Sojourn times in G/M/1 fork‐join networks

We consider a processing network in which jobs arrive at a fork‐node according to a renewal process. Each job requires the completion of m tasks, which are instantaneously assigned by the fork‐node to m task‐processing nodes that operate like G/M/1 queueing stations. The job is completed when all of its m tasks are finished. The sojourn time (or response time) of a job in this G/M/1 fork‐join network is the total time it takes to complete the m tasks. Our main result is a closed‐form approximation of the sojourn‐time distribution of a job that arrives in equilibrium. This is obtained by the use of bounds, properties of D/M/1 and M/M/1 fork‐join networks, and exploratory simulations. Statistical tests show that our approximation distributions are good fits for the sojourn‐time distributions obtained from simulations. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Netwar Revisited: The Fight for the Future Continues

This work continues to develop the 'netwar' concept that the authors introduced in 1993 and have expanded upon in their various RAND and other writings ever since. Deeper understanding of the nature, strengths and vulnerabilities of networks will prove useful in combating terrorism and transnational crime, but also in understanding militant social activism, both of the violently disruptive sort and that which aims at fostering the rise of a global civil society. This essay also assesses recent US performance in the terror war, and concludes by raising concerns over the possible rise of a new form of network-based fascism.     

Algorithms and heuristics for variable-yield lot sizing

We consider the multiperiod lot-sizing problem in which the production yield (the proportion of usable goods) is variable according to a known probability distribution. We review two economic order quantity (EOQ) models for the stationary demand continuous-time problem and derive an EOQ model when the production yield follows a binomial distribution and backlogging of demand is permitted. A dynamic programming algorithm for an arbitrary sequence of demand requirements is presented. Heuristics based on both the EOQ model and appropriate modification of the underlying perfect-yield lot-sizing policies are discussed, and extensive computational evaluation of these heuristics is presented. Two of these heuristics are then modified to include the notion of supply safety stock. The modified heuristics consistently produce near-optimal lot-sizing policies for problems with stationary and time-varying demands.     

The outfit planning problem: Production planning in shipbuilding

Shipbuilding as currently practiced in U.S. commercial shipyards employs little quantitative modeling or analysis in production planning. This paper presents a brief discussion of the shipbuilding process and focuses on one major component which is referred to as outfitting. The outfit planning problem is described in detail and then formally modeled as a generalization of the resource constrained project scheduling problem. The value of the approach as well as barriers to its adoption are also discussed.     

Joint determination of optimum variable and attribute target means

This article considers the problem of joint control of attribute and variable quality characteristics of a given product. Items are acceptable if they meet the specifications for both types of quality characteristics at the same time. Otherwise, the items are sold as scrap at reduced prices. The objective is to determine simultaneously the target values for each characteristic so as to maximize the expected profit per item. Several item-by-item quality-inspection plans are formulated on the basis of various inspection strategies. These strategies are defined in terms of whether the inspection is to be carried out simultaneously for both characteristics, or sequentially, or whether inspection for one of the characteristics is to be ignored. All these plans are shown to differ in terms of their profitability. However, they all yield equivalent quality standards. A numerical example is provided to illustrate the application of these models.     

树形挠性多体系统的 Kane 动力学方程 ——一种面向计算机的建模方法

本文针对具有树形结构的空间挠性多体系统,建立了Kane 动力学模型。挠性多体系统由任意数目的挠性体或刚体组成,假定铰链点之间具有三自由度相对转动和平动,选取相对平动速度和转动角速度,以及模态坐标的导数为系统的广义速度,建立了系统的最小维数运动方程,所得结果便于计算机自动生成和进行数值仿真。     

Empirical bayes single sampling plans for specified posterior consumer and producer risks

Empirical Bayes single-sample acceptance sampling procedures are derived. These procedures assume that the lot fraction defective varies randomly according to a completely unknown and unspecified prior distribution. The unknown prior density function is estimated based on sampling results from previous lots. A procedure is developed for obtaining single-sampling plans that achieve specified posterior consumer and producer risks. The procedures are illustrated for a real-data example.     

Finding equivalent transportation formulations for constrained transportation problems

This paper describes a procedure for determining if constrained transportation problems (i.e., transportation problems with additional linear constraints) can be transformed into equivalent pure transportation problems by a linear transformation involving the node constraints and the extra constraints. Our results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables.     

The single server queue in discrete time-numerical analysis III

This paper deals with the stationary analysis of the finite, single server queue in discrete time. The following stntionary distributions and other quantities of practical interest are investigated: (1) the joint density of the queue length and the residual service time, (2) the queue length distribution and its mean, (3) the distribution of the residual service time and its mean, (4) the distribution and the expected value of the number of customers lost per unit of time due to saturation of the waiting capacity, (5) the distribution and the mean of the waiting time, (6) the asymptotic distribution of the queue length following departures The latter distribution is particularly noteworthy, in view of the substantial difference which exists, in general, between the distributions of the queue lengths at arbitrary points of time and those immediately following departures.     

Solving quadratic assignment problems with rectangular distances and integer programming

The problem considered involves the assignment of n facilities to n specified locations. Each facility has a given nonnegative flow from each of the other facilities. The objective is to minimize the sum of transportation costs. Assume these n locations are given as points on a two-dimensional plane and transportation costs are proportional to weighted rectangular distances. Then the problem is formulated as a binary mixed integer program. The number of integer variables (all binary) involved equals the number of facilities squared. Without increasing the number of integer variables, the formulation is extended to include “site costs” Computational results of the formulation are presented.