Manufacturing lines under surplus-based control: multiple products and bounded buffers

Challenged by the scheduling complexity for production flow processes in industrial facilities, we study the performance of multi-product producing lines. We analyse the performance of multi-product lines that consist a number of machines and bounded buffers with preselected base stock levels. It is assumed that each manufacturing machine in the line is capable of working with several product types, but only operate on one product at a time. The network is operated under a surplus-based production control policy in the presence of perturbations and production demand fluctuations. We derive bounds on the demand tracking accuracy for each product type, regardless its flow direction in the multi-product line. In addition, for a multi-product line with unidirectional product flow, we obtain a quantitative relation between demand tracking accuracy, its inventory levels, numbers of product types, buffer capacity limits and perturbations. The accuracy of the obtained demand tracking bounds is illustrated by numerical simulations. By means of simulation experiments, we show that the obtained results have a valuable meaning and can be used as a reference tool in practice.     

Performance analysis of re-entrant manufacturing networks under surplus-based production control

Motivated by the problem of planning and scheduling in large semiconductor manufacturing facilities we study the performance of re-entrant production networks. In such networks, each product has to go multiple times through the entire manufacturing line before it is ready. Each machine in a re-entrant network can receive products from different routings, but the products from only one of the routings can be served at a time. This complicated network structure makes it difficult, and at the same time important, to estimate in advance the performance of such a network under a demand-driven control policy. In this paper we present results on the influence of perturbations, buffer inventory levels and the number of manufacturing stages on the production tracking error of each machine in the re-entrant network operated under a surplus-based production control policy. The results are provided in the form of so-called ‘worst case scenario’ bounds on the steady-state production demand tracking accuracy of each stage as well as bounds on the content of each intermediate inventory level. By means of simulation examples we show that the results obtained have an important meaning and can be used as a practical reference tool.     

Scheduling manufacturing systems with work-in-process inventory control: Reentrant systems

In this paper, we propose a procedure for production flow control in reentrant manufacturing systems. The system under study consists ofN machines and producesM product types simultaneously. Each part goes through the system following a predefined process and may visit a machine many times. All machines are subject to random failures and need random repair times. The scheduling objectives are to keep the production close to demand and to keep the WIP inventory level and cycle times at low values. The model is motivated by semiconductor fabrication production. A three-level hierarchical controller is constructed to regulate the production. At the top level of this hierarchy, we perform capacity planning by selecting the desirable buffer sizes and the target production level for each operation. A production flow rate controller is at the middle level which recalculates the production rates whenever a machine fails or is starved or blocked. The loading times for individual parts are determined at the bottom level of the hierarchy. Comparison with alternative control is made through simulation and it shows that the control policy performs well.     

On the uncertainties of decentralized controllers in a transfer production line

In this paper, an information theoretic approach is applied to analyze the performance of a decentralized control system. The control system plays the role of a correcting device which decreases the uncertainties associated with state variables of a production line by applying an appropriate “correcting signal” for each deviation from the target. In particular, a distributed feedback control policy is considered to govern a transfer production line, which consists of machines and buffers and processes a single part type in response to a stochastic demand. It is shown how the uncertainty of the demand propagates dynamically into the production system, causing uncertainties associated with buffer levels and machine production rates. The paper proposes upper estimates for these uncertainties as functions of the demand variance, parameters of the distributed controllers and some physical properties of the production line. The bounds are based on dynamic entropy measures of the system state and the control variables. Some practical implications into the area of decentralized controller design are proposed, an information-economical analysis is presented and a numerical study is performed.     

Performance evaluation for tandem multi-factory supply chains: an approximate solution

Predicting the performance of multistage manufacturing systems is usually viewed as challenging because of unexpected machine breakdowns, random processing times, uncertain inter-factory transportation times, etc. In this paper, the authors formulate an approximate model for the tandem manufacturing systems, where the inventory in each buffer is monitored based on the (s, Q) discipline. This model divides a multistage system into a series of primitive line segments, each of which is characterised by a continuous time discrete state Markov process. The model may be applied in two types of systems: (1) tandem flow lines with batch processing and (2) multi-factory manufacturing supply chain, where inter-factory material transportation is required. Based on the model, a number of commonly used performance measures, including throughput, inventory, transportation frequency, etc., can be estimated. These estimates may enable manufacturers to evaluate the performance of the systems, and hence improve the management of production and inventory.     

Exact analysis of a discrete material three-station one-buffer merge system with unreliable machines

In this paper, a model of a discrete material flow line consisting of three unreliable machines and one buffer of limited capacity is analysed. A similar system, but with continuous flow of material was examined by Helber and Mehrtens (2001) and Tan (2001). In our system it is assumed that the buffer has two immediate preceding machines, performing the same operations and one immediate succeeding machine that receives material from the buffer. For the case where the buffer reaches its own capacity, one of the two preceding machines has priority over the other to dispose its processed part into the buffer. Processing times are assumed to be deterministic and identical for all machines and are taken as the time unit. Geometrically distributed operation dependent failures at the machines are assumed. All possible transition equations for the examined model are derived and a recursive algorithm that generates the transition matrix for any value N of the storage level is developed. Once the transition matrix is known the performance measures of the model under consideration can be easily evaluated. This model may be used as a building block in a decomposition method to evaluate large production systems with split/merge operations (for example, flow lines with quality inspections and rework loops).     

Queuing network analysis approach for estimating the sizes of the time buffers in Theory of Constraints-controlled production systems

The present paper describes an open queuing network modelling approach to estimate the size of the time buffers in production systems controlled by the Theory of Constraints philosophy. Workstations in the production network are modelled as GI/G/m queues and a queuing network analysis multiproduct open queuing network modelling method is used to estimate the average flow time to the time buffer origin and the standard deviation of flow time. Using these two values together with an assumption of normally distributed flow times and a chosen service level, the final time buffer length is determined. The queuing network analysis method has been modified to enable the modelling of production networks with machine failures, batch service and varying transfer batch sizes. The modelling approach has also been incorporated in a computerized tool that uses product specific information such as bill-of-material and routing data, and production network information such as resource data to estimate the sizes and location of the necessary time buffers for each product. Simulation experiments indicate that the procedure is sufficiently accurate to provide an initial quick estimate of the needed time buffer lengths at the design stage of the line.     

A new method for the placement of buffers in serial production lines

The placement of buffers in a production line is an old and well-studied problem in industrial engineering/operations research that is still relevant today. Decisions regarding the amount and placement of buffers in a production line occur repeatedly in system design. In this paper we document a new buffer placement method for serial production lines that operate under a variety of assumptions. The method uses information generated in a production line simulation, whose conceptual representation of job flow and workstation interaction can be described with a network, to place buffers in order to maximise throughput. This buffer placement method is very efficient and can be implemented in a spreadsheet. We demonstrate the effectiveness of the method by comparing our results against those produced by a genetic algorithm for buffer placement. Experiments are conducted on a variety of test cases. This new buffer placement optimisation method will permit designers to quickly and effectively evaluate many design alternatives and thus improve final production system performance.     

Real time production improvement through bottleneck control

Variability is a key characteristic for evaluating the performance of a process. Small variability for a bottleneck machine can generate high production variability. Short-term production analysis and bottleneck identification are imperative for enabling optimal response to dynamic changes within the system. In comparison to the rich and abundant literature available on long-term analysis, only a small section of the literature addresses the dynamic bottleneck control policies, which may be used to maximise sustainable benefits. In this paper, a real time bottleneck control method is introduced to efficiently utilise the finite manufacturing resources and to mitigate the short-term production constraints by using two practical approaches: initial buffer adjustment and maintenance task prioritisation. The objective for real time bottleneck control is to obtain a continuous production improvement towards a balanced-line status to increase the throughput efficiently. The benefits of this method are presented by considering an industrial case study of an automotive assembly line. The results obtained from this case study show significant production improvements as compared to traditional approaches.     

Allocating buffer storages in a pull system

This report proposes a method of estimating the amount of safety stock needed in each station of a production line due to variation in processing times, machine breakdowns and demand fluctuation in order to meet a predetermined desired level of performance. The production line is assumed to operate as a pull system and the measure of performance is the average percentage of demand backlogged. Multiple machines and different batch sizes in the stations are included in the model. Dynamic production control is used and is based on the current inventory level in every station of the system. Simulation results are used to test the performance of the system in which the maximum inventory level allowed in each station is based on the estimation given by our method.     

A tabu search approach for buffer allocation in production lines with unreliable machines

The optimal allocation of buffers is an important research issue in designing production lines. In this study, a tabu search (TS) algorithm is proposed to find near-optimal buffer allocation plans for a serial production line with unreliable machines. The main objective is to maximize the production rate, i.e. throughput, of the line. The efficiency of the proposed method is also tested to solve buffer allocation problems with the objective of total buffer size minimization. To estimate the throughput of the line with a given specific buffer allocation, an analytical decomposition approximation method is used. The performance of the tabu search algorithm is demonstrated on existing benchmark problems. The results obtained by the TS algorithm are clearly encouraging, as the TS algorithm is much better than the other algorithms for all considered benchmark problems.     

Event-driven model of unreliable production lines with storage

We have developed an event-driven algorithm for simulating a factory production line with storage. Using this algorithm a production line, with an arbitrary number of machines each processing items at different rates and with buffers of any size, can be modelled efficiently. The algorithm is based on computing the time to the next event for each buffer and machine, where the events are: a buffer becomes full, a buffer becomes empty, a machine fails and a machine is repaired. By collapsing the production line to exclude empty buffers that stay empty and full buffers that stay full, piece-by-piece computation is avoided. Computation time is reduced further by updating a buffer only when the input or output rate of that buffer changes or when the state of that buffer changes. The implementation of this model is compared to a piece-by-piece simulator.     

Automatic Petri Net Simulation Model Generation for a Continuous Flow Transfer Line with Unreliable Machines

A production line is studied with several machines in series. The machines are separated with finite buffers. They can break down and have to be repaired. Production is assumed to be continuous, i.e. no individual products can be identified. Analytical models for the performance evaluation of such a system are scarce. Analytical results for the throughput can be obtained only under very restrictive assumptions. The performance study of longer transfer lines requires either approximation or simulation. A Petri net model is developed for an n‐machine ‐buffer system. The rules to design the Petri net transitions are given. The automatic generation of a discrete‐event simulation model from the Petri net model is explained. Finally, some potential applications of the Petri net are illustrated. These applications include the simulation of transfer lines with complex stochastic behaviour, the optimization of buffer size and allocation and the evaluation of approximation models for long transfer lines. Using the simulation model described in this paper, quality and reliability engineers can simulate the performance of a given continuous flow transfer line and evaluate the effect of performance‐increasing measures such as the insertion of extra buffer space or the use of more reliable machines. Copyright © 2004 John Wiley & Sons, Ltd.     

Approximate analysis of production systems operated by a CONWIP/finite buffer hybrid control policy

We present a decomposition method for approximate performance analysis of tandem production systems that are controlled by a hybrid control policy, in which the finite buffers of a flow line are augmented by a CONWIP cell enforcing release control to the line. The method decomposes the system into a set of three different types of building blocks. One is the continuous material two-machine line described in the literature; the second is a special case of the first in which the buffer is infinite. The third type of building block is a synchronization stage that is described and analyzed in this paper. Using these building blocks, we represent both the flow of material and the flow of information in the system. We derive new decomposition equations to relate the parameters of the building blocks. An iterative algorithm is constructed to determine the values of the parameters and to estimate the performance measures of the system. It has been observed to be fast and accurate for a large class of systems.     

Modeling and analysis of an unreliable flow line composed of parallel-machine stages

This paper focuses on flow lines composed of multiple parallel-machine stages. The system is similar to a classical flow line, the only difference being that a given stage may consist of parallel machines. A method for modeling and analyzing this type of flow lines is presented. The technique used amounts to replacing each parallel-machine stage by a single equivalent machine in order to obtain a classically-structured flow line with machines in series. Equations for computing the parameters of equivalent machines are submitted. These parameters can then be used to carry out performance diagnosis of the corresponding stage, or as input data for existing analysis methods to evaluate the production performance of flow lines. The method presented in this paper has been successfully implemented and tested in the industry over the past few years.     

Performance evaluation of a make-tO-stock production line with a two-parameter-per-machine policy: the control point policy

This paper presents a decomposition method for evaluating the performance of a production line with finite buffers controlled by the Control Point Policy (CPP), a policy with two parameters per machine. (One parameter is the buffer size; the other is a local hedging point.) Policies with two parameters per machine show very good performance while remaining simple to use. However, decomposition methods have not yet been developed for their analysis. We consider a production line, with exponentially distributed processing, failure, and repair times, controlled by a CPP. We decompose this line into two-machine CPP-controlled lines, which considerably simplifies the decomposition equations. Furthermore, the information loops are then included in the building blocks, and can be solved numerically. A numerical study shows that the method is accurate.     

Production Rate of Transfer Lines Without Buffer Storage

We consider transfer lines without buffer storage in between the machines and with synchronous transfer. The processing time of each machine is a constant but machines are unreliable. Our analysis is based on the overall completion time of the transfer line, which is the time between successive transfers of parts within the line. Two techniques are presented. The first one provides lower and upper bounds on the production rate. These bounds can be made as tight as desired. The second technique provides an approximation of the production rate. It is based on the approximation of some distributions by simpler distributions having the same mean and coefficient of variation. We first consider the case of transfer lines with identical processing times and exponential times to failure and times to repair. Extensions to different processing times and general repair times are also discussed.     

A linear programming approach to capacity estimation of automated production lines with finite buffers

This paper considers a highly automated manufacturing line which consists of a sequence of workstations. Relatively small buffers are assigned between workstations in order to guarantee a small manufacturing interval and quick feedback in the event of process failure to make acceptable product. These small buffers could lead to a noticeable loss of line capacity due to the phenomenon of blocking and starvation. We show by means of simple examples how the buffer sizes and the mix and loading sequence of different types of jobs could significantly affect the production rate of the line. A linear programming based method is then developed to estimate the line capacity for a given configuration of machines and buffers sizes and for a given job mix and sequence. This method also gives the expected machine utilizations, the time machines are blocked/starved and, more importantly, the reason for this lost production capacity. By judiciously interpreting this information, one or more of the following steps can be taken to improve the production rate: (a) change the loading sequence, (b) increase the buffer space selectively, (c) make the products in smaller or larger batches, and (d) add new machines.     

Modified drum–buffer–rope scheduling mechanism for a non-identical parallel machine flow shop with processing-time variation

The drum–buffer–rope (DBR) is a scheduling mechanism under the Theory of Constraints (TOC) philosophy. In DBR, ‘drum’ is a production schedule on the capacity-constrained resources (CCRs), which controls the speed of production for the whole system; ‘rope’ is a mechanism to release the required material to the CCRs; and ‘buffer’ is used to protect the CCRs from starvation due to statistical fluctuations. For a non-identical parallel machine flow-shop environment, estimating an efficient rope and time buffer for DBR implementation is not an easy task because of the complexity of non-identical parallel machine loading. This paper proposes a new scheduling method, which is called the modified DBR (MOD-DBR). It applies a backward finite capacity scheduling technique, including machine loadings and detail scheduling, instead of the rope mechanism in DBR. The scheduling performances of MOD-DBR are evaluated under variable processing time situations. The experimental results indicate that the MOD-DBR without a time buffer outperformed the DBR with a considerable level of buffer on the average flow time, while they have the same performance on tardiness, constraint resource utilization, and throughput.     

Analysis of approximately balanced production lines

This paper develops two analytical formulas for estimating the throughput of a reliable production line with exponential service times and finite intermediate buffers. The formulas apply in the case of an approximately balanced line with identical buffers or near optimal buffer allocations, where the processing times of the machines are close to each other but not necessarily the same. The derivation of the formulas is based on the standard decomposition method. Moreover, it is proved that, in general cases, both formulas provide upper bounds for the throughput obtained by the decomposition method. Numerical experiments show that the proposed formulas achieve good accuracy for approximately balanced production lines. Finally, the formulas are applied to the buffer allocation problem, and two closed-form expressions are obtained for estimating the smallest buffer capacity which is necessary to achieve the desired throughput.