An analytical model for interactive failures

In some systems, failures of certain components can interact with each other, and accelerate the failure rates of these components. These failures are defined as interactive failure. Interactive failure is a prevalent cause of failure associated with complex systems, particularly in mechanical systems. The failure risk of an asset will be underestimated if the interactive effect is ignored. When failure risk is assessed, interactive failures of an asset need to be considered. However, the literature is silent on previous research work in this field. This paper introduces the concepts of interactive failure, develops an analytical model to analyse this type of failure quantitatively, and verifies the model using case studies and experiments.     

一种基于P圈的ASON混合故障保护模型

在研究自动交换光网络(ASON)中发生节点/链路混合故障时的保护方法的基础上,设计了一种同时考虑节点故障和链路故障情况的基于P圈的保护模型,同时给出了一种保证在混合故障时可以达到100%业务恢复率的预配置P圈保护的启发式算法,并且综合考虑了实际网络中保护恢复速度和资源效率等因素,给出了具有最大P圈跳数限制的P圈配置方案.利用OPNET软件搭建了ASON仿真平台,在泛欧Cost239网络拓扑和北美NSFnet网络拓扑上,采用静态业务模型对该算法进行了仿真分析.仿真结果证明,该算法在拥有故障业务快速恢复能力的同时,相比已有算法具有更低的资源冗余度.     

A mathematical programming model for production planning using CONWIP

Push-based MRP and pull-based Kanban systems are effective planning tools for a wide range of manufacturing production. Both of them, however, have certain limitations when they are implemented in different production environments. In recent years, CONWIP (CONstant Work-In-Process) has been proposed and studied to take advantage of MRP and Kanban systems for optimal work-inprocess (WIP) inventory control. In this paper, an integer nonlinear mathematical programming model was developed to determine an optimal production sequence and lot sizes in a CONWIP production line. The nonlinear programming model was linearized and solved directly for a number of illustrative example problems.     

Internal failures in model elastomeric composites

Finite element methods have been used to calculate the rate of release of strain energy caused by growth of an internal crack in some model elastic composites under tension. A layer of a linearly elastic material was considered, bonded between two flat or two spherical rigid surfaces. The reduction in strain energy caused by a small circular crack at the interface was found to be only about one-half of that due to a similar crack in the centre of the layer, in accord with the conjecture of Andrews and King. Cracks in the centre of a thin layer bonded between flat surfaces caused about the same release of energy as a crack in the centre of a thick specimen under the same tensile stress. On the other hand, a crack in a thin layer bonded between two spherical surfaces caused a much larger rate of energy release, depending on the radius of the layer relative to its minimum thickness. Growth of an initial crack would thus occur at a small applied stress. For thin layers between both flat and spherical surfaces, the rate of release of energy decreased as the crack grew, indicating that the crack would stabilize at a finite size. These conclusions are in accord with some observations of cracks in thin elastic layers.     

A stochastic dynamic programming model for stream water quality management

This paper deals with development of a seasonal fraction-removal policy model for waste load allocation in streams addressing uncertainties due to randomness and fuzziness. A stochastic dynamic programming (SDP) model is developed to arrive at the steady-state seasonal fraction-removal policy. A fuzzy decision model (FDM) developed by us in an earlier study is used to compute the system performance measure required in the SDP model. The state of the system in a season is defined by streamflows at the headwaters during the season and the initial DO deficit at some pre-specified checkpoints. The random variation of streamflows is included in the SDP model through seasonal transitional probabilities. The decision vector consists of seasonal fraction-removal levels for the effluent dischargers. Uncertainty due to imprecision (fuzziness) associated with water quality goals is addressed using the concept of fuzzy decision. Responses of pollution control agencies to the resulting end-of-season DO deficit vector and that of dischargers to the fraction-removal levels are treated as fuzzy, and modelled with appropriate membership functions. Application of the model is illustrated with a case study of the Tungabhadra river in India.     

A mixed integer programming model for a closed-loop supply-chain network

In this paper, a new mixed integer mathematical model for a closed-loop supply-chain network that includes both forward and reverse flows with multi-periods and multi-parts is proposed. The proposed model guarantees the optimal values of transportation amounts of manufactured and disassembled products in a closed-loop supply chain while determining the location of plants and retailers. Finally, computational results are presented for a number of scenarios to show and validate the applicability of the model.     

A model of storage reliability with possible initial failures

Recently, storage reliability has attracted attention because of the increasing demand for high reliability of products in storage in both military and commercial industries. In this paper we study a general storage reliability model for the analysis of storage failure data. It is indicated that the initial failures, which are usually neglected, should be incorporated in the estimation of storage failure probability. Data from the reliability testing before and during the storage should be combined to give more accurate estimates of both initial failure probability and the probability of storage failures. The results are also useful for decision-making concerning the amount of testing to be carried out before storage. A numerical example is also given to illustrate the idea.     

A mathematical programming model for reconfiguration of flexible manufacturing cells

In flexible manufacturing cells, changes in demand size, product mix, part variety, existing routings and set-up/operation times may require reconfiguration of the cells. In this study, an approach is developed to decide when and how such a reconfiguration should be carried out for existing cells. This study considers reconfiguration in terms of changing part routings, adding a new machine type in a cell, duplicating an existing machine type, removing an existing machine from a cell and transferring a machine to another cell. The study also shows the total number of tools of each type on each machine located in each cell after reconfiguration. To make the optimal reconfiguration decisions, a mathematical programming model to minimize the total reconfiguration cost is developed. The developed model considers the lower and upper bounds on machine utilizations and the time limits on machine cycle times to decide when to reconfigure the system.     

Production outsourcing: A linear programming model for the Theory-Of-Constraints

This paper presents an analysis of the outsourcing problem. Pertinent variables are identified and the relationships between them are defined. We formulate the outsourcing problem as a Linear-Programming (LP) problem and identify an analytical solution. We proceed with an example examining three decision models: standard cost accounting, standard Theory-Of-Constraints (TOC) and our own solution. The model enables managers to determine which products to manufacture and which to outsource. The solution of the LP formulation enables managers to apply the model by computing an operational ratio, without having to solve a linear programming problem. The final model is simpler to apply and requires the computation of fewer variables than other prevalent models.     

A multi-objective mixed-integer programming model for a multi-floor facility layout

We consider a multi-floor facility layout problem in which the overall length and width of the facility, the size and location of each department, the number and the location of elevators and the number of floors in the facility are all modelled as decision variables. We adapt a linear approximation scheme to represent the area of each department. We consider two objective functions in our model, namely minimising material handling and facility building costs, and propose a lexicographic ordering technique to handle multiple objectives. The numerical experiments show that the slack used in the lexicographic ordering approach has a significant impact on the optimal solution. The experiments also show that the material handling cost can be significantly reduced in a multi-floor facility compared with a single-floor facility.     

A mixed integer linear programming model for set-up reduction superstructures

The objective of this research is to introduce the concept of a set-up reduction superstructure and evaluate its utility in set-up reduction projects. For a given set-up project, consisting of several interdependent activities as well as existing ones, a superstructure is defined. For this superstructure, a corresponding mixed integer linear programming model is developed with a view to selecting the optimum set-up project. The resulting model is applied to the set-up reduction problem in a real example of the fabrication in a CNC lathe of a vibration reduction pulley for lorry motors. The model is implemented in the Mathematica platform. It is shown that the set-up reduction superstructure is a useful concept in practice.     

A goal programming model for the operation of closed-loop supply chains

The implementation of closed-loop supply chains to handle the problem of increasing levels of electronic and electrical equipment waste can be beneficial both economically and ecologically. Three different problem analysis techniques—why–what's stopping analysis, fundamental objective hierarchy, and means objective network—are used to analyse the problem from various perspectives. A non-preemptive goal-programming model and solution approach have also been developed, with goals being assigned different weights according to the respective goal priorities. The model considers multiple products, as well as operations associated with the product, subassembly, part, and material levels. A major contribution of the research involves the fact that the objectives and related constraints for each member of the supply chain are explicitly modeled. The results of the analysis show both the effect of varying the priority/weight associated with a goal, and how the values of the deviational variables can aid a decision maker in model analysis.     

A stochastic programming model for resequencing buffer content optimisation in mixed-model assembly lines

In mixed-model assembly lines, smooth operation of the assembly line depends on adherence to the scheduled sequence. However, during production process, this sequence is altered both intentionally and uninstentionally. A major source of unintentional sequence alteration in automobile plants is the paint defects. A post-paint resequencing buffer, located before the final assembly is used to restore the altered sequence. Restoring the altered sequence back to the scheduled sequence requires three distinct operations in this buffer: Changing the positions (i.e. resequencing) of vehicles, inserting spare vehicles in between difficult models and replacing spare vehicles with paint defective vehicles. We develop a two-stage stochastic model to determine the optimal number of spare vehicles from each model-colour type to be placed into the Automated Storage and Retrieval System resequencing buffer that maximises the scheduled sequence achievement ratio (SSAR). The model contributes to the literature by explicitly considering above three distinct operations and random nature of paint defect occurrences. We use sample average approximation algorithm to solve the model. We provide managerial insights on how paint entrance sequence, defect rate and buffer size affect the SSAR. A value of stochastic solution shows that the model significantly outperforms its deterministic counterpart.     

集成启发式规则的混合整数规划调度模型

针对生产调度优化问题,提出了一种集成启发式规则的混合整数规划调度模型。在分析启发式规则逻辑关系的基础上,用布尔逻辑变量表达启发式规则建立了启发式规则的基本逻辑表达式及其等价代数表达式,基于基本表达式给出了启发式规则的数学表达。将启发式规则的代数表达式与混合整数规划相结合,实现了启发式规则的集成。集成启发式规则的混合整数规划调度模型在结合启发式规则的基础上进行数学优化,克服了混合整数规划难以直接利用经验规则和基于规则的调度优化性难以保证的不足。最后以某炼油过程生产调度为例说明了模型的有效性。     

An interval programming model for continuous improvement in micro-manufacturing

Continuous quality improvement in micro-manufacturing processes relies on optimization strategies that relate an output performance to a set of machining parameters. However, when determining the optimal machining parameters in a micro-manufacturing process, the economics of continuous quality improvement and decision makers’ preference information are typically neglected. This article proposes an economic continuous improvement strategy based on an interval programming model. The proposed strategy differs from previous studies in two ways. First, an interval programming model is proposed to measure the quality level, where decision makers’ preference information is considered in order to determine the weight of location and dispersion effects. Second, the proposed strategy is a more flexible approach since it considers the trade-off between the quality level and the associated costs, and leaves engineers a larger decision space through adjusting the quality level. The proposed strategy is compared with its conventional counterparts using an Nd:YLF laser beam micro-drilling process.     

A fuzzy fractional chance-constrained programming model for air quality management under uncertainty

A fuzzy fractional chance-constrained programming model (FFCCPM) was developed for dealing with air quality management under uncertainty. FFCCPM integrates a fractional programming model and a double-sided fuzzy chance-constrained programming model. It considers the ratio between total treated pollutant amounts and system cost in the objective function; the constraints with fuzzy variables can be satisfied under some predetermined confidence levels and reliability scenarios. The air quality management system in Fengrun district, Tangshan City, China, was used to demonstrate the applicability of the proposed method. The obtained results indicated that the proposed model was suitable in describing and providing an overview of a studied management system for decision makers, generating various cost-effective air pollution-abatement alternatives. The strategy with a balance between system economy and reliability was recommended for decision makers. The successful application of FFCCPM in Fengrun district provides a good example of real-world regional air quality management.     

A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty

Humanitarian relief logistics is one of the most important elements of a relief operation in disaster management. The present work develops a multi-objective robust stochastic programming approach for disaster relief logistics under uncertainty. In our approach, not only demands but also supplies and the cost of procurement and transportation are considered as the uncertain parameters. Furthermore, the model considers uncertainty for the locations where those demands might arise and the possibility that some of the pre-positioned supplies in the relief distribution center or supplier might be partially destroyed by the disaster. Our multi-objective model attempts to minimize the sum of the expected value and the variance of the total cost of the relief chain while penalizing the solution’s infeasibility due to parameter uncertainty; at the same time the model aims to maximize the affected areas’ satisfaction levels through minimizing the sum of the maximum shortages in the affected areas. Considering the global evaluation of two objectives, a compromise programming model is formulated and solved to obtain a non-dominating compromise solution. We present a case study of our robust stochastic optimization approach for disaster planning for earthquake scenarios in a region of Iran. Our findings show that the proposed model can help in making decisions on both facility location and resource allocation in cases of disaster relief efforts.     

Multiple failures in a multi-item spares inventory model

Most inventory models dealing with spare parts assume independent part failures and hence one-at-a-time failure occurrences. In practice, for example when an aircraft engine undergoes repair, there is usually more than one part requiring replacement or repair; we denote this situation as 'multiple failures'. In this paper we represent multiple failures in a continuous, infinite horizon, order-for-order spares replenishment inventory model with cannibalization. We derive exact expressions for the distribution function and the expectation of the number of backlogged jobs; approximations are also provided. The results can be used to optimize spares inventories, to evaluate the effects of correlated failures, and to model the impact of parts commonality.     

A fuzzy-stochastic robust programming model for regional air quality management under uncertainty

This paper proposes a hybrid fuzzy-stochastic robust programming (FSRP) method and applies it to a case study of regional air quality management. As an extension of the existing fuzzy-robust programming and chance-constrained programming methods, FSRP can explicitly address complexities and uncertainties without unrealistic simplifications. Parameters in the FSRP model can be expressed as PDFs and/or membership functions, such that robustness of the optimization process can be enhanced. In its solution process, the FSRP model is converted to a deterministic version through transforming m imprecise constraints into 2 km precise inclusive constraints that correspond to k f -cut levels (under each given significance level). Results of the case study indicate that FSRP is applicable to problems that involve a variety of uncertainties. Air pollution control invariably involves a number of processes with socio-economic and environmental implications. These processes are associated with extensive uncertainties due to their complex, interactive, dynamic, and multiobjective features. Through the FSRP modeling study, useful solutions for planning regional air quality management practices have been generated. They reflect complex trade-offs between environmental and economic considerations. Willingness to pay higher operating costs will guarantee meeting environmental objectives; however, a desire to reduce the costs will run the risk of potentially violating the emission and/or ambient-air-quality standards.