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.     

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.     

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.     

Optimal buffer allocation in production lines

The optimal allocation of buffers in production lines is an important research issue in the design of a manufacturing system. We present a new hybrid algorithm for this complex design problem: the hybrid Nested Partitions (NP) and Tabu Search (TS) method. The Nested Partitions method is globally convergent and can utilize many of the existing heuristic methods to speed up its convergence. In this paper, we incorporate the Tabu Search heuristic into the NP framework and demonstrate through numerical examples that using the hybrid method results in superior solutions. Our numerical results illustrate that the new algorithm is very efficient for buffer allocation problems in large production lines.     

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.     

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.     

Buffers and backup machines in automatic transfer lines

Buffer storage of the work-in-process inventory, decouples successive stages of automatic transfer production lines, assuring partial operability under machine failure. Certain special features such as secondary (standby) machines, special maintenance and diagnostic systems can lengtben the uptime or shorten the downtime of individual stages. When special features for K stages and spaces for M buffers are available, it is of great interest to system designers to know which stages should have the special features and where the buffer spaces should be inserted to maximize the line output rate. This paper addresses itself to such design problems. A bivariate dynamic programming procedure is developed which provides a layout for the buffers and an allocation of special features, maximizing the line output rate as defined by Buzacott (1967, 1968). The Buzacott formula is based on a heuristic argument which provides, in general, an upper bound on the true system output rate.     

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.     

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.     

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.     

Joint optimization of maintenance,buffers and machines in manufacturing lines

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.     

Performance evaluation of production lines with finite buffer capacity producing two different products

This paper presents an approximate analytical method for the performance evaluation of a production line with finite buffer capacity, multiple failure modes and multiple part types. This paper presents a solution to a class of problems where flexible machines take different parts to process from distinct dedicated input buffers and deposit produced parts into distinct dedicated output buffers with finite capacity. This paper considers the case of two part types processed on the line, but the method can be extended to the case of n part types. Also, the solution is developed for deterministic processing times of the machines which are all identical and are assumed to be scaled to unity. The approach however is amenable of extension to the case of inhomogeneous deterministic processing times. The proposed method is based on the approximate evaluation of the performance of the k-machine line by the evaluation of 2(k-1) two-machine lines. An algorithm inspired by the DDX algorithm has been developed and the validation of the method has been carried out by means of testing and comparison with simulation. Correspondence to: T. Tolio     

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.     

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.     

一种飞船返回舱座椅缓冲器力学特性设计

建立了一个典型的飞船返回舱座椅缓冲系统垂直着陆冲击的动力学响应模型,分析了不同工况对于缓冲器特性的要求,针对定缓冲力阈值的缺点,提出了分段变缓冲力的设计和分析方法,并给出了典型条件下的三段缓冲力方案设计的实例.结果表明,变缓冲力的设计方法可以更加优化缓冲特性,满足不同工况对加速度、加速度的增长率、阈值、行程的限制和要求;对于特定的系统,综合各个方面因素可以得到优化的缓冲力设计组合方案;而采用更多的节段设计会适应更宽的着陆工况范围.     

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.     

PERFORMANCE ANALYSIS OF A TRANSFER LINE WITH UNRELIABLE MACHINES AND FINITE BUFFERS

This paper examines the performance analysis of a transfer line with unreliable machines and finite buffers. All machines have the same processing times. We propose a new decomposition method which decomposes a line into a set of two-machine lines. A set of equations is established to find performance measures such as production rate and average buffer levels. A simple iterative algorithm is then proposed to solve these equations. We also prove that the set of decomposition equations has a unique solution and that die computation algorithm converges to this unique solution. Experimental results show that the computation algorithm leads to a good solution.     

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.     

A stochastic model of an unreliable kanban production system

We analyze a stochastic model of a production line withk stations (machines) in series. There are finitecapacity buffers between the machines and at the end of the line. The movement of the workpieces through the line is demand-driven, i.e. we deal with a pull (kanban) production system. Processing times are assumed to be deterministic and constant. There are two sources of randomness in the model: Demand for workpieces from outside is stochastic, and the machines may break down (and then be repaired) with a given probability. A demand from outside is lost if the final buffer is empty. This system is described by a discrete-time Markov chain. The steadystate distribution is given for k=1. This is the basis of a decomposition algorithm which approximates the throughput of the line and the percentage of satisfied demand for arbitraryk. A comparison with simulation results shows that this algorithm is very accurate.     

Planning of buffers within mixed-model lines

Summary This paper deals with the planning of buffers within a mixed-model line, which is typical of vehicle industries. The positioning of the buffers will be of special interest and will be discussed by an exact method and three heuristics. In addition the determining of buffer sizes will briefly be addressed. All aspects are considered concerning their influence on scheduling criteria. We will demonstrate that the placing of buffers leads to an improvement in job sequencing problems. In particular a balanced capacity usage will be achieved.