Allocation of buffers to serial production lines with bottlenecks

The optimal placement of a predetermined amount of buffer capacity in balanced serial production lines is a well-understood problem: in lines with moderate variability, the optimal allocation involves equal numbers of buffers at each site; in lines with severe variability, the equal allocation is modified slightly to place more buffers toward the center of the line. Buffering unbalanced lines is a much less well-understood problem. We study the problem of buffering serial lines with moderate variability and a single bottleneck; i.e., a single station with a larger mean processing time than all other stations. Our analysis shows that a bottleneck station draws buffers toward it, but the optimal allocation depends on the location and severity of the bottleneck, as well as the number of buffers available. Furthermore, relatively large imbalances in mean processing times are required to shift the optimal buffer allocation away from an equal allocation. Finally, line length appears to have a relatively small effect on the optimal allocation with a given bottleneck. These results suggest that, at least for the class of lines studied here, equal buffer allocations may be optimal except in severely unbalanced lines. Furthermore, in severely unbalanced lines, throughput appears to be insensitive to the allocation of buffers.     

An algorithm for optimal buffer placement in reliable serial lines

The optima] allocation of buffer capacity in unbalanced production lines with reliable but variable workstations is a complex and little-researched topic. Analytic formulas for the throughput of these lines do not exist, so simulation is the only practical alternative for estimating throughput. Exhaustive search over all possible buffer allocations quickly becomes impractical beyond short lines and few buffers. Thus an algorithm is needed to efficiently find optimal or near-optimal allocations. We develop a simple search algorithm for determining the optimal allocation of a fixed amount of buffer capacity in an n-station serial line. The algorithm, which is an adaptation of the Spendley-Hext and Nelder-Mead simplex search algorithms, uses simulation to estimate throughput for every allocation considered. An important feature of the algorithm is that the simulation run length is adjusted during the running of the algorithm to save simulation run time when high precision in throughput estimates is not needed, and 10 ensure adequate precision when it is needed. We describe the algorithm and show that it can reliably find the known optimal allocation in balanced lines. Then we test the ability of the algorithm to find optimal allocations in unbalanced lines, first for cases in which the optimal allocation is known, and subsequently for cases in which the optimal allocation is not known. We focus particularly on lines with multiple imbalances in means and variances. In general, our algorithm proves highly efficient in finding a near-optimal allocation with short simulation run times. It also usually finds the true optimal allocation, but it is in the nature of this problem that many buffer allocations differ in throughput by small amounts that are difficult to resolve even with long simulation runs.     

An improved decomposition method for the analysis of production lines with unreliable machines and finite buffers

We consider production lines consisting of a series of machines separated by finite buffers. The processing time of each machine is deterministic and all the machines have the same processing time. All machines are subject to failures. As is usually the case for production systems we assume that the failures are operation-dependent (Buzacott and Hanifin 1978, Dallery and Gershwin 1992). Moreover, we assume that the times to failure and the times to repair are exponentially distributed. To analyze such systems, a decomposition method was proposed by Gershwin (1987). The computational efficiency of this method was later significantly improved by the introduction of the so-called DDX algorithm [Dallery et al. 1988, 1989). In general, this method provides fairly accurate results. There are however cases for which the accuracy of this decomposition method may not be so good. This is the case when the reliability parameters (mean times to failure and mean times to repair) of the different machines have different orders of magnitude. Such a situation may be encountered in real production lines. The purpose of this paper is to propose an improvement of Gershwin's original decomposition method that provides accurate results even in the above mentioned situation. The basic difference between the decomposition method presented in this paper with that of Gershwin is that the times to repair of the equivalent machines are modeled as generalized exponential distributions (Kouvatsos 1986) instead of exponential distributions. This allows us to use a two-moment approximation instead of a one- moment approximation of the repair time distributions of these equivalent machines.     

Selecting machines and buffers in unreliable series-parallel production lines

This article formulates a new optimal design problem of a series-parallel manufacturing production line, where parallel machines and in-process buffers are included to achieve a greater production rate. The objective is to maximise production rate subject to a total cost constraint. Machines and buffers are chosen from a list of products available in the market. The buffers are characterised by their cost and size. The machines are characterised by their cost, failure rate, repair rate and processing time. To estimate series-parallel production line performance, an analytical decomposition-type approximation is proposed. Simulation results show that this approximate technique is very accurate. The optimal design problem is formulated as a combinatorial optimisation one where the decision variables are buffers and types of machines, as well as the number of parallel machines. To solve this problem, ant colony optimisation and simulated annealing are compared empirically through several test problems.     

Predictive models for performance evaluation of serial production lines

An efficient predictive model is proposed for analysing the throughput rate of balanced serial production lines where all stations are identical and buffers between stations have the same capacity. The predictive model is based on the simulation data. The experimental design and analysis technique is used to conduct the simulation experiments and the regression analysis method is used to build the predictive model. The model can be applied to a wide range of values in terms of the coefficient of variation of processing times at stations, the buffer size between stations and the number of stations in a system. Comparisons are made with simulation results and previous works. The model can also be extended to account for situations where different stations have different coefficients of variation of processing times.     

Lean buffering in serial production lines with non-exponential machines

In this paper, lean buffering (i.e., the smallest level of buffering necessary and sufficient to ensure the desired production rate of a manufacturing system) is analyzed for the case of serial lines with machines having Weibull, gamma, and log-normal distributions of up- and downtime. The results obtained show that: (1) the lean level of buffering is not very sensitive to the type of up- and downtime distributions and depends mainly on their coefficients of variation, CV _up and CV _down ; (2) the lean level of buffering is more sensitive to CV _down than to CV _up but the difference in sensitivities is not too large (typically, within 20%). Based on these observations, an empirical law for calculating the lean level of buffering as a function of machine efficiency, line efficiency, the number of machines in the system, and CV _up and CV _down is introduced. It leads to a reduction of lean buffering by a factor of up to 4, as compared with that calculated using the exponential assumption. It is conjectured that this empirical law holds for any unimodal distribution of up- and downtime, provided that CV _up and CV _down are less than 1. Correspondence to: Semyon M. Meerkov     

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.     

Transient behavior of serial production lines with Bernoulli machines

The steady-state performance of production systems with unreliable machines has been analyzed extensively during the last 50 years. In contrast, the transient behavior of these systems remains practically unexplored. Transient characteristics, however, may have significant manufacturing implications. Indeed, if, for example, transients are sluggish and the steady state is reached only after a relatively long settling time, the production system may lose some of its throughput, thus leading to a lower efficiency. This paper is devoted to analytical and numerical investigation of the transient behavior of serial production lines with machines having the Bernoulli reliability model. The transients of the states (i.e., the probabilities of buffer occupancy) are described by the Second Largest Eigenvalue (SLE) of the transition matrix of the associated Markov chain. The transients of the outputs (i.e., production rate, PR, and work-in-process, WIP) are characterized by both the SLE and Pre-Exponential Factors (PEF). We study SLE and PEF as functions of machine efficiency, buffer capacity and the number of machines in the system. In addition, we analyze the settling times of PR and WIP and show that the former is often much shorter than the latter. Finally, we investigate production losses due to transients and show that they may be significant in serial lines with relatively large buffers and many machines. To avoid these losses, it is suggested that all buffers initially be half full. For two- and three-machine lines these analyzes are carried out analytically; longer lines are investigated by simulations.     

Effective process times for multi-server flowlines with finite buffers

An Effective Process Time (EPT) approach is proposed for the building of aggregate models to represent multi-server tandem queues with finite buffers. EPT distributions of the workstations in the flow line are measured without identifying the contributing factors. A sample path equation is used to compute the EPT realizations from arrival and departure events of lots at the respective workstations. If the amount of blocking in the line is high, the goodness of fits of the EPT distribution determines the accuracy of the EPT-based aggregate model. Otherwise, an aggregate model based on just the first two moments of the EPT distributions is sufficient to obtain accurate predictions. The approach is illustrated in an industrial case study using both simulation and analytical queueing approximations as aggregate models.     

Reducing energy consumption in serial production lines with Bernoulli reliability machines

This paper is devoted to developing an integrated model to minimise energy consumption while maintaining desired productivity in Bernoulli serial lines with unreliable machines and finite buffers. For small systems, such as three- and four-machine lines with small buffers, exact analysis to optimally allocate production capacity is introduced. For medium size systems (e.g. three- and four-machine lines with larger buffers, or five-machine lines with small buffers), an aggregation procedure to evaluate line production rate is introduced. Using it, optimal allocation of machine efficiency is searched to minimise energy consumption. Insights and allocation principles are obtained through the analyses. Finally, for larger systems, a fast and accurate heuristic algorithm is presented and validated through extensive numerical experiments to obtain optimal allocation of production capacity to minimise energy consumption while maintaining desired productivity.     

光电经纬仪中高速串行通信的一种新途径

IEEE 1394是一种新型的高速串行总线标准,支持400Mbps到3.2Gbps的串行数据传输速率。介绍了IEEE 1394的总体性能和体系结构,回顾了以往应用于光电经纬仪中串行数据传输的几种技术,分析了它们各自的特点与不足,提出了采用IEEE 1394的光电经纬仪中串行数据传输的实验性方案。     

A new model for open-pit production and waste-dump scheduling

An open-pit mine schedule defines the optimal sequence of mining valuable (ore) and waste material with the objective of maximizing the value of the project. Given this production schedule, a waste-dump schedule is then developed to determine the optimal waste-rock allocation in waste dumps. Thus, production and waste-dump schedules are managed separately, which leads to an inappropriate consideration of the material haulage cost, suboptimal schedules generating less value, and the incorrect classification of ore and waste. This article proposes a mixed-integer programming-based model that determines the optimal production and waste-rock dumping schedule concurrently with the objective of maximizing the discounted cash flow [net present value (NPV)] of the project. An implementation of the proposed model on a gold-mining operation outperforms the two existing methods [traditional and two-step mixed-integer programming (TSMIP) model] in the context of project NPV as well as its practicality.     

A mixed-integer programming formulation and Lagrangean relaxation for the cross-dock door assignment problem

In a cross-dock, goods are unloaded from incoming trucks, consolidated according to their destinations, and then, loaded into outgoing trucks with little or no storage in between. In this paper, we study the cross-dock door assignment problem in which the assignment of incoming trucks to strip doors, and outgoing trucks to stack doors is determined, with the objective of minimising the total material handling cost. We present a new mixed integer programming formulation which is embedded into a Lagrangean relaxation that exploits the special structure of the problem to obtain bounds on the optimal solution value. A primal heuristic is used at every iteration of the Lagrangean relaxation to obtain high quality feasible solutions. Computational results obtained on benchmark instances (with up to 20 origins and destinations, and 10 strip and stack doors) and on a new and more difficult set of instances (with up to 50 origins and destinations, and 30 strip and stack doors) confirm the efficiency of the algorithm.     

一种激光引信成像探测新方法

提出了激光引信环视扫描成像探测新方法,其原理是探测目标表面反射回波,是主动探测方式。该方法成像独特,利用弹目交会过程中的周向扫描和相对高速运动,使目标各部位依次进入和退出探测视场来完成对目标各部位成像探测。通过目标回波功率和图像边缘弱化的计算,获得目标二维形体图像。以后对图像进行处理,识别出目标易损部位并输出弹目交会信息作为引爆控制信号,对战斗部实施定向起爆控制,以精确打击目标。仿真结果表明,该成像探测方法及所建仿真模型是正确有效的。     

Performance analysis for serial production lines with Bernoulli Machines and Real-time WIP-based Machine switch-on/off control

In recent years, achieving high energy efficiency has become one of the primary goals in manufacturing, along with maintaining high productivity and quality. In many manufacturing systems, it is sometimes possible to temporarily switch off a machine to reserve energy, and switch it back on when a certain condition is met. Indeed, production control-based shop floor continuous improvement is recognised as one of the most cost-effective ways to achieve energy-efficient production. In this paper, we study serial production lines with Bernoulli machines and finite capacity buffers and assume that some of the machines in the line can be switched on and off during the production process according to a state-based feedback control policy. Mathematical models for the system under consideration are derived and analytical methods are developed for calculating the system performance measures during transients. Specifically, exact Markovian analysis is used for two- and three-machine lines in which the switch-on/off operations of only one machine is considered. For longer lines, the switch-on/off operations of multiple machines are considered and an aggregation-based approximation approach is applied to evaluate the system performance measures. Numerical experiments show that the method developed can be used to efficiently calculate the system’s performance with high accuracy.     

The effect of breakdowns on U-shaped production lines

Consider a synchronized line performing assembly or fabrication tasks. Tasks are grouped into stations and stations are positioned on a line that is U-shaped. Stations may break down and be repaired. Small buffer inventories may be placed between stations to lessen the effect of breakdowns at one station on production at other stations. This paper investigates the effect of the U-shape of the line on the line effectiveness. We find that effectiveness increases when the line is U-shaped, compared with the traditional straight line shape.     

A decision support system for the design of unpaced production lines

Consider a realistic unpaced-line problem: there is a set of discrete tasks, whose task-time distributions have diverse shapes. The line designer must (i) decide to which work station to assign each task, and (ii) specify the size of each buffer area in such a way that the configuration has the ‘best’ operating characteristics. This paper describes a decision support package that can efficiently generate the operating characteristics of the many alternative line designs which the line designer may want to try. We also show that the package can be conveniently used to extend earlier results in theoretical unpaced-line research.     

Multi-job production systems: definition,problems, and product-mix performance portrait of serial lines

This paper pursues two goals: (a) Define a class of widely used in practice flexible manufacturing systems, referred to as Multi-Job Production (MJP) and formulate industrially motivated problems related to their performance. (b) Provide initial results concerning some of these problems pertaining to analysis of the throughput and bottlenecks of MJP serial lines as functions of the product-mix. In MJP systems, all job-types are processed by the same sequence of manufacturing operations, but with different processing time at some or all machines. To analyse MJP with unreliable machines, we introduce the work-based model of production systems, which is insensitive to whether single- or multi-job manufacturing takes place. Based on this model, we investigate the performance of MJP lines as a function of the product-mix. We show, in particular, that for the so-called conflicting jobs there exists a range of product-mixes, wherein the throughput of MJP is larger than that of any constituent job-type manufactured in a single-job regime. To characterise the global behaviour of MJP lines, we introduce the Product-Mix Performance Portrait, which represents the system properties for all product-mixes and which can be used for operations management. Finally, we report the results of an application at an automotive assembly plant.