Application of Markov renewal theory and semi-Markov decision processes in maintenance modeling and optimization of multi-unit systems

In this paper, a condition-based maintenance model for a multi-unit production system is proposed and analyzed using Markov renewal theory. The units of the system are subject to gradual deterioration, and the gradual deterioration process of each unit is described by a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of the system is influenced by the deterioration process and the demand is constant. The states of the units are observable through regular inspections and the decision to perform maintenance depends on the number of units in each state. The objective is to obtain the steady-state characteristics and the formula for the long-run average cost for the controlled system. The optimal policy is obtained using a dynamic programming algorithm. The result is validated using a semi-Markov decision process formulation and the policy iteration algorithm. Moreover, an analytical expression is obtained for the calculation of the mean time to initiate maintenance using the first passage time theory.     

Optimal operating policies in a commodity trading market with the manufacturer's presence

With the help of the Internet and express delivery at relatively low costs, trading markets have become increasingly popular as a venue to sell excess inventory and a source to obtain products at lower prices. In this article, we study the operational decisions in the presence of a trading market in a periodic‐review, finite‐horizon setting. Prices in the trading market change periodically and are determined endogenously by the demand and supply in the market. We characterize the retailers'optimal ordering and trading policies when the original manufacturer and the trading market co‐exist and retailers face fees to participate in the trading market. Comparing with the case with no trading fees, we obtain insights into the impact of trading fees and the fee structure on the retailers and the manufacturer. Further, we find that by continually staying in the market, the manufacturer may use her pricing strategies to counter‐balance the negative impact of the trading market on her profit. Finally, we extend the model to the case when retailers dynamically update their demand distribution based on demand observations in previous periods. A numerical study provides additional insights into the impact of demand updating in a trading market with the manufacturer's competition. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A facility reliability problem: Formulation,properties, and algorithm

Having a robustly designed supply chain network is one of the most effective ways to hedge against network disruptions because contingency plans in the event of a disruption are often significantly limited. In this article, we study the facility reliability problem: how to design a reliable supply chain network in the presence of random facility disruptions with the option of hardening selected facilities. We consider a facility location problem incorporating two types of facilities, one that is unreliable and another that is reliable (which is not subject to disruption, but is more expensive). We formulate this as a mixed integer programming model and develop a Lagrangian Relaxation‐based solution algorithm. We derive structural properties of the problem and show that for some values of the disruption probability, the problem reduces to the classical uncapacitated fixed charge location problem. In addition, we show that the proposed solution algorithm is not only capable of solving large‐scale problems, but is also computationally effective. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

军事供应链不确定性产生机理研究

军事供应链中不可避免地存在不确定性。构建了军事供应链不确定性产生机理的概念模型,从需求、供应、环境三个方面分析了军事供应链不确定性产生的原因,同时,对军事供应链中可能存在的各种不确定性进行了讨论,明确了加剧不确定性影响的因素是军事供应链系统的复杂性。具体表现为军事供应链成员交互关系的复杂性和军事供应链网络结构的复杂性。提出正是由于这两个原因的存在,对军事供应链的保障性能产生了巨大的影响。     

Supply chain coordination with shelf‐space and retail price dependent demand and heterogeneous retailers

We consider supply chain coordination in which a manufacturer supplies some product to multiple heterogeneous retailers and wishes to coordinate the supply chain via wholesale price and holding cost subsidy. The retail price is either exogenous or endogenous. The market demand is described by the market share attraction model based on all retailers'shelf‐spaces and retail prices. We obtain optimal solutions for the centralized supply chain, where the optimal retail pricing is a modified version of the well‐known cost plus pricing strategy. We further get feasible contracts for the manufacturer to coordinate the hybrid and decentralized supply chains. The manufacturer can allocate the total profit free to himself and the retail market via the wholesale price when the retail price is exogenous, but otherwise he cannot. Finally, we point out that different characteristics of the retail market are due to different powers of the manufacturer, and the more power the manufacturer has, the simpler the contract to coordinate the chain will be. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

运动目标轨迹分类与识别

运动目标轨迹识别是运动分析中的基本问题,其目的是解释所监视场景中发生的事件,对所监视场景中运动目标轨迹的行为模式进行分析与识别,智能地做出自动分类.对轨迹有效性判断后采用K均值聚类,引入改进的隐马尔可夫模型算法,针对轨迹的复杂程度对各个轨迹模式类建立相应的隐马尔可夫模型,利用训练样本训练模型得到可靠的模型参数,计算测试样本对于各个模型的最大似然概率,选取最大概率值对应的轨迹模式类作为轨迹识别的结果,对两种场景中聚类后的轨迹进行训练与识别,平均识别率较高,实验结果表明该方法是有效的.     

Dynamic server assignment policies for assembly‐type queues with flexible servers

We seek dynamic server assignment policies in finite‐capacity queueing systems with flexible and collaborative servers, which involve an assembly and/or a disassembly operation. The objective is to maximize the steady‐state throughput. We completely characterize the optimal policy for a Markovian system with two servers, two feeder stations, and instantaneous assembly and disassembly operations. This optimal policy allocates one server per station unless one of the stations is blocked, in which case both servers work at the unblocked station. For Markovian systems with three stations and instantaneous assembly and/or disassembly operations, we consider similar policies that move a server away from his/her “primary” station only when that station is blocked or starving. We determine the optimal assignment of each server whose primary station is blocked or starving in systems with three stations and zero buffers, by formulating the problem as a Markov decision process. Using this optimal assignment, we develop heuristic policies for systems with three or more stations and positive buffers, and show by means of a numerical study that these policies provide near‐optimal throughput. Furthermore, our numerical study shows that these policies developed for assembly‐type systems also work well in tandem systems. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Threshold incentives over multiple periods and the sales hockey stick phenomenon

In this article, we study threshold‐based sales‐force incentives and their impact on a dealer's optimal effort. A phenomenon, observed in practice, is that the dealer exerts a large effort toward the end of the incentive period to boost sales and reach the threshold to make additional profits. In the literature, the resulting last‐period sales spike is sometimes called the hockey stick phenomenon (HSP). In this article, we show that the manufacturer's choice of the incentive parameters and the underlying demand uncertainty affect the dealer's optimal effort choice. This results in the sales HSP over multiple time periods even when there is a cost associated with waiting. We then show that, by linking the threshold to a correlated market signal, the HSP can be regulated. We also characterize the variance of the total sales across all the periods and demonstrate conditions under the sales variance can be reduced. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal maintenance policies for a safety‐critical system and its deteriorating sensor

We consider the integrated problem of optimally maintaining an imperfect, deteriorating sensor and the safety‐critical system it monitors. The sensor's costless observations of the binary state of the system become less informative over time. A costly full inspection may be conducted to perfectly discern the state of the system, after which the system is replaced if it is in the out‐of‐control state. In addition, a full inspection provides the opportunity to replace the sensor. We formulate the problem of adaptively scheduling full inspections and sensor replacements using a partially observable Markov decision process (POMDP) model. The objective is to minimize the total expected discounted costs associated with system operation, full inspection, system replacement, and sensor replacement. We show that the optimal policy has a threshold structure and demonstrate the value of coordinating system and sensor maintenance via numerical examples. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 399–417, 2017     

基于随机Petri网的综合航电系统建模及分析

提出了一种利用随机Petri网对综合航电系统进行建模和性能分析的方法.首先,建立了综合航电系统数据总线传输系统的随机Petri网系统模型,通过系统模型进行综合航电系统的性能分析;其次,给出了航空电子综合系统数据总线传输基于固定主控端周期指令的总线性能分析结果;最后,通过两种分析结果的比较,得出了基于随机Petri网对航空电子综合系统数据总线传输建模分析是可行的结论.