一种基于随机森林的备件预测模型研究

对舰船零部件发生故障问题进行故障诊断,并对故障诊断结果进行分析,建立舰船零部件备件需求模型,给出零部件之间的发生故障概率的关系与备件需求特征;将随机森林回归原理应用到了舰船零部件的备件需求预测领域,构建了基于随机森林的预测模型,以及预测结果准确率的评价。用诊断结果数据对算法进行验证,结果表明,将随机森林算法运用到舰船的备件预测领域可以为舰船装备在一次海上任务期内备件配置问题提供参考价值。     

关于反共轭有序分拆的几个恒等式

In this paper, we first present several identities related to the inverse-conjugate compositions having parts of size ≤ 3, the compositions into parts equal to 1 or 2, the compositions into odd parts and the compositions into parts greater than 1. In addition, we provide a bijective proof of a relation for inverse-conjugate compositions having parts of size ≤ k.     

基于保障度的战时三级备件保障优化研究

针对装备备件保障度问题,结合现有的研究现状,综合考虑了战时装备保障的实际情况和新旧备件使用寿命的差异,深入分析了备件调度对保障度的影响,以保障度为目标函数,建立了战时三级备件保障模型,运用经典的排序算法对模型进行求解。最后,算例表明该方法是有效性的。     

提前期不确定条件下的预防性维修备件存储模型研究

在考虑预防性维修周期和提前期不确定的条件下,分别研究备件存储与其相关的维修费用、缺货费用、库存费用以及订购费用等四种费用之间的关系,明确了备件存储量对各项费用的影响.以各项费用总和最小化为目标,构建了提前期不确定条件下的预防性维修备件存储模型.通过备件存储模型的构建,对备件存储过程中的各项成本进行分析,以期对备件库存策略的确定给出一种解决方案.     

Balanced partitions

A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. We begin by establishing a less well-known companion result, which states that both of these quantities are equal to the number of partitions of n into even parts along with exactly one triangular part. We then introduce the characteristic of a partition, which is determined in a simple way by the placement of odd parts within the list of all parts. This leads to a refinement of the aforementioned result in the form of a new type of partition identity involving characteristic, distinct parts, even parts, and triangular numbers. Our primary purpose is to present a bijective proof of the central instance of this new type of identity, which concerns balanced partitions—partitions in which odd parts occupy as many even as odd positions within the list of all parts. The bijection is accomplished by means of a construction that converts balanced partitions of 2n into unrestricted partitions of n via a pairing of the squares in the Young tableau.     

Efficient approaches for furnace loading of cylindrical parts

This paper addresses the heat treatment operation in a manufacturing plant that produces different types of cylindrical parts. The immediate prior process to heat treatment is furnace-loading, where parts are loaded into baskets. The furnace-loading process is complex and involves issues relating to geometry, and heterogeneity in the parts and in their processing requirements. Currently, furnace-loading is accomplished by operator ingenuity; consequently, the parts loaded in heat treatment often do not use furnace capacity adequately. Efficiency in furnace operation can be achieved by improving basket utilization, which is determined by the furnace-loading process. This paper describes the development of integer and mixed integer LP models for 3D loading of cylindrical parts into furnace baskets. The models consider the exact location of parts to be loaded on the basket and incorporate three models with different objectives; the first addresses the nesting of parts within one another, the second addresses the number of basket layers used, and the third addresses the number of baskets used.     

A stochastic model for joint spare parts inventory and planned maintenance optimisation

Spare parts demands are usually generated by the need of maintenance either preventively or at failures. These demands are difficult to predict based on historical data of past spare parts usages, and therefore, the optimal inventory control policy may be also difficult to obtain. However, it is well known that maintenance costs are related to the availability of spare parts and the penalty cost of unavailable spare parts consists of usually the cost of, for example, extended downtime for waiting the spare parts and the emergency expedition cost for acquiring the spare parts. On the other hand, proper planned maintenance intervention can reduce the number of failures and associated costs but its performance also depends on the availability of spare parts. This paper presents the joint optimisation for both the inventory control of the spare parts and the Preventive Maintenance (PM) inspection interval. The decision variables are the order interval, PM interval and order quantity. Because of the random nature of plant failures, stochastic cost models for spare parts inventory and maintenance are derived and an enumeration algorithm with stochastic dynamic programming is employed for finding the joint optimal solutions over a finite time horizon. The delay-time concept developed for inspection modelling is used to construct the probabilities of the number of failures and the number of the defective items identified at a PM epoch, which has not been used in this type of problems before. The inventory model follows a periodic review policy but with the demand governed by the need for spare parts due to maintenance. We demonstrate the developed model using a numerical example.     

运筹学在汽车零部件入厂物流中的应用

汽车物流包括供应物流(零部件入厂物流)、生产物流、销售物流和回收物流,其中零部件入厂物流因其技术性强、复杂度高,被公认为汽车物流系统良性运作的关键环节.在分析汽车零部件入厂物流的基础上,研究运筹学在汽车零部件入厂物流中的应用, 构建数学模型,并用贪婪算法求解.     

A Note on Partitions into Distinct Parts and Odd Parts

Bousquet-Mélou and Eriksson showed that the number of partitions of n into distinct parts whose alternating sum is k is equal to the number of partitions of n into k odd parts, which is a refinement of a well-known result by Euler. We give a different graphical interpretation of the bijection by Sylvester on partitions into distinct parts and partitions into odd parts, and show that the bijection implies the above statement.     

Modelling the cost of poor quality in a five-state part manufacturing operation: a case study

The quality history of individual parts from a critical operation can be modeled by a five-state Markov chain involving factory rework operation, customer inspection and field test, parts scrapped, parts defective but used-as-is by concession or re-graded for alternative applications, and defect-free parts satisfying customer requirements. We estimate total failure cost by a five-state Markov chain model and present a case study to demonstrate relationship of the total failure cost to appraisal and prevention costs.     

On a partition identity of Lehmer

Euler's identity equates the number of partitions of any non-negative integer n into odd parts and the number of partitions of n into distinct parts. Beck conjectured and Andrews proved the following companion to Euler's identity: the excess of the number of parts in all partitions of n into odd parts over the number of parts in all partitions of n into distinct parts equals the number of partitions of n with exactly one even part (possibly repeated). Beck's original conjecture was followed by generalizations and so-called “Beck-type” companions to other identities.In this paper, we establish a collection of Beck-type companion identities to the following result mentioned by Lehmer at the 1974 International Congress of Mathematicians: the excess of the number of partitions of n with an even number of even parts over the number of partitions of n with an odd number of even parts equals the number of partitions of n into distinct, odd parts. We also establish various generalizations of Lehmer's identity, and prove related Beck-type companion identities. We use both analytic and combinatorial methods in our proofs.     

马尔科夫决策过程在R/M系统库存控制中的应用

给出了有限阶段R/M(再制造/制造)系统集成库存模式,利用马尔科夫决策理论对库存容量有限、具有随机再制造零部件的R/M系统集成库存进行研究,考虑再制造零部件单位成本、新零部件可变费用和固定费用、超过库存容量的那部分再制造零部件的附加费用及有缺货赔偿的情况,给出了马尔科夫决策过程模型,得到了随机最优控制策略.     

高原驻训航材有寿件需求预测研究

高原驻训航材保障中,有寿件重要度较高,部队必须携带足够的备件数量来满足任务需要.根据高原驻训条件下航材有寿件需求特点,将有寿件的需求分为到寿更换需求和随机故障消耗产生的需求两部分,分别用数学公式和仿真计算方法进行预测,再将两者结果相加为总需求量.通过实例分析验证,采用工程测算方法可以避免逐一分析器材寿命的繁杂,而单独考虑随机故障消耗可以进一步保证有寿件备件不短缺率在90%以上.该预测,该模型可以为航材有寿件到寿情况分析以及有寿件的携行方案制定提供参考.     

备件品种选择的rough方法

分析了影响备件储备品种选择的重要性、可更换性、消耗性、获得难度和经济性等五个因素,利用粗集方法,按条件属性的不同顺序对备件储备品种的选择规则进行了约简,根据工程实践,从中选择一个更加合理的约简结果作为最终的备件储备品种的选择规则,并得到了相应的决策算法.该方法能够克服各影响因素在备件品种选择过程中的影响不足或影响过强等弱点,具有简单、操作方便等特点,为导弹武器装备备件保障部门选择导弹备件品种提供了一种新的理论依据.     

Divisions of symmetric designs into two parts

We answer a question of Peter Cameron by showing that no non-degenerate symmetric design has a division into two parts each of which is a symmetric design. We also exhibit a class of symmetric designs each member of which has a division into two parts such that the parts are symmetric tactical configurations with the same parameters. These parts arise as tactical configurations consisting of (i) absolute elements, and (ii) non-absolute elements, of certain highly uniform polarities.     

基于战役的多机种战伤备件需求模型

为了合理储备战时航材备件,通过分析战时故障备件的需求特点,改进了传统的单机故障备件需求模型.根据多机种协同作战任务的不同,引入备件工作运行比的概念,建立了基于作战任务的多机种故障备件需求模型.为解决多机种协同作战时的保障资源配置问题提供了思路和方法.     

On the Number of Even Parts in All Partitions of $$\varvec{n}$$n into Distinct Parts

Annals of Combinatorics - A famous theorem of Euler asserts that there are as many partitions of n into distinct parts as there are partitions into odd parts. The even parts in partitions of n into...     

Forecasting both time varying MTBF of fighter aircraft module and expected demand of minor parts

A fundamental aspect of inventory management of fighter aircraft is to forecast the demand of minor parts installed in the main module. Most of the existing inventory models do not take into account the time-varying characteristics of modules composed of minor parts even though the demand rate of minor parts is sensitive to the conditions of module. In this paper, we propose random-effects regression models to forecast the mean time between failure (MTBF) of modules and the expected demand for the minor parts in the module based on time-varying characteristics of modules. Subsequently, we show how they can be applied to find necessary seasonal demand of minor parts. Our study is expected to contribute to ROKAF (Republic of Korea Air Force) in terms of providing base information for inventory policy for minor parts.     

On the Integration by Parts and Characterization of a Fractional Diffusion Process北大核心CSCD

本文研究分数扩散过程和其分部积分公式的关系.首先利用Bismut方法给出拉回公式,进而得到分数扩散过程的分部积分公式。反过来,证明了分数扩散过程可由其分部积分公式唯一刻画.     

The final order problem for repairable spare parts under condemnation

We consider a manufacturer of complex machines that offers service contracts to her customers, committing herself to repair failed spare parts throughout a fixed service period. The suppliers of spare parts often discontinue the production of some parts as technology advances and ask the manufacturer to place a final order. We address the problem of determining final orders for such spare parts. The parts that we consider are repairable, but they are subject to the risk of condemnation. We build a transient Markovian model to represent the problem for a repairable spare part with a certain repair probability and repair lead time and we present some approximations that allow for further real-life characteristics to be included. Furthermore, an approximate model that can be computed more efficiently is presented, and the sensitivity of the results obtained with respect to the problem parameters is discussed, helping us develop several managerial insights.