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.     

Extending economic design of p charts to handle user specified constraints using a genetic algorithm

For certain processes, the quality of the output can be monitored using attribute inspection statistical process control. Various approaches have been used to determine optimal or near-optimal parameters for such a plan. Since most of these approaches use an unconstrained model, some solutions can result in theoretical and pragmatic problems. In this paper we used Duncan's loss function as the objective function for the development of a Genetic Algorithm (GA). In addition to formulating a GA to find a solution to the model, user constraints concerning the frequency of inspection, the number of defects allowed and the production rate are used to limit the search space for the GA. The GA is selected over other search techniques such as traditional calculus-based, enumeration, or undirected random search methods because the GA is more robust than other search techniques.     

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.     

Optimal buffer space size in two-stage machining systems with Markovian or non-Markovian tool life processes

This paper presents a model for obtaining the optimal buffer space size in two-stage machining systems. It is shown that the optimal buffer space size is the one necessary to keep the critical machine running even when there are tool failures and subsequent tool changes on the non-critical machine. An analytical expression for the optimal buffer space size is derived when tool failures follow a Markovian process and the objective function is the minimization of the unit cost. A simulation mode! is developed for obtaining the optimal buffer space size when tool failures follow a non-Markovian process. It is shown that the optimal buffer space size depends on the expected delay time per part due to tool failures on the non-critical machine (which depends on the probability of tool failure on the non-critical machine during machining on the critical machine), on the labour and the buffer space cost, and on the tool-change time. The model can be extended to cover the case of two or more identical parallel machines per stage and the case of multi-stage machining systems.     

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.     

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.     

Integrated quality and quantity modeling of a production line

During the past three decades, the success of the Toyota Production System has spurred much research in manufacturing systems engineering. Productivity and quality have been extensively studied, but there is little research in their intersection. The goal of this paper is to analyze how production system design, quality, and productivity are inter-related in small production systems. We develop a new Markov process model for machines with both quality and operational failures, and we identify important differences between types of quality failures. We also develop models for two-machine systems, with infinite buffers, buffers of size zero, and finite buffers. We calculate total production rate, effective production rate (ie, the production rate of good parts), and yield. Numerical studies using these models show that when the first machine has quality failures and the inspection occurs only at the second machine, there are cases in which the effective production rate increases as buffer sizes increase, and there are cases in which the effective production rate decreases for larger buffers. We propose extensions to larger systems. Correspondence to: Stanley B. GershwinWe are grateful for support from the Singapore-MIT Alliance, the General Motors Research and Development Center, and PSA Peugeot-Citroën.     

Characterizing the optimal allocation of storage space in production line systems with variable processing times

We consider the optimal allocation of buffer storage spaces in unpaced production lines with variable processing times. It is known that for a fixed total number of buffer spaces, the production rate can often be improved by deliberately unbalancing the buffer allocations in an inverted bowl pattern (the storage bowl phenomenon), with more storage space allocated to the internal stations than to the end stations. It has been hypothesized that if the total number of buffer spaces is also a decision variable, then for a reasonable cost model the optimal allocation would have one additional storage space at each of the internal stations. This paper uses a cost model to show that the optimal allocation is more complicated than this. For balanced lines, the inverted bowl pattern is typically optimal, but the bowl shape becomes more and more pronounced (in an absolute sense) with larger numbers of buffer spaces. However, the relative shape of the bowl stays fairly constant. However, if the workload is unbalanced, the buffer space pattern deviates from the bowl pattern by reducing the number of buffer spaces in buffers that are not adjacent to the bottleneck machine.     

ON THE USE OF BUFFER INVENTORIES TO MINIMIZE COSTS WITH AN UNRELIABLE MACHINE

In this paper, we discuss the problem of quality control with an unreliable machine which produces defects at a rate of Λ₀, per unit when in-control and a rate of Lambda; ₁, when out-of-control (where Λ₁ Λ ₀). Every h time periods, we sample n units, count the number of defects, and (using a process based on a Shewart c-chart) test the hypothesis that the machine is in control by comparing the total number of defects to an upper control limit (UCL). More important, we introduce the concept that a buffer inventory which immediately follows the unreliable machine may reduce expected total costs. This buffer serves to delay the movement of items from the unreliable machine to the next stage of the production process. In this way, we can isolate and repair most defective items before they are embedded in a product downstream or sold to customers where repair is more costly. To search for the optimal control policy, we find bounds for n, h, and UCL; given values for these variables, we show how the optimal buffer size can be determined directly. Numerical results illustrate the magnitude of potential savings.     

Automated production line design with flexible unreliable machines for profit maximization

A model is presented for jointly determining the profit-maximizing configuration of machines (both type and number) and buffer capacities along an automated flexible production line. A heuristic solution procedure is developed for the general case of finite buffer capacities. The procedure combines an optimal solution algorithm for the case of infinite buffers with a heuristic algorithm which determines the finite buffer capacities.     

Determination of Optimal Buffer Storage Capacities and Optimal Allocation in Multistage Automatic Transfer Lines

One way to improve the efficiency of automatic transfer lines is to provide intermediate storage buffers. These buffers divide the transfer line into stages, each with one or more machines. The machines in a stage are completely integrated, whereas, the stages are partially decoupled. Here, we study a problem related to buffer storage allocation. The objective is to find optimal distribution of a total storage space among the intermediate buffers. This is formulated as a dynamic programming problem and a heuristic solution is presented.     

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.     

Job-shop scheduling with limited capacity buffers

In this paper we investigate job-shop problems where limited capacity buffers to store jobs in non-processing periods are present. In such a problem setting, after finishing processing on a machine, a job either directly has to be processed on the following machine or it has to be stored in a prespecified buffer. If the buffer is completely occupied the job may wait on its current machine but blocks this machine for other jobs. Besides a general buffer model, also specific configurations are considered. The aim of this paper is to find a compact representation of solutions for the jobshop problem with buffers. In contrast to the classical job-shop problem, where a solution may be given by the sequences of the jobs on the machines, now also the buffers have to be incorporated in the solution representation. In a first part, two such representations are proposed, one which is achieved by adapting the alternative graph model and a second which is based on the disjunctive graph model. In a second part, it is investigated whether the given solution representation can be simplified for specific buffer configurations. For the general buffer configuration it is shown that an incorporation of the buffers in the solution representation is necessary, whereas for specific buffer configurations possible simplifications are presented.     

On the Optimality of a Simplified Multicharacteristic Component Inspection Model

Inspection for multicharacteristic components is an important means to assure product quality. A component is inspected with respect to its characteristics of which non-conformance of one would result in the rejection of the component. Based on a cost-minimization model developed recently by Raoul et al., this paper develops a simplified version of the model to capture the cost implication of false rejection, false acceptance and inspection of the components. The simplified model is computationally more efficient than the earlier one. Optimality of the sequencing of characteristics to be inspected is explored. Based on the simplified model, the optimal number of cycles for inspection can be readily determined. A stopping rule is developed for the search of the optimal number of cycles. Sufficient conditions for performing one cycle of inspection or no multicharacteristic inspection at all are given. Finally, the results are extended to the case where the probabilities of defectives are random.     

Risk-informed optimisation of railway tracks inspection and maintenance procedures

Nowadays, efforts are being made by the railway industry for the application of reliability-based and risk-informed approaches to maintenance optimisation of railway infrastructures, with the aim of reducing the operation and maintenance expenditures while still assuring high safety standards.In particular, in this paper, we address the use of ultrasonic inspection cars and develop a methodology for the determination of an optimal strategy for their use. A model is developed to calculate the risks and costs associated with an inspection strategy, giving credit to the realistic issues of the rail failure process and including the actual inspection and maintenance procedures followed by the railway company.A multi-objective optimisation viewpoint is adopted in an effort to optimise inspection and maintenance procedures with respect to both economical and safety-related aspects. More precisely, the objective functions here considered are such to drive the search towards solutions characterized by low expenditures and low derailment probability. The optimisation is performed by means of a genetic algorithm. The work has been carried out within a study of the Norwegian National Rail Administration (Jernbaneverket).     

Scheduling of a job-shop problem with limited output buffers

ABSTRACT

This article addresses a job-shop problem with limited output buffers (JS-LOB) with the objective of minimizing the process makespan. An integer nonlinear mathematical programming model is proposed to describe this problem. Based on the model, a two-stage algorithm consisting of obtaining feasible solutions and a local search is proposed to solve the JS-LOB problem. The local search has two operators: the first is a neighbourhood structure based on a disjunctive graph model, and the second is similar to crossover in the genetic algorithm to avoid falling into local optima. Computational results are presented for a set of benchmark tests. The results show the effectiveness of the proposed algorithm and indicate whether the processing time of the job conforms to a uniform distribution. When the proportion between the capacity of the buffer and the number of jobs is larger than 20%, the influence of the buffer becomes very small.     

Enhancement of Theory of Constraints replenishment using a novel generic buffer management procedure

Managing a distribution system requires the right inventory in the right place at the right time. A Theory of Constraints replenishment solution is presented to aggregate inventory buffers at the central warehouse in plant and change the mode of operation from push to pull. The solution is powerful, but the optimal amount of buffer remains undetermined. In Theory of Constraints, choosing a specific buffer size is not crucial if the buffer is accurately monitored in a timely manner. Accordingly, Theory of Constraints is offered a buffer management approach for monitoring the buffer. Such buffer management is feasible and effective but is insufficiently rigorous. This paper elucidates a generic buffer management procedure, based on the concept of Theory of Constraints buffer management that rigorously defines a method of monitoring to size and adjust the buffer. An example demonstrates the feasibility of the proposed generic buffer management procedure.     

Economical Quality Control Policies for a Single Cause System

We consider four types of process control procedures; variables control charts, attributes control charts, a never-inspect policy, and a regular inspection policy consisting of periodic process reset and/or repair. Using a designed experiment, we compare the optimal economic designs associated with these policies for a practical range of costs and other system parameters. We find that the regular inspection policy is economically optimal in many configurations. Moreover, we find that the type of policy that yields minimum cost depends primarily on the expected magnitude of the process shift, the relative cost of variable versus attribute sampling, and the expected search time for an assignable cause. Some general guidelines for the appropriate type of control procedure for use in practice are given.     

Economic development of specifications for 100% inspection based on asymmetric quality loss functions

As a means of providing protection for both the producer and the consumer, for example as in airport security, 100% inspection plays an important role in today's environment. The same is true for some industrial or other decision-making processes where the consequences of excessive deviations from target values are very high. Motivated by Deming's “all or none” inspection rule and associated philosophy for quality improvement, we develop an inspection strategy by considering the costs to both the producer and the customer, and thus to the whole system. A general optimization model is formulated to determine whether 100% inspection is to be performed or no inspection to be performed. If complete inspection is chosen then the optimal specification limits can be determined at the same time. Specifically, we consider two types of asymmetric quality loss functions for the “target the best” quality characteristic: the asymmetric quadratic quality loss function, and the asymmetric piecewise linear loss function. For each loss function, we propose an optimization model to determine the optimal process mean and specification limits. Numerical examples are given to illustrate the proposed models that can be used to improve the quality of the output of any process.     

Optimisation design of attribute control charts for multi-station manufacturing system subjected to quality shifts

The qualities of products are a major concern in any production system; thus implementing efficient inspection policies is of great importance to reduce quality-related costs. This article addresses the problem of finding optimal inspection policies for the multi-station manufacturing system (MMS) subjected to quality shifts to minimise total quality-related cost. Each station of the MMS may stay at either in-control condition or out-of-control condition, which may lead to different nonconforming product rates. Markov chain method is used to calculate the steady-state probability distribution (SSPD). Based on the SSPD, the cost structure of this MMS is analysed. The economical optimisation model of attribute control charts (ACCs) is then established, in which the decision variables are the control chart parameters: sampling interval, sample size and control limit. The ACCs optimisation model is resolved by the proposed integrated algorithm combining heuristic rule and tabu search. This approach is verified through an application case taken from a mobile phone shell production company. The results of comparative analysis show that the proposed model is much more economical than both the current outgoing inspection strategy and the regular np control chart. The sensitivity analysis of four input parameters is also conducted.