On the number of games played in a best of (2n – 1) series

Let p(⩾0.5) denote the probability that team A beats B in a single game. The series continues until either A or B wins n games. Assuming that these games are independent replications, we study some features of the distribution of X_n, the number of games played in the series. It is shown that X_n is unimodal, has an IFRA distribution, and is stochastically decreasing in p. Close approximations to its mode, mean, and variance are given. Finally, it is shown that the maximum-likelihood estimator of p based on X_n is unique.     

Discount pricing policies for inventories subject to declining demand

Until only recently, the mechanism behind determining item price has been ignored and the discount price taken as a given in quantity-discount inventory decision problems. Inventory subject to declining demand further complicates both pricing and replenishment decisions. This article provides the vendor with the means for optimally determining both the discount price and replenishment order frequency for all buyers in the system in an environment of declining demand. In the multiple-buyer case, we provide an efficient algorithm for classifying buyers into homogeneous subgroups to further enhance joint cost savings among all system participants.     

Should we be using cost of capital in calculating holding costs of consumable inventory?

The DOD directs the usage of 10% of item cost as the cost of capital in the calculation of inventory holding costs. This 10% cost is not totally justified and a complete review must be accomplished to bring this factor to a meaningful and more useful value. The current logic supporting a 10% cost of capital results in a continuing perturbation which forces the Air Force to operate in a less than efficient mode when using the economic order quantity for consumable purchases.     

Algorithms for the design of finite-capacity service units

Finite-capacity queues arise naturally in many practical situations, notably in communications and manufacturing engineering. In this article, the matrix formalism of probability distributions of phase type is used to develop fast algorithms to compute various steady-state distributions for the finite-capacity PH/PH/1 queue. This algorithm is an important ingredient in solving nontraditional but significant design problems. Some of these are described as illustrative examples.     

A survey of preventive maintenance models for stochastically deteriorating single-unit systems

A survey of the research done on preventive maintenance is presented. The scope of the present survey is on the research published after the 1976 paper by Pierskalla and Voelker [98]. This article includes optimization models for repair, replacement, and inspection of systems subject to stochastic deterioration. A classification scheme is used that categorizes recent research into inspection models, minimal repair models, shock models, or miscellaneous replacement models.     

金属靶体材料动力硬度测试及动态阻力分析

以高速侵彻下45钢靶体侵彻阻力为研究对象,开展了弹体高速侵彻45钢靶体试验,获取了典型弹体对45钢靶体的成坑参数。基于高速侵彻阻力模型对靶体侵彻阻力及影响因素进行分析。结合流体动力学侵彻模型对不同弹体材料侵彻45钢靶体侵彻深度规律进行研究。研究结果表明:随着撞击速度的增大,45钢的靶体阻力从5. 13 GPa减小到3. 7 GPa;基于材料动力硬度测试方法的靶体动态阻力测试结果和理论计算结果吻合较好;随着靶体动态屈服强度的增大,靶体阻力呈线性增大的趋势;侵彻深度及靶体动态阻力理论计算结果和试验数据吻合较好,说明所提动态阻力确定方法可行,可为高速侵彻动力学研究提供参考。     

未知新生目标强度的多目标概率假设密度滤波算法

针对标准概率假设密度滤波器要求,新生目标强度作为先验信息需已知的工程限制,提出一种未知新生目标强度的多目标概率假设密度算法。该算法以概率假设密度滤波器为基础,通过充分利用目标运动信息及其与监视区域的相对关系来获取源于潜在新生目标的量测,并以此建模下一时刻滤波器所需的新生目标强度。仿真结果表明,所提算法在含有未知新生目标跟踪场景具有鲁棒的滤波性能,且其跟踪精度和计算代价均优于相关多目标PHD滤波器。     

Multiechelon inventory systems with lateral supply

We develop approximations to estimate the expected backorders in a multiechelon system in which lateral supply actions between bases are allowed when a backorder occurs. These approximations are easy to compute, and the average absolute error over a wide range of parameter values is less than 4% when items are depot repairable, even when bases are dissimilar. With lateral supply, backorder reductions of 30-50% are not uncommon, and a 72% reduction was observed in two cases. Lateral supply becomes more important with low demand rates. A similar approach was unsuccessful for base-repairable items. However, lateral supply has a beneficial effect only when the lateral supply time is very short, 1/4 or less of the average base repair time. Even in such cases lateral supply is unlikely to be important in an actual application, because base management can expedite repair of critical items.     

A multi-run interactive method for bicriterion optimization problems

This article introduces a new conceptual and methodological framework for the use of decision makers and their interactions with the computer in bicriterion decision making. The new method, called the multirun interactive method, attempts to estimate the prior of the decision maker on his uncertain preference nature using the minimum cross-entropy principle. A computational study is performed with four hypothesized prior distributions under various interaction conditions. Other important aspects related to the method, such as implementation of the method, decision making under certainty, decision making with multiple decision makers, and bicriterion integer programming, are also discussed.     

Scheduling with earliness and tardiness penalties

We show that the deterministic nonpreemptive scheduling problem with earliness and tardiness penalties can be solved in polynomial time for certain forms of an objective function provided that a certain optimization problem can be solved. We give instances where this problem has a solution and show that this generalizes several results from the literature. These results do not require symmetric penalization and the penalty functions need only be lower semicontinuous.