of strategies to group workers with similar learning profiles. This paper proposes a framework to form homogeneous groups of workers based on their learning profiles by integrating learning curve (LC) modeling and cluster analysis. For that, performance data are collected and modeled through LCs, such that LC parameters quantify workers’ adaptation to tasks. Principal Components Analysis (PCA) is applied to the dataset consisting of the LC parameters; PCA outputs give rise to an importance index that guides a backward parameter selection process. After each LC parameter is removed from the dataset, a new grouping using the Fuzzy C-Means (FCM) clustering technique is carried out using the remaining LC parameters, and the quality of the formed groups is assessed by means of three metrics. When applied to a shoe manufacturing process, 8 out of the original 29 LC parameters were retained, and used to insert workers into two clusters. The reduced subset of parameters elevated the quality of the clustering procedure by 29.4% (from 0.476 to 0.616) according to the Silhouette Index; similar improvements were indicated by the other two metrics. The retained parameters are related to workers’ performance at the first repetition and previous experience, highlighting the importance of well-designed training programs.
Article
The average time in the system (or average throughput time) is recognized as a crucial performance measure of manufacturing systems and, in recent years, has become even more relevant as markets have shifted towards mass-customization scenarios, since it directly affects the average inventory in the system. Modern manufacturing systems design paradigms, Industry 4.0 on top, focus on the need to achieve high responsiveness by shortening throughput time as the main lever to maintain cost efficiency and competitiveness in such market scenarios. In the contexts in which the human impact on production operations is not negligible, the learning phenomenon may reasonably affect the average time in the system. This paper analyses the learning effect on this performance measure through batching policies. Here, batching is considered as the possibility to group customized orders presenting similarities in the production processes, thus making it possible the exploitation of learning effect. Both single- and multi-item systems under Markovian arrivals are studied, also deterministic and stochastic processing times are considered. The problem that we pose consists in determining the batch size for each product that minimizes the average time in the system taking into consideration the learning effect, which is included by means of the Plateau model. A solution procedure for each case is discussed and, through numerical experiments, the sensitivity of the model to variations in parameter values is studied.
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Many problems in manufacturing systems can be formulated via Markov stochastic modeling. This paper gives a review and classification of timed models of manufacturing systems with particular emphasis on Markov models. As the associated Markov chains of even small systems are characterized by the well-known state explosion or largeness problem, the review continues on with the models and methods for the numerical solutions of large Markov chains. In addition, the software tools are summarized. Finally, the paper provides some challenges and directions for further research on the modeling of manufacturing systems.
Article
The learning curve is a powerful tool for estimating either the production cost or time in production analysis. Our work focuses on the characterization of the uncertain nature of the learning effect. Traditionally, the learning curve of a new product can be derived by processing the past data obtained for similar products. However, due to the complicated environment, in some cases, the data for similar products may be lacking, preventing the use of the traditional methods to find the learning curve. To address this issue, we develop an uncertain learning curve by utilizing uncertainty theory. Moreover, some useful theorems are developed to characterize the uncertain learning curve. An experiment is conducted to compare the proposed model and the standard model. Finally, we apply the uncertain learning curve to the single-machine optimization problem.
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Decision support models for production and logistics have neglected human factors to a large extent in the past. For this reason, researchers have called for the development of more realistic planning models for production and logistics problems incorporating human factors. This call has recently been addressed by an increasing number of innovative approaches, which makes the study of human factors in decision support models for production and logistics a more and more maturing research field. The aim of this paper is to present the evolution of works that incorporate human factors into decision support models for production and logistics. For this reason, a systematic literature review is performed. The results of the literature review reveal the current state of research and highlight areas and approaches where additional research is promising.
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Assembly lines with non-constant task time attribute are widely studied in the literature. For the SALBP-II assembly line balancing problem, we take account of stochastic task time changes, which is more practical than the deterministic times often assumed in industrial application. An algorithm – ENCORE, which leverages the traditional algorithm SALOME2, is proposed to address the assembly line balancing problem with stochastic task time attribute. Computational and statistical experiments are conducted to show the efficiency of proposed algorithms over traditional methods with regards to the improvement of total production times.
Article
The aim of this research is to demonstrate how human learning models can be integrated into discrete event simulation to examine ramp-up time differences between serial and parallel flow production strategies. The experimental model examined three levels of learning rate and minimum cycle times. Results show that while the parallel flow system had longer ramp-up times than serial flow systems, they also had higher maximum throughput capacity. As a result, the parallel flow system frequently outperformed lines within the first weeks of operation. There is a critical lack of empirical evidence or methods that would allow designers to accurately determine what the critical learning paramters might be in their specific operations, and further research is needed to create predictive tools in this important area.
Article
The learning curve is a fundamental model used by engineers in cost estimating. In industry, it is typical to use the deterministic model for projecting cost, which is also suggested in standard textbooks. However, the parameters for the model are obtained from actual data, which usually come from a stochastic process. In this technical note, we investigate a particular phenomenon of the stochastic learning model that indicates that a bias may exist in the parameter estimates simply due to random behaviour in learning. The findings suggest that, on average, projections of cost from a model whose parameters are estimated from early data points are, on average, optimistic about the future cost reduction.
Article
The time that a part may spend in a buffer between successive operations is limited in some manufacturing processes. Parts that wait too long must be reworked or discarded due to the risk of quality degradation. In this paper, we present an analytic formulation for the steady-state probability distribution of the time a part spends in a two-machine, one-buffer transfer line (the part sojourn time). To do so, we develop a set of recurrence equations for the conditional probability of a part's sojourn time, given the number of parts already in the buffer when it arrives and the state of the downstream machine. Then we compute the unconditional probabilities of the part sojourn time using the total probability theorem. Numerical results are provided to demonstrate how the shape of the distribution depends on machine reliability and the buffer size. The analytic formulation is also applied to approximately compute the part sojourn time distribution in a given buffer of a long line. Comparison with simulation shows good agreement. © 2015 Elsevier B.V. and Association of European Operational Research Societies (EURO) within the International Federation of Operational Research Societies (IFORS). All rights reserved.
Article
The effect of workers’ learning curves on the production rate in manual assembly lines is significant when producing relatively small batches of different products. This research studies this effect and suggests applying a work-sharing mechanism among the workers to improve the makespan (time to complete the batch). The proposed mechanism suggests that adjacent cross-trained workers will help each other in order to reduce idle times caused by blockage and starvation. The effect of work sharing and buffers on the makespan is studied and compared with a baseline situation, where the line does not contain any buffers and work sharing is not applied. Several linear programming and mixed-integer linear programming formulations for makespan minimization are presented. These formulations provide optimal work allocations to stations and optimal parameters of the work-sharing mechanism. A numerical study is conducted to examine the effect of buffers and work sharing on the makespan reduction in different environment settings. Numerical results are given along with some recommendations regarding the system design and operation.
Article
For almost a century, researchers and practitioners have studied learning curves in production economics. Learning, in this context, refers to performance improvements of individuals, groups or organizations over time as a result of accumulated experience. Various learning curves, which model this phenomenon, have been developed and applied in the area of production economics in the past. When developing planning models in production economics, the question arises which learning curve should be used to best describe the learning process. In the past, the focus of the literature has been on empirical studies that investigated learning processes in laboratory settings or in practice, but no effort has been undertaken so far to compare existing learning curves on a large set of empirical data to assess which learning curve should be used for which application. This study systematically collected empirical data on learning curves, which resulted in a large database of empirical data on learning. First, the data contained in the database is categorized with the help of meta-tags along different characteristics of the studies the data was taken from. Second, a selection of well-known learning curves is fitted to the empirical datasets and analyzed with regard to goodness of fit and data characteristics. We identify a set of data/task characteristics that are important for selecting an appropriate learning curve. The results of the paper may be used in production economics to assist researchers to select the right learning curve for their modeling efforts.
Article
In a two-sided assembly line, tasks can be executed simultaneously on both sides of the line. One task cannot be started until both of its direct predecessors on the left and right sides are completed. Therefore, the start time of the task is the maximum of the two predecessors’ finish times. In many realistic situations, it is assumed that the task times are independent and normally distributed with known means and variances. However, the maximum of two normal variables is not normally distributed, but can be well approximated by results from extreme value theory. In this paper, we utilise these results to develop a solution methodology to balance two-sided assembly lines with stochastic task times, minimising the line length and the number of stations while guaranteeing all tasks are completed within the cycle time with a given confidence level.
Article
This paper studies the effects of learning and forgetting on a two-stage production system and the position of a potential bottleneck in the system. We start with developing a model for a two-stage serial production system where semi-finished items are fed by the first stage to the second stage, which, in turn, processes the items to their final state. The finished items are transferred either to a subsequent stage or to customers. The paper assumes that both stages of the production system considered are subject to learning and forgetting effects. Learning quickens the production rate as more experience is gained (i.e., when the number of repetitions increases), while forgetting has the opposite effect when production is intermittent (i.e., experience is lost over production breaks). The paper studies how different values of the learning and forgetting parameters influence the ratio of the production rates of both stages and the flow of material in the system. The results of the paper indicate that learning may cause a bottleneck to shift its position in a production system. This happens when an initially slower stage overtakes a previously faster stage over time due to a higher learning rate. The paper thus contributes to the literature on moving bottlenecks and provides practitioners with a model that helps predicting where bottlenecks may arise in the production system, and which enables the system to flexibly react to moving bottlenecks.
Article
In the ramp-up phase, or time to volume of new products, pronounced learning effects are observed. They are present especially on assembly lines producing mass-goods because of a high number of repetitions of the tasks. Shortening the ramp-up phase and reaching the steady-state production as soon as possible generates main advantages for firms that introduce new products. Moreover, a careful planning of the ramp-up stage is getting even more important in view of shorter product life cycles and a growing importance of the 'time to payback' financial indicators. Former studies on incorporation of learning effects into assembly line balancing have limited applicability, because they rely on unrealistic assumptions. We model learning effects, based on general and realistic assumptions, as an extension of the Simple Assembly Line Balancing Problem. We propose exact and heuristic solution procedures and perform extensive computational tests. We found that for instances similar to the problems, which arise in firms, the duration of the learning stage can be reduced by up to 10% if our specialised methods are applied.
Article
Order picking is a time-intensive and costly logistics process as it involves a high amount of manual human work. Since order picking operations are repetitive by nature, it can be observed that human workers gain familiarity with the job over time, which implies that learning takes place. Even though learning may be an important source of efficiency improvements in companies, it has largely been neglected in planning order picking operations. Mathematical planning models of order picking that have been published earlier thus provide an incomplete picture of real-world order picking, which affects the quality of the planning outcome. To contribute to closing this research gap, this paper presents an approach to model worker learning in order picking. First, the results of a case study are presented that emphasize the importance of learning in manual order picking. Subsequently, an analytical model is developed to describe learning in order picking, which is then evaluated with the help of numerical examples. The results show that learning impacts order picking efficiency. In particular, the results imply that worker learning should be considered when planning order picking operations as it leads to a better predictability of order throughput times. In addition, the effects of learning are relevant for the allocation of available resources, such as the allocation of workers to different zones of the warehouse. The results of the numerical analysis indicate that it is beneficial to assign workers with the lowest learning rate in the workforce to the fast moving zone to gain experience.
Article
The learning curve or start-up model is extended to three examples of labour-intensive manufacture-automobile assembly, apparel manufacture and the production of large musical instruments. Prediction of the parameters of the model and the occurrence of steady-state "plateaux" are examined in relation to the findings. The results of the investigation suggest the wider applicability of the learning curve model in labour-intensive industries, provide additional data to evaluate an empirical approach to parameter prediction and demonstrate the difficulty of generalizing about the occurrence and predictability of steady-state plateaux. In addition, the application of different cost indices in learning curve research is demonstrated among new product start-ups in both single and multiple facilities.
Book
Mainly deal with queueing models, but give the properties of many useful statistical distributions and algorithms for generating them.
Article
Models are developed which 'explain' why new automobile assembly systems are abandoning traditional moving assembly line concepts if human operators perform most of the tasks. The new systems incorporate parallel stations, asynchronous work flow and small inventories. However, the paralleling creates problems in synchronizing parts delivery, and models are developed to illustrate these problems and the effect of alternative part delivery systems and the impact of job resequencing requirements.