System performance analysis of flexible flow shop with match processing constraint

Blocking makes the analytical modelling of open queuing networks with finite buffers intractable because the product-form solutions are unavailable. In this paper, about mould manufacturing, a four-stage flexible flow shop with match processing constraint is first modelled as an open queuing network with finite buffers. According to the characteristics of the matching node, the inter-arrival time distributions of parts arriving at the nodes are assumed to be exponential or general. Next, based on approximation of queuing theory, the Decomposition of State Space Method and the Generalized Expansion Method are developed for system performance evaluation. Then, experiments to assess the accuracy of the proposed methods are reported by comparing the analytical results with simulations. Finally, a case of a real-life production system of mould manufacturing is studied to show the application of the proposed methods. The results of experiments reveal that the proposed methods are feasible and effective for system performance evaluation and they can even solve large-size practical problems in a reasonable time. The results in this paper can provide a basis for system design or resource planning, to solve buffer allocation problems and capacity configuration problems.     

Performance analysis of open general queuing networks with blocking and feedback

Queuing network models have been extensively used for performance evaluation in many modern manufacturing and communication systems. The phenomenon of feedback reflects many practical situations, e.g. reworking in the production systems. However, existing research on open queuing network with feedback mainly concentrates on the models with infinite buffers or the models with finite buffers but exponentially distributed inter-arrival and service times. Research on open queuing networks with finite buffers, feedback and general inter-arrival and service times has not been reported. In this paper, a Rate Iterative Method embedded with the Generalised Expansion Method, is proposed for modelling this type of queuing network. System performance measures include the mean throughput, work-in-process and sojourn time all calculated by the proposed method. The accuracy and the efficiency of the proposed method are tested by comparing the results with other methods or simulation results from the experiments. Finally, a case study of a practical production system used in the manufacturing industry is studied and illustrates the applications of the proposed method. The results in this paper can be used as a basis for system design analysis and resource planning.     

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.     

Capacity estimation of a multi-product unreliable production line

This paper addresses the problem of capacity estimation of a multi-product production line composed of m unreliable workstations and ( m - 1) intermediate buffers. A simulation-based experimental design methodology is proposed to improve the performance of this flexible production line, which is expressed as the cycle time. The modelling approach integrates, in a more representative manner, the many parameters that impact the capacity of the manufacturing system. These are: workstation failure, repair, and set-up as product type changes. An experimental optimization to judiciously locate/allocate buffers between workstations is used to determine the maximum contribution of buffers on the overall performance of this serial manufacturing system. A case study is presented to show the modelling steps and to assess the contribution of each buffer. Analysis of the results shows the trade-offs between the different levels of buffers and the cycle time of the production line. The results present the percentage of workstations' operation, set-up, downtime, blocking and starving. In addition, for each combination of buffer sizes, the bottleneck workstation is identified. Changing a buffer size impacts directly the cycle time and, in some cases, a new bottleneck workstation evolves. The results provide insights into the performance of the system, including detection of important interactions and critical parameters. Considering various design scenarios, our methodology helps to identify the best strategy of buffer location/allocation that ensures a minimum cycle time, while considering other criteria. This could be achieved with less experimental effort and the manager could make the selection of the best design scenario. An analysis of the dynamic behaviour of buffers and their effectiveness is also given and commented upon.     

Analytical model to estimate performances of autonomous vehicle storage and retrieval systems for product totes

In today's competitive scenario of increasingly faster deliveries and smaller order sizes, material-handling providers are progressively developing new solutions. A recent, automated material-handling technology for unit load storage and retrieval consists of an autonomous vehicle storage and retrieval system (AVS/RS). The present paper presents an analytical model to estimate the performances (the transaction cycle time and waiting times) of AVS/RS for product tote movement. The model is based on an open queuing network approach. The model effectiveness in performance estimation is validated through simulation.     

Semi-open queuing networks: a review of stochastic models,solution methods and new research areas

Capturing the waiting times (at an external queue) for a customer to access a movable resource is an important step towards measuring customer service and system performance in manufacturing, logistics, communication and health care systems. Such waiting time measures are typically used for sizing resource and buffer capacities, and thereby minimising customer waiting time probabilities. In this regard, semi-open queuing networks (SOQNs), which decouple the arriving customers/transactions from the network resources using a synchronisation station (also known as a semaphore queue), can potentially capture the customer/transaction waiting times/costs more precisely and provide a rich network modelling construct. Hence, modelling manufacturing or service systems using SOQNs is an important step towards measuring customer flow times (sojourn times) wherein the customer waiting times at an external queue are a critical component. In this paper, we present several stochastic models for manufacturing and service systems using SOQNs and also discuss the potential applications of SOQNs. We then review the solution methods for SOQNs and also compare the numerical accuracies for three promising methods. Finally, we include the potential research areas in SOQNs.     

Optimal feeding buffers for projects or batch supply chains by an exact generalization of the newsvendor result

In project scheduling or batch supply chain operations, a positive (negative) feeding buffer is created by starting an activity before (after) its expected latest start time. Positive feeding buffers provide protection against project tardiness. Assuming linear costs for starting activities earlier and a linear project tardiness penalty, early optimization models for project buffers addressed particular project network structures. By these models it can be shown that when the gating activities precede the only stochastic elements in a project, then there exists an exact generalization of the newsvendor optimal result that characterizes the optimal feeding buffers: the marginal cost of a buffer should match its criticality. This insight is associated with an effective and efficient solution approach by simulation. We show that this result also holds when stochastic elements exist anywhere else within the project and when activities are statistically correlated. Furthermore, the same simulation approach applies. This yields practically optimal feeding buffers even when it is impossible to compute the completion time distribution.     

Two-level manufacturing system performance analyser

Open queuing network is a commonly used analytical tool for modelling manufacturing systems. Parametric decomposition is a proven solution method for analysing open queuing networks and can estimate key performance measures such as work-in-process inventory, cycle time, and machine utilisation, fairly accurately. This paper presents a two-level hierarchical open queuing network model, which considers numerous features seen in a real manufacturing system including, machine set-up, material handling device setup (for example, loading and unloading operations), process as well as transfer batching, empty travel of the material handling device and machine or material handling device failures. The model first analyses a higher level open queuing network whose nodes are aggregations of a set of machines. The higher level network is solved via the parametric decomposition method and the results are then disaggregated to get lower level, e.g. machine specific, results. The motivation, algorithm and its relationship with the one-level model are discussed. Experimental results are provided to show that the two-level model provides comparable results with the one-level model in addition to its computational and managerial advantages. In addition, both are shown to provide better results than a recent method available in the literature that is based on the well-known queuing network analyser.     

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.     

Optimal batching in a wafer fabrication facility using a multiproduct G/G/c model with batch processing

Wafer fabrication, the first portion of semiconductor manufacturing, typically involves numerous batch-processing operations. These operations play an important role in determining how the system performs in terms of throughput, WIP and cycle time. In this paper, batch sizes that minimize the expected cycle time of batch-processing operations for a real-world semiconductor manufacturer are determined by a new approximated analytical model. This model, denoted by G / G ( bp ) , represents multiple products, multiple servers, batch-processing, incompatible products and unequal batch service size queues. Incompatible products mean that different products are not allowed to be in the same batch. Unequal batch service size means that batch service sizes depend upon products. Steady-state approximation formulas for cycle time and WIP of this queuing system are derived. These approximate performance measures are compared with those of discrete-event simulation. The results are reasonable and the approximation formulas much more computationally efficient than conducting the corresponding simulation studies. Finally, a batch-processing system with the goal of minimizing the total expected cycle times of items by determining the 'optimal' batch sizes is presented. Solutions are obtained using genetic algorithms.     

Determining inventory levels in a CONWIP controlled job shop

We extend the concept of CONWIP control to a job shop setting, in which multiple products with distinct routings compete for the same set of resources. The problem is to determine the fixed overall WIP level and its allocation to product types (WIP mix) to meet a uniformly high customer service requirement for each product type. We formulate an optimization problem for an open queuing network model in which customer orders pull completed products from the system. Then, assuming heavy demand, we derive a throughput target for each product type in a closed queuing network and provide a simple heuristic to find a minimum total WJP and WIP mix that will achieve an operating throughput close to this target. In numerical examples, the WIP mix suggested by this approach achieves the customer service requirement with a relatively low total WIP     

Large production line optimization using simulated annealing

We present a robust generalized queuing network algorithm as an evaluative procedure for optimizing production line configurations using simulated annealing. We compare the results obtained with our algorithm to those of other studies and find some interesting similarities but also striking differences between them in the allocation of buffers, numbers of servers, and their service rates. While context dependent, these patterns of allocation are one of the most important insights which emerge in solving very long production lines. The patterns, however, are often counter-intuitive, which underscores the difficulty of the problem we address. The most interesting feature of our optimization procedure is its bounded execution time, which makes it viable for optimizing very long production line configurations. Based on the bounded execution time property, we have optimized configurations of up to 60 stations with 120 buffers and servers in less than five hours of CPU time.     

面向定制生产系统的缓冲区优化配置方法

针对定制型装备制造企业中具有有限缓冲区的开排队网制造单元,其车间负荷界限即缓冲设置难以确定的问题（buffer allocation problem,BAP）,文章对每阶段具有有限缓冲区且含有多台加工设备的三阶段柔性流水车间(flexible flow shop,FFS)进行排队网建模,应用状态空间分解法对该模型进行分析求解,获得系统的一系列性能指标值。为了对该方法的有效性进行验证,对该模型设计仿真实验,并利用扩展法对模型进行求解,将数值结果进行比较分析,验证了利用该方法对FFS缓冲区进行优化配置的合理性,这对较大规模的多节点每阶段具有多台设备的流水车间负荷界限的有效设定及其规划具有参考和指导意义。     

Using queuing theory and simulated annealing to design the facility layout in an AGV-based modular manufacturing system

An automated guided vehicle-based flow production system is used for manufacturing prefabricated bathroom units. One unit can occupy a space of more than 10?m². Due to large time deviations in sequential processes, queues are formed and greater plant space is needed. Reducing work-in-progress helps to save plant space but renders manufacture less efficient. The research explores better workstation arrangements. An open queuing network (OQN) model was used to approximate the flow production system. Since the problem of workstation arrangement is a combinatorial optimisation problem, simulated annealing (SA) was applied to search for a good solution. The combination of an OQN model and SA provides a powerful tool to solve the facility layout problem for a stochastic flow production system. The experimental results show that the proposed approach has the potential to guide industrial layout design and practice.     

一类批处理排队网络的稳定性

在标准排队网络稳定性研究的基础上,本文通过引进批长度随机向量,确立了一类批处理排队网络的流体模型和对应的标准排队网络的流体模型。证明了在批优先排队原则下,这两类排队网络的流体模型具有相同的稳定性,为批处理排队网络的稳定性研究提供了一种有效的方法。     

Detecting bottlenecks in serial production lines – a focus on interdeparture time variance

This work addresses an important problem in industry – locating the bottleneck in a production line – and suggests a practical approach to accomplish that end. We describe and validate, using discrete event simulation, a novel method of bottleneck detection in open, asynchronous serial production lines with finite buffers. The technique uses a single measure – station interdeparture time variance – to locate the system bottleneck. The proposed method is compared to other bottleneck detection approaches and it is shown that the proposed method performs as well and sometimes better than other methods. We conclude that the proposed approach has a number of significant advantages. It is easy to use and implement, not requiring data about failure and repair times, raw process times, buffer sizes, etc., but instead uses a single piece of easily obtained real-time production line data – station work-in-process (WIP) interdeparture time. The proposed method can identify production constraints without the need to build an analytical or simulation model, is well suited for use in industry, and can be readily implemented in standard simulation tools.     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

Approximation of Flow Lines with Integrally Controlled Buffers

Production lines with integral control limits are studied in this paper. The behaviour of such lines can be shown to be approximated by that of flow lines with local buffers. The reduction of an integrally controlled line to a locally controlled one is computationally simple and accurate in the estimation of such performance measures as throughput, probabilities of buffers being full or empty and throughput time.

The advantage of such a reduction is that good techniques are available for estimating the performance of flow lines with local buffers only. Furthermore, a direct method is described for obtaining an estimate of the throughput of lines with integrally controlled buffers only. In the model used here, the product flow is continuous and the production units are unreliable. Both lifetimes and repair times of machines are distributed exponentially.     

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.     

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.