Stochastic Comparison of Age-Dependent Block Replacement Policies

The age-dependent block replacement policy is a modified block replacement policy with an age limit for preventive replacements. Under this policy, any failed component is repaired, but only the components whose ages exceed a fixed age limit are replaced preventively at the scheduled maintenance times. Using the compensator method, we compare stochastically the failure counting processes of the age-dependent block replacement policies with different parameters, and show that the age-dependent block replacement policy, although cost effective, leads to more failures than the age and block replacement policies. AMS 2000 Subject Classification 60K10     

Optimal Repair Limit Replacement Policies with Imperfect Repair

This paper considers the repair limit replacement policies with imperfect repair. The repair is imperfect in the sense that the mean life of a repaired system is less than the mean life of a new system. Furthermore, we examine the repair limit replacement policy for the case in which there are two types of repair-local and central repair. The local repair is imperfect whilst the central repair is perfect (i.e. the system is as good as new after central repair). The optimal policies are derived to minimize the expected cost per unit of time for an infinite time span. Analytical results are presented along with numerical examples.     

Optimal Continuous Policies for Repair and Replacement

This paper investigates the problem of finding optimal replacement policies for equipment subject to failures with randomly distributed repair costs, the degree of reliability of the equipment being considered as a state of a Markov process. Algorithms have been devised to find optimal combined policies both for preventive replacement and for replacement in case of failure by using repair-limit strategies.First a simple procedure to obtain an optimal discrete policy is described. Then an algorithm is formulated in order to calculate an optimal continuous policy: it is shown how the optimal repair limit is the solution to an ordinary differential equation, and how the value of the repair limit determines the optimal preventive replacement policy.     

Optimal Control of Markov Processes with Age-Dependent Transition Rates

We study optimal control of Markov processes with age-dependent transition rates. The control policy is chosen continuously over time based on the state of the process and its age. We study infinite horizon discounted cost and infinite horizon average cost problems. Our approach is via the construction of an equivalent semi-Markov decision process. We characterise the value function and optimal controls for both discounted and average cost cases.     

Replacement Policies with Used Items Constraint

Various block replacement policies with used items have appeared in the literature. These policies use new as well as used items (created by the policies) for replacement. In these policies no constraint is placed on the number of used items used in each cycle. This paper considers these policies with a constraint (of practical significance) to ensure that the expected number of used items used per cycle is less than or equal to the expected number of used items created per cycle.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

A Condition Based Maintenance Model with Exponential Failures and Fixed Inspection Intervals

This paper discusses a condition based maintenance model with exponential failures, and fixed inspection intervals. A condition of the equipment, such as vibration, is monitored at equidistant time intervals. If the variable indicating the condition is above a threshold an instantaneous maintenance action is performed and the monitored condition takes on its initial value. The equipment can fail only once within an inspection interval. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming and compare it to an approximate steady state solution based on renewal theory.     

Start-Up Demonstration Tests with Rejection of Units upon Observing d Failures

The probability generating function of number of trials for the start-up demonstration test with rejection upon d failures is derived. The exact distribution of the number of trials is obtained. Some recurrence relations for the probabilities are also established. The average length of the test is derived. Some illustrative examples are finally presented.     

基于NBUMg类分布的更换策略比较

证明了年龄更换策略和成批更换策略依矩母函数序减少(增加)任意时间间隔内的失效次数的充要条件是基分布具有NBUMg (NWUMg)性质;更换间隔不同的成批更换策略在相同工作时间内的失效次数也作了比较.     

Optimal Policies for Investment with Time-Varying Return Distributions

We develop a model in which investors must learn the distribution of asset returns over time. The process of learning is made more difficult by the fact that the distributions are not constant through time. We consider risk-neutral investors who have quadratic utility and are selecting between two risky assets. We determine the time at which it is optimal to update the distribution estimate and hence, alter portfolio weights. Our results deliver an optimal policy for asset allocation, that is, the sequence of time intervals at which it is optimal to switch between assets, based on stochastic optimal control theory. In addition, we determine the time intervals in which asset switching leads to a loss with high probability. We provide estimates of the effectiveness of the optimal policy.     

考虑不完美检测的两阶段点检与备件订购策略联合优化

针对设备维修与备件管理相互影响与制约的问题, 在基于延迟时间理论的基础上, 提出了两阶段点检与备件订购策略联合优化。点检是不完美的, 当点检识别设备的缺陷状态时, 进行预防更新; 设备故障时, 进行故障更新。结合设备更新时备件的状态, 采用更新报酬理论建立了以第一阶段点检时间、第二阶段点检周期和备件订购时间为决策变量, 以最小化单位时间期望成本为目标的模型。最后, 通过人工蜂群算法对模型求解, 并在数值分析中将两阶段点检策略与定期点检策略进行比较, 结果表明:两阶段点检策略始终优于定期点检策略, 验证了所建模型的有效性。     

坏账和延期支付策略下采购商最优订货模型

在供应商、采购商及其顾客组成的三级供应链结构中,供应商提供给采购商较长的延期支付期限,采购商提供给其顾客较短的延期支付期限。且由于顾客为不特定多数,存在一定的坏账风险。文章从采购商的角度出发,分析在二阶延期支付策略下,坏账影响下采购商的最优订货策略。首先,考虑到坏账会影响采购商的利息收入和利息支出,因此文章从低坏账率和高坏账率两种情形出发,探讨了坏账影响下采购商的利息收入与利息支出,建立了相应的决策模型。其次,通过模型的分析求解,得出采购商的最优订货周期和最优订货批量的判定方法,进一步分析了各参数对采购商最优决策的影响。最后,通过数值分析对有关结论进行了验证,文章的分析研究不仅具有一定的理论意义,而且可以更好地指导采购商的订货决策。     

系统元件带有延时的最佳年代更换策略

Das等研究过关于年代更换策略的一种简单模型[1,2],但这个模型不具有现实性.本文考虑的年代更换模型是具有现实意义的.在我们的模型中,元件的寿命T为＂功能衰减＂变量U和延时变量H之和,即T=U＋H.在U和H满足某些条件下,可得出：T∈IFR的结论（引理1）.此外,我们得到保证最佳年代更换策略的解的存在性与唯一性的充分条件,但不必要求T∈IFR（定理1）.     

Optimal Ordering Policies for Inventory Systems with Emergency Ordering

This paper considers dynamic single- and multi-product inventory problems in which the demands in each period are independent and identically distributed random variables. The problems considered have the following common characteristics. At the beginning of each period two order quantities are determined for each product. A “normal order” quantity with a constant positive lead time of λ _n periods and an “emergency order” quantity with a lead time of λ _e periods, where λ _e = λ _n - 1. The ordering decisions are based on linear procurement costs for both methods of ordering and convex holding and penalty costs. The emergency ordering costs are assumed to be higher than the normal ordering costs. In addition, future costs are discounted.For the single-product problem the optimal ordering policy is shown to be the same for all periods with the exception of the last period in the N-period problem. For the multi-product problem the one- and N-period optimal ordering policy is characterized where it is assumed that there are resource constraints on the total amount that can be ordered or produced in each period.     

Optimal Replacement Policy for a General Model with Imperfect Repair

A general model is considered which incorporates imperfect repair and repair cost which depends on time and on the number of repairs in the cycle. This model is an extension of models examined previously in the literature. The objective of this paper is to find the optimal replacement policy and compare it with the replacement policies considered earlier for some variants of this model. The form of the optimal replacement policy is found in the general case and the expected average cost per unit time is derived in two special cases. Numerical examples show that the optimal policy is considerably better than the optimal periodic policy. This paper generalizes and unifies previous research in the area.     

考虑保质期的非即时易腐品最优订购与定价决策

针对有保质期约束的非即时易腐品,零售商可以在产品非腐败阶段和腐败阶段进行差异化定价来调整市场需求。即零售商可以调整产品非腐败阶段的定价策略,使得非即时易腐品在进入腐败阶段之前全部售出;或者在产品腐败阶段降低零售价格以刺激市场需求。因此,在需求依赖价格的假设下,本文研究了零售商关于有保质期约束的非即时易腐品的最优订购与定价决策。通过分析零售商单位时间利润函数的理论性质,得到了零售商的最优订购与定价策略。基于线性和指数型两种需求函数形式进行数值算例,可以发现针对保质期较长或者非腐败阶段较长的易腐品,零售商会延长订货周期来增加销售收入。特别是在指数型需求函数情境下,当市场需求与零售价格高度相关时,零售商更有意愿降价来刺激销量,从而使得易腐品在非腐败阶段内销售完毕。     

保险公司的最优投资和再保险策略

在保险公司既可以做证券(股票和债券)投资,同时又采取比例再保险策略的情况下,通过对经典的Cramér-Lundberg保险公司盈余过程模型的连续扩散近似,利用动态规划原理分别得出了在破产概率最小和终值期望效用最大两种目标函数下,保险公司的最优投资和最优再保策略的显式解和对应的目标函数值.对两种目标函数下的最优策略做了比较研究.