An optimal multi-machine replacement policy in a serially dependent production system

Here we investigate the serially dependent, multi-machine replacement problem. Given a planning horizon with T periods, M machines of T+ 1 possible vintages, costs for machine operations, machine replacements, and shutdown times, we investigate a linear programming reformulation which involves half the variables and a factor of T fewer constraints than earlier forms. Only T binary variables are necessary, a factor of M fewer than currently employed by heuristic procedures on alternate formulations. Specialized monotone cost structures are no longer necessary, thus extending the class of problems which can be solved efficiently. Computations done using the reformulation's linear programming relaxation on randomly generated problems typically produced integer solutions without branching, even in problems with 75 machines and 15 time periods. In situations where exact optimal solutions are required, the reformulation partially remedies the slow convergence witnessed in earlier studies using branch and bound techniques.     

Analysis of a single stage production system with heterogeneous machines

The performance of a single stage production system with two heterogeneous machines and two classes of jobs is investigated. The machines have a common buffer with jobs of both classes waiting for service. The arrivals are assumed to follow a Poisson process and the service times to be distributed exponentially. The evaluated production system differs from a classical homogeneous multiple server queueing system with regard to inhomogeneities of the two machines. Time inhomogeneity – the service times of the two machines being unequal – and functional inhomogeneity – one of the machines can handle only one class (A) of jobs – are to be distinguished. In the case of time inhomogeneity the calculation of system performance parameters may be carried out using an explicit formula, whereas for the analysis of functional inhomogeneity a numerical solution has to be derived. The impact of time inhomogeneity is very small and decreases with the system workload. On the contrary, functional inhomogeneity leads to elevated cycle times of up to 40% depending on the degree of inhomogeneity (measured by the fraction of A jobs) and the workload. Therefore, in contrast to the time-inhomogeneous case, single stage production systems with functional inhomogeneity can only be approximated tolerably by a homogeneous multiple server queueing system if the fraction of one-machine jobs is less than 30%. The increased throughput times above 30% are supplied by the diagram developed from the numerical solutions. RID="*" ID="*" While this research was constructed the author was affiliated to Institute of Conveying Technology and Logistics. Correspondence to: C. R. Lippolt     

Optimising lot sizing with nonlinear production rates in a multi-product multi-machine environment

In a variety of discrete manufacturing environments, it is common to experience a nonlinear production rate. In particular, our interest is in the case of an increasing production rate, where learning creates efficiencies. This leads to greater output per unit time as the process continues. However, the advantages of an increasing production rate may be offset by other factors. For examples, JIT policies typically lead to smaller lot sizes, where the value of an increasing production rate is largely lost. We develop a general model that balances the impact of various competing effects. Our research focuses on determining lot sizes that satisfy demand requirements while minimising production and holding costs. We extend our prior work by developing a multi-product, multi-machine method for modelling and solving this class of production problems. The solution method is demonstrated using the production function from the PR#2 grinding process for a production plant in Carlisle, PA. The solution heuristic provides solution times that are on average only 0.22 to 0.55% above optimum as the solution parameters are varied and the ratio of heuristic solution times to optimal solution times varies from 18.16 to 14.15%.     

INAR implementation of newsvendor model for serially dependent demand counts

The classic newsvendor model was developed under the assumption that period-to-period demand is independent over time. In real-life applications, the notion of independent demand is often challenged. In this paper, we propose a dynamic implementation of the newsvendor model based on a class of integer-valued autoregressive (INAR) models when facing correlated discrete demand. Motivated by application, we consider INAR models with underlying Poisson error innovations and with underlying negative-binomial error innovations to accommodate overdispersion scenarios. We numerically compare our proposal with the standard newsvendor solution and with a standard autoregressive-based newsvendor solution. Our results show that an appropriately specified INAR-based newsvendor solution not only outperforms the standard case but also the approximating forecasting approaches. Moreover, even in the presence of autocorrelation, the use of the standard autoregressive model as an approximating approach can lead to increased costs over and above the standard implementation of the newsvendor model based on no forecasting.     

Optimal production plan for a multi-products manufacturing system with production rate dependent failure rate

This study deals with the problem of dependence between production and failure rates in the context of a multi-product manufacturing system. It provides an answer about how to produce (i.e. the production rates) and what to produce (i.e. which product) over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable manufacturing system producing two products P_a and P_b . The product P_a is produced to supply the strategic demand d(k) of the principal customer via a buffer stock S over k periods (k?=?1,?2,?…?,?H). The second product P_b is produced to meet a secondary but very profitable demand. It is produced during a given interval at the end of each period k. We develop a genetic algorithm to determine simultaneously the optimal production rate of the first product during each period k and the optimal duration of the production interval of the second product, maximising the total expected profit.     

橡胶支座与柱串联体系的动力特性分析

针对工程界比较关注的橡胶隔震支座与柱串联的隔震体系,研究了串联隔震体系横向振动的固有频率,探讨了轴向压力和不同隔震支座等效弯曲刚度对串联隔震系统固有频率的影响。考虑横截面转动和剪切变形以及轴向压力的影响,建立了串联隔震系统横向自由振动的数学模型;采用微分求积单元法（DQEM）对所得控制方程和边界条件进行离散处理,避免了繁琐的偏微分方程求解;数值求解固支—自由边界条件下串联隔震体系的横向固有频率,并得到该系统横向固有频率参数随压力变化的曲线。数值结果表明：轴向力的增加将显著降低串联隔震系统的低阶固有频率;在总高度一定的情况下,隔震支座尺寸的增大对串联隔震体系的力学特性也有显著的影响。     

Optimal periodic replacement for a deteriorating production system with inspection and minimal repair

Here we discuss an inspection policy model for a deteriorating production system with minimal repair. A minimal repair is resorted to as and when the system is found to be in a failed state during an inspection unless it is apre-set overhaul/replacement time in which case the system is overhauled or replaced. Using a dynamic programming formulation, and assuming that the cost of minimal repair is a non-decreasing function of age, we arrive at the optimal inspection time that maximizes the profit per unit time for a given overhaul/replacement time. The procedure is then extended to determine the optimal periodic overhaul/replacement time and the corresponding optimal number of inspections and their schedule.     

Robust production control policy for a multiple machines and multiple product-types manufacturing system with inventory inaccuracy

Inventory inaccuracy often exists in manufacturing systems, which has great negative impact on the performance of production control, e.g. very high work-in-process holding cost or backlog penalty. To hedge against inventory inaccuracy, the robust production control problems will be investigated for a multiple machines and multiple product-types manufacturing system with uncertain production capacity. The objective of our problem is to minimise the average production cost. To solve this problem, a robust production control policy is developed, which is insensitive to the inventory record errors, and whose robustness is better than the traditional hedging point policy for optimal production control. Finally, numerical experiments are conducted to examine the performance of the proposed robust production control policy against inventory inaccuracy. Based on the experimental results, the conditions of applying the proposed policy are also obtained.     

Simultaneous determination of preventive maintenance and replacement policies in a queue-like production system with minimal repair

This paper addresses the joint effects of preventive maintenance and replacement policies on a queue-like production system with minimal repair at failures. We consider a policy which calls for a preventive maintenance operation whenever N parts have been processed. If a failure occurs and at least K preventive maintenance operations have been carried out, the system is replaced by a new one. Otherwise, a failure is handled by minimal repair. An analytical model is developed and the argument of renewal–reward theory is used to provide long-run expected profit per unit time for a given maintenance and replacement policy. Numerical examples are given to provide some managerial insights.     

基于OPC UA的多机系统互联互通技术研究

在制造技术逐渐数字化、信息化与智能化的背景下,本文提出了一种基于开放平台通信统一架构(OPC UA)的多机系统互联互通的实现方法.首先,对3PRR并联机械系统与选择顺应性装配机器手臂(SCARA)机器系统建立了基于OPC UA的信息模型,实现了语义统一;然后,给出了一种基于OPC UA的多机系统互联互通的架构,并针对跨...     

Maintenance-outsourcing contracts for a system with backup machines

In this paper, we consider a system with multiple components, each prone to failure, during which production is halted. Minimal repair is performed by an external contractor whenever a component breaks down. The contractor also conducts a general preventive maintenance (PM) for the whole system at pre-determined times. The contractor’s goal is to minimise maintenance-related costs; however, the system (made up of the contractor and the manufacturer, who gains revenue whenever the system is up) profit would be maximised if the revenue is also considered. Since these goals usually require different PM schedules, we propose a cost subsidisation scheme which coordinates the system. We then extend this basic model by considering the existence of a backup machine which will allow the system to continue running (albeit, generating a lower revenue) whenever a component fails. We show that the existence of such a machine reduces the profit difference between uncoordinated and coordinated systems.     

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     

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.     

The equipment maintenance scheduling problem in a coal production system

This paper addresses an equipment maintenance scheduling problem in a coal production system which includes three consecutive stages: the coal mining stage, the coal washing stage and the coal loading stage. Each stage is composed of different equipment that needs maintenance each day. There exists intermediate storage with finite capacities and the finished products are transported by train. Moreover, some equipment has a different preference for (aversion to) the start time of maintenance (STOM). The objective is to minimise the weighted sum of aversion about STOM, changeover times and train waiting time. We first formulate this problem into a mixed integer linear programming (MILP) model, then a hybrid genetic algorithm (HGA) is proposed to solve it. The proposed method has been tested on a practical coal enterprise in China and some randomly generated instances. Computational results indicate that our algorithm can produce near-optimal solutions efficiently.     

Tool replacement for production with a low fraction of defectives

In manufacturing industry, the tool replacement cost is, in many cases, a significant portion of the production cost. Early tool replacement increases the production cost. Overdue tool replacement, however, results in poor production quality. Accordingly, improving production quality while maintaining a low production cost is essential. The index C_pk is regarded as a yield-based index. For a fixed C_pk value, the production yield and fraction of defectives can be calculated. In this paper, we present an analytical approach using C_pk to determine the optimal tool replacement time. An accurate process capability must be calculated, particularly when the data contain assignable cause variation. Tool wear is a dominant and inseparable component in many machining processes (a systematic assignable cause), and ordinary capability measures become inaccurate because process data are contaminated by the assignable cause variation. Considering process capability changes dynamically, an estimator of C_pk is investigated. The closed form of the exact sampling distribution is derived. An effective tool management procedure for determining the optimal tool replacement time is presented for processes with a low fraction of defectives. For illustrative purposes, an application example involving tool wear is presented.     

Optimal replacement policy for a redundant system

Summary This paper considers the reliability of a system which consists ofn components connected in series, the i^thcomponent being supported by (m _i – 1) units in parallel and obtains the optimal policy of replacement by dynamic programming. In the case of a system consisting of identical pairs, the decision depends on the number of operable pairs. For this case sample calculations are presented.

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Zusammenfassung Wir untersuchen die Zuverlässigkeit eines Seriensystems ausn Komponenten, bei dem für diei-te Komponentem _i – 1 Reserveelemente zur Verfügung stehen. Mit Hilfe der dynamischen Optimierung bestimmen wir die optimale Ersetzungspolitik. Besteht das System aus identischen Paaren, hängt die Entscheidung von der Zahl der intakten Paare ab. Für diesen Fall geben wir beispielhaft einige numerische Ergebnisse.

     

Maintenance scheduling for a manufacturing system of machines with adjustable throughput

This paper considers the problem of analyzing and optimizing joint schedules of maintenance and throughput adjustment operations in manufacturing systems. The purpose of joint scheduling of maintenance and throughput changing operations is to maximize the cost benefits of maintenance operations in manufacturing systems in which some or all of the machines can execute their function under different process settings, resulting in different machine and system throughputs. Such a capability enables one to strategically slow down more degraded machines or accelerate freshly maintained machines so that production targets can be met and maintenance operations can be offset to times when they are less intrusive on the manufacturing process. A Monte-Carlo-simulation-based method is proposed for the evaluation of cost effectiveness of any schedule of maintenance and throughput changing operations, and a genetic-algorithm-based method is proposed to enable searching for schedules that would maximize the cost benefits of these operations. A matrix chromosome representation of the joint schedules of maintenance and throughput adjustment operations is introduced and several mechanisms of chromosome evolution and selection are proposed and analyzed in numerical simulations of such manufacturing systems. Results indicate a good ability for the newly proposed methods to achieve a tradeoff between cost benefits of production and losses due to maintenance operations through strategic allocation of maintenance and throughput changing actions.     

Optimisation-based control coordination of PSSs and FACTS devices for optimal oscillations damping in multi-machine power system

An optimal procedure for designing co-ordinated controllers of power system stabiliser and flexible ac transmission system devices is developed for achieving and enhancing small-disturbance stability in multi-machine power systems. A constrained optimisation approach is applied for minimising an objective function formed from selected eigenvalues of the power systems state matrix. The eigenvalue-eigenvector equations associated with the selected modes form a set of equality constraints in the optimisation. There is no need for any standard eigenvalue calculation routines, and the use of sparse Jacobian matrix in the case of large system for forming the eigenvalue-eigenvector equations leads to the sparsity formulation. Inequality constraints include those for imposing bounds on the controller parameters. Constraints which guarantee that the modes are distinct ones are derived and incorporated in the control coordination formulation using the property that eigenvectors associated with distinct modes are linearly independent. The robustness of the controllers is achieved very directly through extending the sets of equality constraints and inequality constraints in relation to selected eigenvalues and eigenvectors associated with the state matrices of power systems with loading conditions and/or network configurations different from that of the base case. Simulation results of a multi-machine power system confirm that the procedure is effective in designing controllers that guarantee and enhance the power system small-disturbance stability.     

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.     

Selection of a pull production control system in multi-stage production processes

In this paper, we conduct an analytical comparison of three pull production control systems: Kanban, CONWIP and Base-stock in multi-stage production processes. First, we compare the three control systems in a multi-stage serial production process. Then, we compare them in multi-stage assembly production processes, and present guidelines that allow us to select the best system. As a result, we show which structural parameters decide the superiority of one control scheme to the others, and how they are related. A key for superiority is a configuration of parameters, such as processing times and number of cards employed in the system. We show that there is no general superiority amongst the analysed concepts. Finally, we verify the effect of variability on the system performance, and generalise the analytical results of deterministic cases by conducting numerical experiments.