Continuous-review,lost-sales inventory models with Poisson demand,a fixed lead time and no fixed order cost

This paper considers continuous-review lost-sales inventory models with no fixed order cost and a Poisson demand process. There is a holding cost per unit per unit time and a lost sales cost per unit. The objective is to minimise the long run total cost. Base stock policies are, in general, sub-optimal under lost sales. The optimal policy would have to take full account of the remaining lead times on all the orders currently outstanding and such a policy would be too complex to analyse, let alone implement. This paper considers policies which make use of the observation that, for lost sales models, base stock policies can be improved by imposing a delay between the placement of successive orders. The performance of these policies is compared with that of the corresponding base stock policy and also with the policy of ordering at fixed and regular intervals of time.     

自动化车床最优刀具检测模型研究

针对自动化车床工序最优检测和刀具更换问题进行了探讨.将定期检测和将刀具更换作用于同一工序流程,在只考虑刀具故障条件下,通过概率论和更新过程理论建立了以单位时间内期望费用为目标函数的数学模型,以检测间隔和刀具更换间隔为策略,确定最优的策略使得目标函数达到最小,并求出了经长期运行单位时间内期望费用的明显表达式.最后还对结果进行了讨论.     

考虑非周期检测的视情维修与备件订购联合策略优化

针对单部件系统/关键部件提出视情维修与备件订购联合策略,其中系统退化服从两阶段延迟时间过程且采用非周期检测策略,退化初期以检测间隔T₁检查系统状态,而在第一次识别缺陷状态时,缩短检测周期为T₂、订购备件且进行不完美维修;若系统在随后的退化中被识别处于缺陷状态,执行不完美维修直至超过阈值次数N_max并采取预防性更换,但若在检测周期内发生故障则进行更换。根据系统状态和备件状态分析各种可能更新事件及相应的联合决策,利用更新报酬理论构建最小化单位时间内期望成本的目标函数,优化T₁,T₂, N_max。与对比模型策略相比,算例结果表明所提出的联合策略能有效降低单位时间内的期望成本。     

Monetary aspects of acquiring technology for price discrimination of a perishable storable product

The remaining shelf-life of perishable storable products can become an additional source of volatility among consumers and a matter for price discrimination. Two models are presented. Both models assume the retailer has the information about consumers’ sensitivity to the remaining shelf-life (eg, their purchasing history). Only the first assumes the retailer has also the technology for price discrimination. An optimal solution for each model is analytically obtained and a numerical example that illustrates the significance is introduced. Numerical illustration indicates that a policy of identical prices for all based on accurate information about consumer sensitivity to remaining shelf-life results in a profit that is just slightly smaller per unit of time compared with the price discrimination policy. Opposing, the numerical illustration also indicates significant difference between the models with respect to their impact on consumers. Following these results, the regulator may consider suggesting the retailer monetary incentives in order to utilize price discrimination.     

Optimal inspection policy for three-state systems monitored by control charts

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.     

Availability and maintenance modeling for systems subject to dependent hard and soft failures

This paper develops availability and maintenance models for single‐unit systems subject to dependent hard and soft failures. A hard failure stops the system immediately, whereas a soft failure only reduces the performance capacity of the system. Dependence between these 2 types of failures is reflected in the fact that each soft failure directly increases the hazard rate of the hard failure. On the basis of such interaction, we derive recursive equations for the system reliability and availability functions. To detect both types of failures, inspections are executed periodically. Furthermore, we investigate the optimal inspection policy via the minimization of the expected cost per unit time. The applicability of the developed availability and maintenance models is validated by a case study on an electrical distribution system.     

An optimal ordering policy for a spare unit with lead time

We consider a generalised ordering policy in which a spare unit for replacement can be delivered only by order after a constant lead time. Introducing the costs for ordering, shortage and holding, we derive the expected cost per unit time in the steady-state. We discuss the optimal ordering policy which minimises the expected cost, and show in a main theorem that the optimal policy is reduced to either one of two typical ordering policies depending on some conditions. We further discuss a similar ordering policy with varying lead times.     

修理工单重定期休假可修系统更换模型研究

针对修理工带有单重休假的单部件可修系统,提出了一种新的维修更换模型.假定系统是可修的,逐次故障后的维修时间构成随机递增的几何过程,系统工作时间构成随机递增的几何过程,在修理工休假时间为定长的情况下,分别选取系统的总工作时间T和故障维修次数N为更换策略,以长期运行单位时间内的期望效益为目标函数,通过更新过程和几何过程理论建立数学模型,导出了目标函数的解析表达式,通过最大化目标函数来获取系统最优的更换策略T*和N*.并在一定条件下给出了策略N比策略T优的充分条件.最后,通过数值例子验证了方法的有效性.     

具有不耐烦顾客和多重工作休假的排队库存系统

研究具有不耐烦顾客和多重工作休假的M/M/1/N排队库存系统模型,分别考虑了系统中库存为零时服务员休假和系统中顾客数为零时服务员休假两种休假方式,基于(s,S)库存策略,运用矩阵迭代方法得到了系统稳态概率分布,并给出系统相关性能指标,进而建立系统平均库存费用函数.通过数值算例对比分析了两种休假方式下的系统主要参数变化对系统重要性能指标的影响,并在最优费用的层面对两个模型的优劣进行了对比分析.     

Approximate Calculation of Optimal Inspection Times

This paper considers an inspection model whose failure is known only through checking. A new approximate calculation of optimal checking procedures is suggested. This computes successive check times backwards, supposing that an appropriate check time is previously given after a large number of checks. This policy is simple to compute and compares fairly well with the optimal policy.     

Filtering Policies in Loss Queuing Network Location Problems

In this paper we deal with two stationary loss queuing network location models. We analyze the influence of filtering policies on the locational aspect of the problems. We assume that requests for service are placed at nodes of a transportation network and they arrive in time as independent homogeneous Poisson processes with different input rates. The considered policies only cover a given proportion of requests even if there are idle service units. This proportion is stationary and fixed in advance and only depends on the node where the request is originated. The objective is to find the location of the facilities together with the filtering policy to be applied that minimize the expected total cost per unit time with respect to a given cost structure. Properties and computational results are presented enabling the resolution of these problems efficiently and showing the good performance of filtering policies in terms of both the overall operating costs, and the demand that is served.     

自动化车床最优刀具检测更换模型

本文通过对自动化车床 1 0 0次刀具故障的记录进行数理统计分析 ,研究了自动化车床连续加工单一零件时刀具的检测及更换模型 .首先利用概率大样本场合的 D检验方法证明了刀具的故障发生规律服从正态分布 [1] ,继而求出系统工序的寿命分布函数 [2 ] ,列出以合格零件单位期望损失为目标 ,关于检测间隔和刀具定期更换间隔为变量的多目标函数方程 ,最后利用计算机进行列举比较求解 ,从而得出取得最大经济效益的系统工序的最优检测间隔以及最优刀具更换策略 .由于刀具的故障发生服从正态分布 ,我们对模型进行了改进 ,采取有规律的不等间隔的检查方式 ,结果取得了相对于等检查间隔的更优解 .本文利用算法较好地解决了问题 ,得到了问题的优化解 .对于问题 1 ,解得换刀间隔和检查间隔分别为369和 1 8,单位合格零件损失 4 .61 5元 ,采用不等间隔的损失为 4 .4 0 5元 ;对于问题 2 ,由于情况复杂 ,解得换刀间隔和检查间隔分别为 30 6和 2 8,单位合格零件损失 9.2 68元 ,采用不等间隔的损失为 9.0 4 7元 ,从而验证了本文提出的不等间隔检查方式的更优性     

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.     

A characterization of cycle-free unit probe interval graphs

A graph is a probe interval graph (PIG) if its vertices can be partitioned into probes and nonprobes with an interval assigned to each vertex so that vertices are adjacent if and only if their corresponding intervals overlap and at least one of them is a probe. PIGs are a generalization of interval graphs introduced by Zhang for an application concerning the physical mapping of DNA in the human genome project. PIGs have been characterized in the cycle-free case by Sheng, and other miscellaneous results are given by McMorris, Wang, and Zhang. Johnson and Spinrad give a polynomial time recognition algorithm for when the partition of vertices into probes and nonprobes is given. The complexity for the general recognition problem is not known. Here, we restrict attention to the case where all intervals have the same length, that is, we study the unit probe interval graphs and characterize the cycle-free graphs that are unit probe interval graphs via a list of forbidden induced subgraphs.     

A graphical method to repair-cost limit replacement policies with imperfect repair

In this paper, we consider a different type of repair-cost limit replacement problem with imperfect repair from earlier models. We focus on the problem of determining the timing to stop repairing a unit after it fails, and propose a nonparametric method to estimate the optimal repair-cost limit which minimizes the total expected cost per unit time in the steady-state, by applying the total time on test (TTT) concept. Through a numerical example, the optimal policy is calculated from the repair-cost data directly, and the benefit of the proposed method is shown.     

A discrete approach to designing optimal hedging-point control policies for production-inventory systems with general stochastic behavior

The hedging-point policy for a production-inventory system is investigated under the effect of probabilistic machine breakdowns and repairs assuming general discrete distributions for the repair time and the time to failure. Using a methodology whereby inventory levels can assume only discrete values, an optimal safety stock size that minimizes the total expected cost per unit time is determined.     

Using aggregate fill rate for dynamic scheduling of multi-class systems

For dynamic scheduling of multi-class systems where backorder cost is incurred per unit backordered regardless of the time needed to satisfy backordered demand, the following models are considered: the cost model to minimize the sum of expected average inventory holding and backorder costs and the service model to minimize expected average inventory holding cost under an aggregate fill rate constraint. Use of aggregate fill rate constraint in the service model instead of an individual fill rate constraint for each class is justified by deriving equivalence relations between the considered cost and service models. Based on the numerical investigation that the optimal policy for the cost model is a base-stock policy with switching curves and fixed base-stock levels, an alternative service model is considered over the class of base-stock controlled dynamic scheduling policies to minimize the total inventory (base-stock) investment under an aggregate fill rate constraint. The policy that solves this alternative model is proposed as an approximation of the optimal policy of the original cost and the equivalent service models. Very accurate heuristics are devised to approximate the proposed policy for given base-stock levels. Comparison with base-stock controlled First Come First Served (FCFS) and Longest Queue (LQ) policies and an extension of LQ policy (Δ policy) shows that the proposed policy performs much better to solve the service models under consideration, especially when the traffic intensity is high.     

Optimal production time and number of maintenance actions for an imperfect production system under equal-interval maintenance policy

This paper deals with the optimal production/maintenance (PM) policy for a deteriorating production system which may shift from the in-control state to the out-of-control state while producing items. The process is assumed to have a general shift distribution. Under the commonly used maintenance policy, equal-interval maintenance, the joint optimizations of the PM policy are derived such that the expected total cost per unit time is minimized. Different conditions for optimality, lower and upper bounds and uniqueness properties on the optimal PM policy are provided. The implications of another commonly used policy, to perform a maintenance action only at the end of the production run, are also discussed. Structural properties for the optimal policy are established so that an efficient solution procedure is obtained. In the exponential case, some extensions of the results obtained previously in the literature are presented. A numerical example is provided to illustrate the solution procedure for the optimal production and maintenance policy.     

Optimal spare ordering policy under a rebate warranty

This paper develops, from the customer’s perspective, the optimal spare ordering policy for a non-repairable product with a limited-duration lifetime and under a rebate warranty. The spare unit for replacement is available only by order and the lead time for delivery follows a specified probability distribution. Through evaluation of gains due to the rebate and the costs due to ordering, shortage, and holding, we derive the expected cost per unit time and cost effectiveness in the long run and examine the optimal ordering time by minimizing or maximizing these cost expressions. We show that there exists a unique optimum solution under mild assumptions. We provide a numerical example and illustrate sensitivity analysis.     

Modeling and analysis for determining optimal suppliers under stochastic lead times

The policy of simultaneously splitting replenishment orders among several suppliers has received considerable attention in the last few years and continues to attract the attention of researchers. In this paper, we develop a mathematical model which considers multiple-supplier single-item inventory systems. The item acquisition lead times of suppliers are random variables. Backorder is allowed and shortage cost is charged based on not only per unit in shortage but also per time unit. Continuous review (s,Q)$(s\text{,}Q)$ policy has been assumed. When the inventory level depletes to a reorder level, the total order is split among n suppliers. Since the suppliers have different characteristics, the quantity ordered to different suppliers may be different. The problem is to determine the reorder level and quantity ordered to each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost, and shortage cost, is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared with the models in the literature. According to our extensive experiments, the model developed in this paper is the best model in the literature which considers order splitting for n-supplier inventory systems since it is the nearest model to the real inventory system.