Integrated production and maintenance planning for parallel machine system considering cost of rejection

Production scheduling and maintenance planning have interdependencies but been often considered and optimized independently in practice and in the literature. Furthermore, product quality has direct relationship with maintenance planning. This paper proposes an integrated approach for production scheduling and maintenance planning for parallel machine system considering the effect of cost of rejection. The approach aims to determine optimal production schedule and maintenance plan such that overall operations cost is minimized. A simulation-based optimization approach is used to solve the problem. A numerical investigation is performed to illustrate the approach. The integrated approach shows between 0.6 and 35.8% improvement in term of overall operations cost over independent approach for various scenarios. The results indicate that simultaneous consideration of production scheduling and maintenance planning results into better system performance.     

How to use a systems diagram to analyse and structure complex problems for policy issue papers

Many policy problems are complex in the sense that natural, technological, social and human elements interact. Problem exploration and structuring are essential as a basis for deliberate and focused approaches towards problem resolution. The results of problem exploration efforts can be laid down in the form of a policy issue paper. We have developed a systemic, stepwise approach, which has been elaborated and taught for over a decade to hundreds of students. This seven-step approach centers on the construction of a system diagram as a means to provide structure to the conceptualisation of a complex problem situation. The approach is based on a conscious combination of existing relatively straightforward analytical methods including objectives hierarchy, means-ends analysis, causal diagramming, stakeholder analysis, and contextual scenarios. The obtained insights are then summed up in a policy issue paper, which is the basis for further planning and research.     

A new MIP model for mine equipment scheduling by minimizing maintenance cost

Mining investment has been recognized as capital intensive due mainly to the cost of large equipment. Equipment capital costs for a given operation are usually within the order of hundreds of million dollars but may reach to billion dollars for large companies operating multiple mines. Such large investments require the optimum usage of equipment in a manner that the operating costs are minimized and the utilization of equipment is maximized through optimal scheduling. This optimum usage is required to ensure that the business remains sustainable and financially stable. Most mining operations utilize trucks to haul the mined material. Maintenance is one of the major operating cost items for these fleets as it can reach approximately one hundred million dollars yearly. There is no method or application in the literature that optimizes the utilization for truck fleet over the life of mine. A new approach based on mixed integer programming (MIP) techniques is used for annually scheduling a fixed fleet of mining trucks in a given operation, over a multi-year time horizon to minimize maintenance cost. The model uses the truck age (total hours of usage), maintenance cost and required operating hours to achieve annual production targets to produce an optimum truck schedule. While this paper focuses on scheduling trucks for mining operation, concept can be used in most businesses using equipment with significant maintenance costs. A case study for a large scale gold mine showed an annual discounted (10% rate) maintenance cost saving of over $2M and more than 16% ($21M) of overall maintenance cost reduction over 10 years of mine life, compared with the spreadsheet based approach used currently at the operation.     

On automorphisms of a distance-regular graph with intersection array {204, 175, 48, 1; 1, 12, 175, 204}

The research is focused on the question of proportional development in economic growth modeling. A multilevel dynamic optimization model is developed for the construction of balanced proportions for production factors and investments in a situation of changing prices. At the first level, models with production functions of different types are examined within the classical static optimization approach. It is shown that all these models possess the property of proportionality: in the solution of product maximization and cost minimization problems, production factor levels are directly proportional to each other with coefficients of proportionality depending on prices and elasticities of production functions. At the second level, proportional solutions of the first level are transferred to an economic growth model to solve the problem of dynamic optimization for the investments in production factors. Due to proportionality conditions and the homogeneity condition of degree 1 for the macroeconomic production functions, the original nonlinear dynamics is converted to a linear system of differential equations that describe the dynamics of production factors. In the conversion, all peculiarities of the nonlinear model are hidden in a time-dependent scale factor (total factor productivity) of the linear model, which is determined by proportions between prices and elasticities of the production functions. For a control problem with linear dynamics, analytic formulas are obtained for optimal development trajectories within the Pontryagin maximum principle for statements with finite and infinite horizons. It is shown that solutions of these two problems differ crucially from each other: in finite horizon problems the optimal investment strategy inevitably has the zero regime at the final stage, whereas the infinite horizon problem always has a strictly positive solution. A remarkable result of the proposed model consists in constructive analytical solutions for optimal investments in production factors, which depend on the price dynamics and other economic parameters such as elasticities of production functions, total factor productivity, and depreciation factors. This feature serves as a background for the productive fusion of optimization models for investments in production factors in the framework of a multilevel structure and provides a solid basis for constructing optimal trajectories of economic development.     

基于不确定需求与产出的计划生产量决策

在复杂多交的市场环境下和生产过程易受多种随机因素影响,产品的需求和产出往往具有不确定性.考虑不确定需求和产出的情况,建立起以最小期望成本(包括生产成本、缺货成本和超产成本)为目标函数,计划生产量为决策变量的决策模型.通过利用费马定理和极值第二充分条件对计划生产量决策模型分析,提出了最优计划生产量必须满足的方程和证明了模型是凹函数,存在着最小期望成本.最后通过数值实例验证了模型的有效性.     

Product and process yield estimation with Gaussian quadrature (GQ) reduction: Improvements over the GQ full factorial approach

Manufacturing or multivariate yield, the fraction of unscreened products which conforms to all product specification limits, is an important and commonly used metric for assessing and improving the quality of a production process. Current procedures for multivariate yield evaluation, such as Monte Carlo simulation, require substantial computing effort, making the iterative adjustment of design parameters often impractical. This paper introduces a new approach to multivariate yield evaluation based on a numerical integration procedure called Gaussian quadrature reduction (GQR). The advantage of this approach is a large reduction in the computational burden associated with multivariate yield evaluation with virtually no loss in accuracy of the estimates. The proposed procedure can be generalized to evaluate many other multivariate criteria such as expected costs and the desirability index. The method is demonstrated for three yield evaluation test problems, and comparisons to Monte Carlo-based evaluations are presented.     

The effect of testing errors on a repetitive testing process

Repetitive testing is a fairly common practice in the final testing stage of a chip manufacturing. Decisions on setting initial lot size and the number of testing repetitions are crucial to the effectiveness of the testing process. The task of setting optimal parameters for a testing process is often difficult in practical situations due to uncertainties in both incoming product yield and testing equipment condition during the testing process. In this paper, we investigate a repetitive testing process where the testing equipment may shift randomly from an in-control state to an inferior state during the testing process which, correspondingly, results in different testing errors. We develop a quantitative model that helps us to find optimal test parameters that maximizes system performance. Based on the model, we performed extensive numerical experiments to test the effects of incoming product defective rate, testing equipment shift rate, especially, type II testing errors on decision and system performance. We find that test equipment condition may significantly affect the optimal decisions on the number of test repetitive and initial testing batch size. Further, we find that, while a small type II testing error may have negligible negative effect of system performance, the effect increases as the error or the incoming product yield increases. The results of this research may potentially provide practitioners with insights and a quantitative tool for designing an efficient repetitive testing process.     

The impact of process deterioration on production and maintenance policies

This paper examines a single-stage production system that deteriorates with production actions, and improves with maintenance. The condition of the process can be in any of several discrete states, and transitions from state to state follow a semi-Markov process. The firm can produce multiple products, which differ by profit earned, expected processing time, and impact on equipment deterioration. The firm can also perform different maintenance actions, which differ by cost incurred, expected down time, and impact on the process condition. The firm needs to determine the optimal production and maintenance choices in each state in a way that maximizes the long-run expected average reward per unit time.     

Simultaneous production and maintenance planning for a single capacitated resource facing both a dynamic demand and intensive wear and tear

This paper presents a generic modeling framework to simultaneously decide about production quantities and maintenance operations for a capacitated resource facing a dynamic demand for different types of products. As the resource needs to be setup for each specific type of product, a lot-sizing problem occurs. In addition it is assumed that production causes intensive wear and tear. For this reason frequent maintenance activities need to be coordinated with the production operations in order to efficiently use the capacitated resource. A single generic model is presented to capture alternative forms of maintenance and different modes of interaction between maintenance and setups. As the model is numerically intractable for standard branch and bound algorithms, we solve it heuristically via a decomposition using a Fix-and-Optimize approach. Numerical results show that the proposed solution method produces high-quality results quickly. We further study the impact of simultaneous vs. sequential decisions about production and maintenance in the case of intensive wear and tear.     

柔性作业车间调度与视情维修的联合决策

针对设备状态可直接或间接检测获得的生产系统,提出柔性作业车间调度和视情维修的联合策略,决策变量分别为调度序列与视情维修序列,并建立两者的联合决策模型。进而根据联合策略,推导了相应的概率密度函数。通过数值分析,对比联合决策与独立决策的优化结果,表明了所建模型的有效性,并进行设备劣化参数的敏感度分析,验证了模型的正确性。     

Incorporating manufacturing lead times in joint production-marketing models: A review and some future directions

In many industries the pricing of a product over time can be used to manage demand for the product. Lead time, or promised delivery time is often a significant factor in price negotiations. However, the production planning literature has largely treated pricing decisions as exogeneous while focusing on the allocation of production capacity between products over time. On the other hand, the marketing literature has generally ignored the effects of capacity constraints and focused on the effects of pricing. In this paper, we begin by reviewing the existing literature on integrative production-marketing research, focusing on those models that consider lead times and capacity. We suggest a number of directions for future research that take advantage of recent developments in production planning models, as well as explicit modeling of feedback loops governing key parameters, which suggest a broader view of the problem.     

A Necessary and Sufficient Condition for Nonnegative Product Linearization of Orthogonal Polynomials

A necessary and sufficient condition for nonnegative product linearization of an orthogonal polynomial system is derived. The method goes through a discrete hyperbolic boundary value problem associated with the three-term recurrence relation. The paper provides a unified approach to nonnegative linearization problems that comprises results obtained earlier and gives new ones.     

A method for integrated process simulation in the mining industry

This paper proposes a method of Integrated Process Simulation (MIPS), which considers the dynamic, stochastic and systemic characteristics of mining operations to support investment decisions in this industry. This MIPS supports development of a Decision Support System (DSS) that considers product quality, process productivity and production costs. A case study is described that used the MIPS to make better investment decisions. The MIPS has proven, in practice, to be effective in several applications; for example, in defining the maintenance policy for critical equipment in an iron ore concentration plant; the process for removing impurities and simulating the company's budget to evaluate the viability of different business plans.     

Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

On the theory of dynamic thermoelasticity : PMM, vol. 42, no. 6, 1978, pp. 1093–1098

Use of the causality principle as radiation condition in dynamical problems of thermoelasticity is proposed. It follows from an analysis of the fundamental mathematical models describing the thermoelastic behavior of a continuous medium and used in the solution of specific problems, that some will yield physically unrealizable solutions. To eliminate the ambiguity in the solution which occurs, an approach is possible which has an explicit physical meaning and is based on the causality principle [1, 2]; it is required that the time source not yield a response earlier than the time of starting up of the source. Different kinds of radiation conditions of the Sommerfeld type are known in thermoelasticity problems [3 – 6].

To extract the unique solution in dynamical thermoelasticity problems, it is proposed in this paper to use the causality principle, which is equivalent to the requirement of analyticity of the solution in the upper half of the complex frequency plane; there are studied the analytic properties of the solutions of the fundamental boundary value problems for the models used most often for thermoelastic media, and there are made deductions about their physical realizability.     

A two-stage prognosis model in condition based maintenance

We often observe in practice that the life of a piece of production equipment can be divided into two stages. The first stage is referred to as the normal working stage where no significant deviation from the normal operating state is observed. The second stage is called the failure delay period, since a defect may be initiated, and progressively develop into an actual failure, i.e., the equipment is in a defective stage but still working during this stage. With the help of condition monitoring, hidden defects already present in the equipment may be detected, but for maintenance planning purposes, the prediction of the initiation point of the second stage, and more importantly, the residual life thereafter is important. This paper reports on the development of a probability model to predict the initiation point of the second stage and the remaining life based on available condition monitoring information. The method for model parameters estimation is discussed and applied to real data.     

装备维修管理费单装标准制定方法研究

装备维修管理费单装标准是领报装备日常维护保养经费的重要依据。如何合理制定单装标准是当前装备维修经费标准化管理中面临的主要难题,针对该问题,本文以满足部队实际需求为出发点,提出了单装标准制定的定量分析策略,基于聚类方法处理原始数据,并引入期望标准的概念,建立了关于期望标准的单位满意度函数,最后,通过粒子群算法实现优化目标的求解。研究结果表明本文方法适用于大规模数据的分析处理,扩展性良好,同时可以有针对性地根据装备重要程度规划单装标准组合,优化了当前以定性分析为主要手段的单装标准确定模式。     

Windowed Green function method for wave scattering by periodic arrays of 2D obstacles

This paper introduces a novel boundary integral equation (BIE) method for the numerical solution of problems of planewave scattering by periodic line arrays of two-dimensional penetrable obstacles. Our approach is built upon a direct BIE formulation that leverages the simplicity of the free-space Green function but in turn entails evaluation of integrals over the unit-cell boundaries. Such integrals are here treated via the window Green function method. The windowing approximation together with a finite-rank operator correction—used to properly impose the Rayleigh radiation condition—yield a robust second-kind BIE that produces superalgebraically convergent solutions throughout the spectrum, including at the challenging Rayleigh–Wood anomalies. The corrected windowed BIE can be discretized by means of off-the-shelf Nyström and boundary element methods, and it leads to linear systems suitable for iterative linear algebra solvers as well as standard fast matrix–vector product algorithms. A variety of numerical examples demonstrate the accuracy and robustness of the proposed methodology.     

Condition-based maintenance optimization considering improving prediction accuracy

Condition-based maintenance (CBM) aims to reduce maintenance cost and improve equipment reliability by effectively utilizing condition monitoring and prediction information. It is observed that the prediction accuracy often improves with the increase of the age of the component. In this research, we develop a method to quantify the remaining life prediction uncertainty considering the prediction accuracy improvement, and an effective CBM optimization approach to optimize the maintenance schedule. Any type of prognostics methods can be used, including data-driven methods, model-based methods and integrated methods, as long as the prediction method can produce the predicted failure time distribution at any given inspection point. Furthermore, we develop a numerical method to accurately and efficiently evaluate the cost of the CBM policy. The proposed approach is demonstrated using vibration monitoring data collected from pump bearings in the field as well as simulated degradation data. The proposed policy is compared with two benchmark maintenance policies and is found to be more effective.     

Responsive pricing under supply uncertainty

Consider a retailer orders a seasonal product from a supplier and sells the product over a selling season. While the product demand is known to be a linear function of price, the supply yield is uncertain and is distributed according to a general discrete probability distribution. This paper presents a two-stage stochastic model for analyzing two pricing policies: No Responsive Pricing and Responsive Pricing. Under the No Responsive Pricing policy, the retailer would determine the order quantity and the retail price before the supply yield is realized. Under the Responsive Pricing policy, the retailer would specify the order quantity first and then decide on the retail price after observing the realized supply yield. Therefore, the Responsive Pricing policy enables the retailer to use pricing as a response mechanism for managing uncertain supply. Our analysis suggests that the retailer would always obtain a higher expected profit under the Responsive Pricing policy. In addition to examining the impact of yield distribution and system parameters on the optimal order quantities, retail prices, and profits under these two pricing policies, we analyze two issues arising from responsive pricing. The first issue deals with the case in which the retailer can place an emergency order with an alternative source after observing the realized yield, while the second issue deals with a situation in which the retailer has to allocate his order among multiple suppliers.