Two-machine Lines Research Articles

Evaluation of stochastic flow lines with provisioning of auxiliary material

Flow lines are often used to perform assembly operations in multi-stage processes. During these assembly operations, components that are relatively small, compared to the work pieces travelling down the flow line, are mounted to the work pieces at a given stage. Those components, or more generally, any kind of auxiliary material, are provisioned to the corresponding production stage in a repetitive but not necessarily deterministic manner using a certain delivery frequency, each time filling the local storage up to a predetermined order-up-to level. Just like random processing times, machine failures, and repairs, the randomness of the provisioning process can impact the long-term throughput of such a flow line. In this paper, we develop a fast and accurate analytical performance evaluation method to estimate the long-term throughput of a Markovian flow line of this type for the practically important case of limited buffer capacities between the production stages. We first give an exact characterization of a two-machine line of that type and show how to determine system state probabilities and aggregate performance measures. Furthermore, we show how to use this two-machine model as the building block of an approximate decomposition approach for longer flow lines. As opposed to previous decomposition approaches, even the state space of the two-machine lines can become so large that an exact solution of the Markov chains can become impractical. We hence show how to set up, train, and use an artificial neural network to replace the Markov chain solver embedded in the decomposition approach, which then leads to an accurate and extremely fast flow line evaluation tool. The proposed methodology is evaluated by a comparison with simulation results and used to characterize the structural patterns describing the behaviour of flow lines of this type. The method can be used to systematically consider the combined impact of the delivery frequency and the local order-up-to levels for the auxiliary material when designing a flow line of this type.

Modeling, Analysis, and Improvement of Batch-Discrete Manufacturing Systems: A Systems Approach

Production systems include both discrete part and batch operations, where an individual part is manufactured in a discrete operation, and a group of parts are processed simultaneously, i.e., in a batch, on one machine for a batch operation. Many manufacturing industries, such as battery, aircraft, and automotive, consist of mixed batch and discrete part operations, referred to as batch-discrete lines. Although such operations are widely encountered, analytical studies of these systems are limited in current literature. In this paper, a systems approach is presented to model and analyze batch-discrete lines. First, a Bernoulli machine reliability model for a two-machine batch-discrete system is introduced. Using a virtual buffer to represent the batch processing feature, performance evaluation formulae are derived and system properties are investigated. Using them, improvement analyses and bottleneck identification are presented. Then, the model is extended to systems with a quality inspection device under different control policies. To illustrate the applicability of the model, a case study in a composite part production process is described. Such a work delivers a quantitative tool for production engineers and managers to design, analyze, and improve batch-discrete manufacturing systems. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many manufacturing systems in aircraft, automotive, battery, medical device, and defense industries include both batch operation and discrete part processing machines. In a batch operation, multiple parts are manufactured simultaneously on a batch machine, while a single part is made in a discrete part machine. Production lines with mixed batch and discrete part operations are named as batch-discrete systems. Analysis and improvement of such systems are critical to ensure high productivity and quality. However, accurate modeling and analysis of batch-discrete systems are lacking in current literature. To bridge this gap, a novel methodology is presented in this paper. Using a Bernoulli reliability machine model with a virtual buffer concept, performance measures are derived for batch-discrete two-machine lines, as well as the reversed discrete-batch lines. Then system properties, such as monotonicity, interchangeability, and reversibility, are investigated, followed by improvement analysis under constraints and bottleneck analysis. By extending to systems with quality inspections, two quality control policies, to scrap either the current batch or the whole inventory after detecting a degraded part, are studied. In addition, a case study of heating (batch) and trimming (discrete) operations in composite panel production lines is presented, and improvement strategies are investigated, to illustrate how to apply the model and analysis in practice.

Parameter Identification for Bernoulli Serial Production Line Model

Model-based analysis of production systems is one of the main areas in manufacturing research. The foundation of the successful application of these theoretical studies is the availability of valid and high-fidelity mathematical models that are capable of capturing the behavior of job flow in production systems. The modeling process of a production system, however, may require a significant amount of nonstandardized work that can only be done properly by someone with solid training in the area and extensive experience through real case studies. This poses a critical challenge in the effective implementation of these valuable theoretical results in the Industry 4.0 era. To overcome this, we propose a new production systems modeling paradigm inspired by system identification: calculate production system model parameters that best match the standard system performance metrics measured on the factory floor. Specifically, in this article, we consider production lines characterized by the Bernoulli serial line model and develop algorithms that identify model parameters to fit the system throughput and work-in-process. Analytical algorithms are derived to solve this problem in a two-machine line case and then extended to multi-machine lines. The accuracy and computational efficiency of the algorithms are demonstrated through extensive numerical experiments. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A high-fidelity mathematical model is of critical importance to the implementation of any model-based production system analysis method. Currently, the construction of such models is carried out in an ad hoc manner. The quality of the resulting models may heavily depend on the training, experience, intuition, and personal preference of the modeler. The proposed model parameter identification method focuses on standard key performance indices commonly measured on the factory floor. The advantage is twofold. First, these standard performance metrics are consistently defined regardless of industry, thus avoiding any data-ambiguity issue that may occur when using complex machine/equipment status data. Second, measuring these performance metrics in real time is typically convenient and cost effective, even for manufacturing plants without high-end IT infrastructure, thus making the technology accessible to not only large but also small- and mid-sized manufacturers. Using the algorithms developed in this article, a practitioner can quickly construct a serial production line model and then utilize it to access the rich library of production analysis, design, and control methods available in the literature.

An effective and efficient divide-and-conquer algorithm for energy consumption optimisation problem in long Bernoulli serial lines

Reducing energy consumption in the energy-intensive production systems is of great significance and attracts more and more attention. Although a lot of efforts have been devoted to formulate and solve the energy consumption optimisation problem in the Bernoulli serial lines, existing methods for solving the problem in long Bernoulli lines either cannot obtain the optimal solution or are time-consuming. For this purpose, this paper divides the problem in the long line into a set of problems in two-machine lines and proposes a computationally efficient and globally convergent algorithm to solve it. Extensive numerical experiments show that the proposed algorithm not only can optimally (in the numerical way) solve the energy consumption optimisation problem in long Bernoulli serial lines, but also is orders of magnitude more efficient than existing algorithms.

A new aggregation algorithm for performance metric calculation in serial production lines with exponential machines: design, accuracy and robustness

Performance metric calculation is one of the most important problems in production system research. In this paper, we consider serial production lines with finite buffers and machines following the exponential reliability model. Analytical formulas are first given for performance analysis of two-machine lines. Based on these formulas, a throughput-equivalent aggregation procedure is derived to represent a two-machine exponential line by a single exponential machine. Following this approach, we propose a new aggregation-based iterative algorithm to calculate the performance metrics of a multi-machine serial line by representing it using a group of virtual two-machine lines. Numerical experiments are used to justify the convergence of the algorithm and to evaluate the accuracy of the calculated performance metrics. The results show that the proposed algorithm significantly improves the performance metric approximation accuracy, compared with two commonly used aggregation-based methods in the literature, without incurring additional computational burden. The improvement is even more prominent for systems with relatively small buffers. We believe that this work makes an important contribution to the field of Production Systems Engineering and has the potential to generate great impact as the new algorithm replaces the existing ones in future research and applications by scholars and practitioners.

Problem Formulation and Solution Methodology for Energy Consumption Optimization in Bernoulli Serial Lines

As the main force of energy consumption, machines consume a huge amount of energy in some production systems. To operate the systems in an energy-efficient way, the efficiencies of the machines should be elaborately optimized so that the total energy consumption in the production lines is minimized while maintaining the required production rate. For this purpose, this article investigates the energy consumption optimization problem in Bernoulli serial lines having more than two machines. Specifically, this problem is first formulated as a nonlinear programming with a production rate constraint; due to difficulties in solving this constrained nonlinear programming, structural characteristics of the problem and properties of the objective function, which are inspired by the results and insights obtained in two-machine lines, are analyzed. Finally, based on the structural characteristics and properties explored, a solution methodology is developed to recursively solve the unique optimal solution of the energy consumption optimization problem. Extensive numerical experiments show that the solution provided by this method, which has the reversibility property and is better than the one provided by an existing method in the literature, is numerically optimal (note that the theoretically optimal solution is extremely hard to obtain if not totally impossible). Note to Practitioners-Machines consume a huge amount of energy in energy-intensive (i.e., high energy-consuming) production systems in, e.g., automobile, semiconductor, and steel companies. Due to economic, social, and environmental concerns, it is a high priority to consider ways to reduce the energy consumption in these production systems. In this article, the problem of minimizing the total energy consumption in Bernoulli serial lines while maintaining the required production rate is investigated. Based on the aggregation method developed for performance analysis of long lines and the optimization results obtained for two-machine lines, the energy consumption optimization problem for long Bernoulli serial lines is elaborately analyzed and a method is proposed to recursively solve its unique optimal solution (i.e., the optimal machine efficiencies). From the point of view of system operation, this research, which makes the system operate in the most energy-efficient manner, offers a new managerial paradigm for the production systems.

Transient Analysis of Multiproduct Bernoulli Serial Lines With Setups

Performance analysis of flexible manufacturing systems has received substantial research attention. Most of the studies focus on steady-state behavior. The transient performance, which is critical for system operation, control, and improvement, is less investigated. No analytical method is available to evaluate the transients in flexible lines with unreliable machines, finite buffers, and setup times. In this article, an analytical model is introduced to study the transient performance of multiproduct serial lines with Bernoulli reliability machines and nonnegligible setups during changeovers. To reduce the state-space dimension, an approximation method is introduced to evaluate the performance in two-machine lines, where the sequence of multiple part types in the inventory is approximated by the ratio of product mix. Such an approximation method leads to high precision of production rate estimation. Then, for longer lines, the analysis approach in two-machine lines is used as a building block in an iterative aggregation procedure. Numerical experiments show that the iteration procedure is convergent and results in an acceptable accuracy in performance evaluation. In addition, system properties, such as monotonicity and reversibility, are investigated.

Switching- and hedging- point policy for preventive maintenance with degrading machines: application to a two-machine line

Maintenance and production are frequently managed as separate activities although they do interact. Disruptive events such as machine failures may find the company unready to repair the machine immediately leading to time waste. Preventive Maintenance may be carried out and maintenance time reduced to the effective task duration, in order to prevent time waste. Companies and researchers have been focusing on policies able to mitigate the impact of Preventive Maintenance on system availability, by exploiting the knowledge about degradation profiles in machines and the joint information from the machine state and the buffer level. In this work, the mathematical proof of the optimal threshold-based control policy for Preventive Maintenance with inventory cost, maintenance cost, backlog cost is provided. The control policy is defined in terms of buffer thresholds and dependency of the thresholds on the degradation condition. The optimal control policy is proved to include a combination of switching points and hedging points, where the first ones activate the Preventive Maintenance for a given condition and the latter ones control the production rate in order to minimize the surplus. An extensive experimental campaign analyzes the impact of system parameters such as the Maintenance duration on the cost function. The results show that there exists cases in which the optimal policy is dominated by the effect of the hedging points or the switching points, alternatively. Therefore, the proposed method is used to provide suggestions to the management for operative decisions, in order to choose the policy fitting best the system.

Bernoulli serial lines with batching machines: Performance analysis and system-theoretic properties

Aiming at Bernoulli serial lines with batching machines and finite buffers, this study develops analytical methods for performance analysis and system-theoretic properties. Batching machines can process several jobs simultaneously as a batch, as long as the number of jobs in a batch does not exceed the machine’s batch capacity. The batch capacities of all machines are not necessarily equal. Batching machines bring about a new characteristic of state transitions depending on batch capacities and machine states. For two-machine lines, the joint impacts of batching machines on state transitions are analyzed. Theoretically, the state transition rules are revealed. Based on the state transition rules, this study proposes a hierarchical state transition diagram, proves the ergodicity condition, and derives analytical formulas to evaluate the performance measures. Then, for multi-machine lines, this study develops a computationally efficient aggregation method with high accuracy. Furthermore, the impacts of system parameters, including machine efficiency pattern, batch capacity pattern, batch capacity mismatch, and system size, on the accuracy are qualitatively analyzed. Finally, this study investigates the reversibility and monotonicity properties. These analytical methods and results help production managers to scientifically evaluate, accurately predict, and continuously improve Bernoulli serial lines with batching machines.

Transient analysis and real-time control of geometric serial lines with residence time constraints

Residence time constraints are commonly seen in practical production systems, where the time that intermediate products spend in a buffer is limited within a certain range. Parts have to be scrapped or reworked if their maximum allowable residence time is exceeded, while they cannot be released downstream before the minimum required residence time is reached. Such dynamics impose additional complexity onto the production system analysis. In order to optimize the production performance in a timely manner, the transient behavior of the production system and a real-time control strategy need to be investigated. In this article, we develop a Markov chain model to analyze the transient behavior of a two-machine geometric serial line with constraints on both maximum allowable residence time and minimum required residence time being. Compared with the simulation, the proposed analytical method is shown to estimate the system’s transient performance with high accuracy. Structural properties are investigated based on the model to provide insights into the effects of residence time constraints and buffer capacity on system performance. An iterative learning algorithm is proposed to perform real-time controls, which improves the system performance by balancing the trade-off between the production rate and scrap rate. Specifically, a control policy derived from Markov Decision Processes is implemented as an initial control policy, and the Bayesian method is then applied to the run time data to improve the control policy.

Serial production lines with geometric machines and finite production runs: performance analysis and system-theoretic properties

A production run is typically referred to as a group of identical goods that is produced by a particular manufacturing process. In many discrete manufacturing practices, the manufacturing activity is carried out by deploying a series of production runs of different products according to customer orders. If the volume of a production run is relatively small and process changeovers are necessary, the production system operates partially (or entirely) in the transient regime, especially at the beginning and near the end of a production run. In this case, the traditional steady-state analysis approach may become inapplicable. In this paper, we consider finite production run-based manufacturing in serial lines with machines obeying the geometric reliability model and buffers having finite capacity. Exact Markovian analysis is first used to derive the closed-form formulae to calculate the transient performance of the production line during a production run as well as the distribution, mean, and standard deviation of its completion time in one- and two-machine lines. For multi-machine lines, an aggregation-based approach is proposed to approximate the system performance measures with high accuracy and computational efficiency. In addition, system-theoretic properties of production run completion time with respect to machine and buffer parameters are discussed.

Serial production lines with waiting time limits: Bernoulli reliability model

Production systems with waiting time constraints are frequently encountered in semiconductor, automotive, battery, food, and many other manufacturing industries. Under the waiting time constraints, the residence time of in-process inventories is constrained by a predetermined time limit. A part exceeding the maximal time limit has to be inspected for quality assurance and it is subject to be scrapped with a certain probability. In this paper, performance evaluation of Bernoulli serial lines with waiting time limits is studied. Analytical formulas are derived to predict the system performance of two-machine lines in steady state. For longer lines, direct analysis is no longer viable due to high complexity, thus an aggregation-based iterative procedure is introduced. Based on extensive numerical studies, the convergence of the procedure can be observed and high accuracy in performance estimation is achieved. In addition, to design such lines, an efficient procedure for near optimal buffer assignment to maximize production rate is also proposed. Analogously, we first propose an exact algorithm for two-machine lines and then extend it to a recursive procedure for longer lines. We then numerically verify that the procedure provides a near optimal solution within a very short computation time. Finally, the impacts of relaxing waiting time constraints on line performance and buffer design are discussed, and operational strategies to achieve better performance are also presented.

Performance evaluation of two-machine lines with generalized thresholds

An analytical model for evaluating the performance of two-machine continuous flow systems with finite buffer capacity, multiple up and down states and generalised thresholds is presented in this paper. The idea is that the machines can behave differently above or below certain buffer levels named thresholds. In addition, when the buffer level crosses one of the thresholds, certain changes of state of the machines can happen. With the method presented in the paper it is possible to consider all the different types of two machine lines which can be modelled with multiple up and down states, like for example cases with machines having phase-type failure and repair time distributions, serial/parallel machines and quality control machines. The proposed approach, allows to include system control by means of thresholds in the system model and provides a way to analyse the performance of a wide range of two-machine systems. Some of these cases are proposed in the numerical examples at the end of the paper. Moreover, the proposed two-machine line can be used as a building block for the analysis of larger systems, including systems with loops.

A threshold-based control policy for scrap reduction of perishable in-process inventories

Sustainability has become a key factor for competitiveness. Sustainable production strategies aim at the scrap reduction of in-process inventory. In some sectors such as food or pharmaceutical sector, in-process inventories must be scrapped after a certain time due to perishability. Therefore, local policies are usually applied to machines in order to mitigate the impact of disruptive events leading to scrap.This work presents an analytical model for the performance evaluation of two-machine lines which integrates a threshold-based control policy for the scrap reduction grounding on the joint system dynamics. Results show that the proposed integrated policy performs better than local policies with respect to the scrap reduction without major losses in throughput. Moreover, it is shown how considerations about operating control policies can be beneficially included in the system configuration phase.

Joint production, quality and maintenance control of a two-machine line subject to operation-dependent and quality-dependent failures

In the literature of operations management, the reliability of multistage manufacturing systems has been always modeled with uncorrelated failure processes where the reliability of each machine is assumed to be independent of any failure in the other machines. However, in real-life, machines may be subject to complex correlated failures such as increased degradation and tool wear caused by defective parts produced in preceding machines. Ignoring the correlation effect when modeling the reliability of multistage systems generally results in inaccurate estimation of the overall system reliability and inefficient operations policy accordingly. In this paper, we deal with the problem of integrated production, quality and maintenance control of production lines where machines are subject to quality and reliability operation-dependent degradation. Also, machines' reliability is correlated with the level of incoming product quality. For illustration, we study in this paper a two-machine line model. We propose a combined mathematics and simulation-based modeling framework to jointly optimize the production, quality and maintenance control settings. The objective is to minimize the total cost incurred under a constraint on the outgoing quality. Numerical examples are given to show the effectiveness of the resolution approach and to study important aspects in multistage systems such as the allocation of inspection and maintenance efforts, the Quality-Reliability chain and the interdependence between production, quality and maintenance control settings. The results obtained demonstrate that failure correlation has a significant impact on the optimal control settings and that maintenance and quality control activities in preceding stages can play an important role in the reliability improvement of the subsequent machines.

Performance evaluation of a two-machine line with a finite buffer and condition-based maintenance

Performance evaluation of a two-machine line with a finite buffer and condition-based maintenance

Modeling and analysis of non-homogenous fabrication/assembly systems with multiple failure modes

This paper presents an approximate decomposition method for the performance evaluation of non-homogeneous fabrication/assembly (F/A) systems with multiple failure modes, finite buffers, and a fixed assembly proportion. First, we introduce a mixed flow combined with fund flow and material flow to convert an F/A system to a virtual transfer line. Then, we decompose the virtual transfer line into several two-machine lines and establish a continuous decomposition model. To tackle the new emerging characteristics of the F/A system, we propose an F/A decomposition algorithm (FADA) for solving this model and obtain the throughput and buffer level of the F/A system to evaluate system performance. Also, we demonstrate the validity of the proposed model and algorithm by comparing with the results of simulation-based method and completion time approximation (CTA)-based method. Finally, we analyze the impact of several key parameters, including failure rates, repair rates, and buffer capacities, on the performance of the F/A system. The results show that our analytical method outperforms the existing methods and can help production managers to evaluate the system performance, analyze the possible modifications, and further find the best performance improvement of such F/A systems.

Performance Evaluation of Bernoulli Serial Lines with Waiting Time Constraints

Manufacturing systems with waiting time constraints are widely observed in battery, automotive, semiconductor, food and many other industries. Under such requirements, the residence time of a part in a buffer is constrained by a given time limit and the part exceeding the limit is subject to quality inspection and could be scrapped with a certain probability. To evaluate the performance of such systems, in this paper, we study Bernoulli serial lines with waiting time limits. For two-machine lines, analytical formulas are derived to predict the system performance in the steady state. In case of longer lines, direct analysis is intractable, thus an iterative aggregation procedure is presented. Based on extensive numerical experiments, the convergent results of the procedure can be obtained and high precision in performance estimation is achieved.

Performance evaluation of a two-machine line with a finite buffer and condition-based maintenance

This paper considers a two-machine continuous flow manufacturing system with a buffer of finite capacity, and where the machines are subjected to failures, minimal repairs, and condition-based preventive maintenance. Each machine can degrade into several discrete states, which are characterized by different performance parameters, ranging from perfect functioning to complete shutdown. When a specified degraded state is exited, a preventive maintenance action is performed to restore the machine to one of the higher performance states. We evaluate the impact of preventive maintenance strategies for each machine, in order to determine their impact on production rate and total cost. A methodology is developed to analyze the complex trade-off between the contributions of preventive maintenance and of the buffer to the system performance. It is shown that preventive maintenance should be scheduled not to optimize the performance for each machine individually; its scheduling is best considered from the perspective of the manufacturing system as a whole. The analysis also reveals the importance of considering machine speeds when optimizing the choice of maintenance policy.

Efficient Algorithms for Analysis and Improvement of Flexible Manufacturing Systems

This paper is devoted to modeling, analysis, and improvement of flexible manufacturing systems with asynchronous exponential machines and finite nondedicated buffers. In such systems, each machine may process multiple types of products with different speeds, and buffers are shared for all products. Efficient algorithms to evaluate the system performance are developed. Formulas are derived to calculate line throughput in one- and two-machine lines, and a convergent recursive algorithm is introduced for longer lines. The numerical results show that the method leads to a high accuracy in performance evaluation. Using such a model, bottleneck analysis has been carried out to identify the machine or product whose improvement will lead to the largest improvement in system throughput. Indicators based on the collected data to identify bottleneck machine and product are derived without complete calculation of the partial derivatives of system performance. Such efficient algorithms provide a quantitative tool for analysis and improvement of flexible manufacturing systems.