Joint production and preventive maintenance scheduling for a single degraded machine by considering machine failures

Production scheduling and maintenance planning are two interdependent issues that most often have been investigated independently. Although both preventive maintenance (PM) and minimal repair affect availability and failure rate of a machine, only a few researchers have considered this interdependency in the literature. Furthermore, most of the existing joint production and preventive maintenance scheduling methods assume that machine is available during the planning horizon and consider only a possible level for PM. In this research, an integrated model is proposed that coordinates preventive maintenance planning with single-machine scheduling to minimize the weighted completion time of jobs and maintenance cost, simultaneously. This paper not only considers multiple PM levels with different costs, times and reductions in the hazard rate of the machine, but also assumes that a machine failure may occur at any time. To illustrate the effectiveness of the suggested method, it is compared to two situations of no PM and a single PM level. Eventually, to tackle the suggested problem, multi-objective particle swarm optimization and non-dominated sorting genetic algorithm (NSGA-II) are employed and their parameters are tuned Furthermore, their performances are compared in terms of three metrics criteria.     

Model for imperfect age-based preventive maintenance with age reduction

The effect of ageing on the deterioration rate of most repairable systems cannot be ignored. Preventive maintenance (PM) is performed in the hope of restoring fully the performance of these systems. However, in most practical cases, PM activities will be only able to restore part of the performance. Bridging the gap between theory and practice in this area requires realistic modelling of the effect of PM activities on the failure characteristics of maintainable systems. Several sequential PM models have been developed for predetermined PM interval policies but much less effort has been devoted to age-based ones. The purpose of this paper is to develop an age-based model for imperfect PM. The proposed model incorporates adjustment factor in the effective age of the system. The system undergoes PM either at failure or after a predetermined time interval whichever of them occurs first. After a certain number of such PMs, the system is replaced. The problem is to determine both the optimal number of PMs and the optimal PM's schedule that minimize the total long-term expected cost rate. Model analysis relating to the existence and uniqueness of the optimal solutions is provided. Numerical examples are presented to study the sensitivity of the model to different cost function's factors and to illustrate the use of the algorithm.     

Modelling preventive maintenance for deteriorating repairable systems

This paper is concerned with practical methods for the analysisand modelling of data for repairable systems which are subjectto preventive maintenance (PM) and still have an increasingrate of occurrence of failures. Aspects of testing for trendand fitting a nonhomogeneous Poission process to data are discussedModels for scheduling preventive maintenance to minimize costor maximize availability are proposed. They show that the optimalPM cycle interval for these systems decreases with increasingequipment age. One-cycle and two-cycle finite-time-zone replacementmodels are also developed to decide the optimal time for replacingthe equipment in current use.     

突发事件应急救援动态调度优化:以KX井喷事故为例

突发事件应急救援具有高度的不确定性和动态性。本文以KX井喷事故为例,研究突发事件应急救援的动态调度优化问题。作者首先给出KX井喷事故的背景资料,在此基础上提炼本文所研究的问题,即如何基于突发事件救援过程中的实际变化,对原定计划进行最优的动态调整。随后,构建突发事件应急救援的动态调度优化模型,针对其NP-hard属性设计专门的禁忌搜索启发式算法。最后,对KX井喷事故应急救援的动态调度问题进行求解,并结合现实情况对求解结果进行讨论分析,得到如下结论:早期发生的计划调整通常会对应急救援产生较大的影响,而后期发生的计划调整的影响则相对较小。本文的研究可为突发事件应急救援的实时指挥提供定量化决策支持。     

Multicriteria optimisation and simulation: an industrial application

This paper deals with multicriteria discrete-continuous problems of scheduling nonpreemptable jobs. The need for reusability and modularity leads us to build a “generic” optimisation and simulation framework, while the need to quickly generate good compromises between conflicting objectives requires the implementation of multicriteria scheduling models. This paper describes the practical possibilities of three hybrid models within this framework. The validation of the framework is presented in terms of its application to a real, highly constrained, discrete-continuous problem. The optimisation model is based on the hybridisation of a classical hill-climber meta-heuristic with the Promethee II multicriteria method.     

A two pass heuristic algorithm for scheduling ‘blocked out’ units in continuous process industry

This paper addresses the problem of scheduling cascaded ‘blocked out’ continuous processing units separated by finite capacity storage tanks. The raw materials for the product lines arrive simultaneously on the input side of the first unit. But every unit can process only one product line at a time, thus giving rise to the possibility of spillage of raw material due to limited storage capacity. The need to process multiple product lines and the added constraint of multiple intermediate upliftment dates aggravate the problem. This problem is quite common in petrochemical industry. The paper provides a MINLP (Mixed Integer Non-Linear Programming) formulation of the problem. However, for any realistic scheduling horizon, the size of the problem is too large to be solved by standard packages. We have proposed a depth first branch and bound algorithm, guided by heuristics, to help planners in tackling the problem. The suggested algorithm could output near optimal solutions for scheduling horizons of 30 time periods when applied to real life situations involving 3 units and 3 product lines. Preliminary version of the paper appeared in the proceedings of MISTA, 2005.     

SINGLE MACHINE SCHEDULING WITH CONTROLLABLE PROCESSING TIMES AND COMPRESSION COSTS （PART I：EQUAL TIMES AND COSTS）

Most papers in scheduling research have treated individual job processing times as fixed parameters. However, in many practical situations, a manager may control processing time by realloeating resources. In this paper, authors consider a machine scheduling problemwith controllable processing times. In the first part of this paper, a special case where the pro-cessing times and compression costs are uniform among jobs is discussed. Theoretical results are derived that aid in developing an O（n^2) algorithm to slove the problem optimally. In the second part of this paper, authors generalize the discussion to general case, An effective heuristic to the genera/ problem will be presented.     

The delay-time modelling of preventive maintenance of plant given limited PM data and Selective repair at PM

This paper presents a maintenance-modelling case study of aplant manufacturing brake linings. A delay–time modelis developed and applied to model and optimize preventive maintenance(PM). A key subsystem in the plant is used to illustrate themodelling process and management reaction. Defects identifiedat PM may not all be removed. This incomplete response to PMis a feature which has not been modelled before. The parametervalues of the delay-time process are estimated from objectivedata from maintenance records of failures, using the methodof maximum likelihood. This is aided by a theorem extendingresults on the NHPP arival rate of failures in a perfect-inspectioncase to the non-perfect-inspection case. Problems of parameterestimation given inadequate data collected at PMs are discussed,and the necessity to augment objective data with subjectiveassessments highlighted. Based upon the estimated model parametersand delay-time distribution, an inspection model is constructedto describe the relationship between the total unit downtimeand the PM interval. The response of management is discussed.     

利用故障数据和估计的检查数据建立维修优化模型

利用时间延迟概念,根据故障记录数据和估计的检查数据建立了预防维修模型.通过对故障记录数据统计分析,提出了模型的假定条件.采用最大似然估计法,估计参数,包括缺陷发生率、不完全检查概率和时间延迟分布.建立了有关预防维修间隔期和总停机时间之间关系的检查模型,并根据估计参数和检查模型,计算最佳维修间隔期.     

Optimizing Preventive Maintenance Models

We deal with the problem of scheduling preventive maintenance (PM) for a system so that, over its operating life, we minimize a performance function which reflects repair and replacement costs as well as the costs of the PM itself. It is assumed that a hazard rate model is known which predicts the frequency of system failure as a function of age. It is also assumed that each PM produces a step reduction in the effective age of the system. We consider some variations and extensions of a PM scheduling approach proposed by Lin et al. [6]. In particular we consider numerical algorithms which may be more appropriate for hazard rate models which are less simple than those used in [6] and we introduce some constraints into the problem in order to avoid the possibility of spurious solutions. We also discuss the use of automatic differentiation (AD) as a convenient tool for computing the gradients and Hessians that are needed by numerical optimization methods. The main contribution of the paper is a new problem formulation which allows the optimal number of occurrences of PM to be determined along with their optimal timings. This formulation involves the global minimization of a non-smooth performance function. In our numerical tests this is done via the algorithm DIRECT proposed by Jones et al. [19]. We show results for a number of examples, involving different hazard rate models, to give an indication of how PM schedules can vary in response to changes in relative costs of maintenance, repair and replacement. Part of this work was carried out while the first author was a Visiting Professor in the Department of Mechanical Engineering at the University of Alberta in December 2003.     

A multilevel machine and vehicle scheduling in a flexible manufacturing system

The paper presents a multilevel decision model for simultaneous machine and vehicle scheduling in a flexible manufacturing system. The system is composed of various machine types and a set of automated guided vehicles that permit each part to move between any pair of machines. The upper level of the decision model involves machine loading and part routing for which a bicriterion integer formulation is presented with the objective of balancing machine workloads and intermachine flows of parts. The lower level involves simultaneous scheduling of machines and vehicles for which a period-by-period heuristic is proposed based on a family of complex dispatching rules. The scheduling objective is to meet all part type requirements in a minimum time. Computational examples are included to illustrate the approach proposed.     

Heavy traffic resource pooling in parallel‐server systems

We consider a queueing system with r non‐identical servers working in parallel, exogenous arrivals into m different job classes, and linear holding costs for each class. Each arrival requires a single service, which may be provided by any of several different servers in our general formulation; the service time distribution depends on both the job class being processed and the server selected. The system manager seeks to minimize holding costs by dynamically scheduling waiting jobs onto available servers. A linear program involving only first‐moment data (average arrival rates and mean service times) is used to define heavy traffic for a system of this form, and also to articulate a condition of overlapping server capabilities which leads to resource pooling in the heavy traffic limit. Assuming that the latter condition holds, we rescale time and state space in standard fashion, then identify a Brownian control problem that is the formal heavy traffic limit of our rescaled scheduling problem. Because of the assumed overlap in server capabilities, the limiting Brownian control problem is effectively one‐dimensional, and it admits a pathwise optimal solution. That is, in the limiting Brownian control problem the multiple servers of our original model merge to form a single pool of service capacity, and there exists a dynamic control policy which minimizes cumulative cost incurred up to any time t with probability one. Interpreted in our original problem context, the Brownian solution suggests the following: virtually all backlogged work should be held in one particular job class, and all servers can and should be productively employed except when the total backlog is small. It is conjectured that such ideal system behavior can be approached using a family of relatively simple scheduling policies related to the cμ rule. This revised version was published online in June 2006 with corrections to the Cover Date.     

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??In this paper, precise large deviations of nonnegative, non-identical distributions and negatively associated random variables are investigated. Under certain conditions, the lower bound of the precise large deviations for the non-random sum is solved and the uniformly asymptotic results for the corresponding random sum are obtained. At the same time, we deeply discussed the compound renewal risk model, in which we found that the compound renewal risk model can be equivalent to renewal risk model under certain conditions. The relative research results of precise large deviations are applied to the more practical compound renewal risk model, and the theoretical and practical values are verified. In addition, this paper also shows that the impact of this dependency relationship between random variables to precise large deviations of the final result is not significant.     

空气中PM2.5问题的建模研究

是针对空气中PM2.5的相关因素分析、分布与演变及应急处理和空气质量控制管理的问题.首先,运用数理统计与分析的相关知识,建立PM2.5含量与5项指标间的相关性分析模型和多元线性回归方程模型,并采用SPSS软件和最小二乘法对其求解;然后,通过建立Shepard二维插值模型、多元线性回归方程模型以及偏微分方程模型研究了PM2.5时空分布、演变及预测评估的一般性规律;最后,引入效用函数建立了以满意度最大为目标的非线性规划模型和以投入总费用最少及PM2.5减排计划实施满意度最大为目标的多目标非线性规划模型,并结合LINGO软件求得最优解,给出了空气质量控制管理的治理计划.     

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.     

A real-time man-in-loop threat evaluation and resource assignment in defense

Efficient weapon threat assignment reflects military proficiency and requires prompt decision while managing the available resources. An important problem which commanders/decision makers face is to optimally utilize the resources in complex and time constraints situations. Several solutions have been proposed in the literature. In this paper, an innovative approach is proposed for threat evaluation and weapon assignment (TEWA) by following 3-dimensional stable marriage algorithm (3-D SMA). This proposed model incorporates new parameters and constraints i.e. supply chain, inventory of resources and multiple threats-weapons assignments that outperforms the previous techniques. This suggested model is based on threat perception followed by an integration of parametric based automatic threat evaluation technique for further weapon scheduling and assignment problem keeping in view that the threat with greater threat index has higher priority to be intercepted and weapons’ kill probability. The experimental section shows that our proposed approach has greatly improved in comparison with other approaches. The results showed that the threat neutralization is improved up to 25% reducing the usage of ammunition till 31.1%. The damage of assets abridged to 28.5% in comparison with existing approaches. The proposed approach elucidates that TEWA is an efficient real-time threat perception and optimal multi-threat scheduling problem at weapons’ resolution. It is a three-stage process, where the first stage perceives the threat, the second stage works on threat evaluation and the final stage focuses on weapon scheduling and assignment problem. The addition of new parameters and constraints in the new proposed model makes it a unique approach in which more accurate results, in neutralizing the threats, are obtained with less use of ammunition and damage of assets that makes TEWA more effective and efficient tool for optimum decision making in time critical situations.     

A profit-maximizing economic lot scheduling problem with price optimization

The economic lot scheduling problem (ELSP) is a well known problem that focuses on scheduling the production of multiple items on a single machine such that inventory and setup costs are minimized. In this paper, we extend the ELSP to include price optimization with the objective to maximize profits. A solution approach based on column generation is provided and shown to produce very close to optimal results with short solution times on a set of test problems. The results are discussed and recommendations for further research are provided.     

An efficient solution approach for real-world driver scheduling problems in urban bus transportation

The driver scheduling problem in public transportation is defined in the following way. There is a set of operational tasks, and the goal is to define the sequence of these tasks as shifts in such a way that every task must be assigned to a shift without overlapping. In real-world situations several additional constraints need to be considered, which makes large practical problems challenging to be solved efficiently. In practice it is also an important request with respect to a public transportation scheduling system to offer several versions of quasi-optimal solutions. In this paper we present an efficient driver scheduling solution methodology which is flexible in the above sense.     

Optimal checkpointing interval of a communication system with rollback recovery

This paper considers a communication system which consists of many processors and studies the problem for improving its reliability by adopting the recovery techniques of checkpoint and rollback. When either processor failure or communication error has occurred, the rollback recovery for processors associated with such an event is executed to the most recent checkpoint, and so, a consistent state in the whole system is maintained. The stochastic model with the above recovery techniques is formulated, using the theory of Markov renewal processes. The mean time to take checkpoint and the expected numbers of rollback recovery caused by processor failures and communication errors are derived. Further, an optimal checkpointing interval which minimizes the expected cost is analytically discussed.     

单水库在线发电调度策略设计与分析

考察单水库电站的多时段发电调度问题,决策者在每个时段初决策该时段的发电量,目标是使得在整个调度期内总发电量最大。针对在每个时段决策时缺乏当前及后续时段来水信息的情形,运用在线理论建立在线发电调度模型,设计给出了竞争比为2/(2-β(1-Ф))的在线发电调度策略,其中,β∈(0,1)表示每个时段最大来水导致的水头最大增幅与水库有效水头最大落差的比值,Ф∈(0,1)表示最低与最高有效水头数值之比。针对各时段可获知当前时段来水信息的情形,给出了在线调度策略,并证明了其竞争比为1+(1-Ф)/(1+Ф)。