Approximating nonstationary two-priority non-preemptive queueing systems

An approximation for analyzing transient and nonstationary two-priority non-preemptive queueing systems is presented. This system has a three-dimensional state space, and through use of state-space partitioning in conjunction with use of conditional surrogate distributions with constant parameters an approximation is designed. Regardless of system capacity K, the approximation requires the numerical solution of only ten differential equations, compared to the K² + K+1 Kolmogorov-forward equations required for the classic solution. Time-dependent approximations of the mean number of entities of type i and of the probability of a type-i entity being in service are obtained. Empirical test results over a wide range of systems indicate the approximation is quite accurate.     

Approximation algorithms for minimizing total weighted completion time of orders on identical machines in parallel

We consider the problem of scheduling orders on identical machines in parallel. Each order consists of one or more individual jobs. A job that belongs to an order can be processed by any one of the machines. Multiple machines can process the jobs of an order concurrently. No setup is required if a machine switches over from one job to another. Each order is released at time zero and has a positive weight. Preemptions are not allowed. The completion time of an order is the time at which all jobs of that order have been completed. The objective is to minimize the total weighted completion time of the orders. The problem is NP‐hard for any fixed number (≥2) of machines. Because of this, we focus our attention on two classes of heuristics, which we refer to as sequential two‐phase heuristics and dynamic two‐phase heuristics. We perform a worst case analysis as well as an empirical analysis of nine heuristics. Our analyses enable us to rank these heuristics according to their effectiveness, taking solution quality as well as running time into account. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Landmarks in defense literature

Tom Wintringham: New Ways of War (1940), People's War (1942) and Weapons and Tactics (1943)     

Parallel machine scheduling with eligibility constraints: A composite dispatching rule to minimize total weighted tardiness

We study a parallel machine scheduling problem, where a job j can only be processed on a specific subset of machines M_j, and the M_j subsets of the n jobs are nested. We develop a two‐phase heuristic for minimizing the total weighted tardiness subject to the machine eligibility constraints. In the first phase, we compute the factors and statistics that characterize a problem instance. In the second phase, we propose a new composite dispatching rule, the Apparent Tardiness Cost with Flexibility considerations (ATCF) rule, which is governed by several scaling parameters of which the values are determined by the factors obtained in the first phase. The ATCF rule is a generalization of the well‐known ATC rule which is very widely used in practice. We further discuss how to improve the dispatching rule using some simple but powerful properties without requiring additional computation time, and the improvement is quite satisfactory. We apply the Sequential Uniform Design Method to design our experiments and conduct an extensive computational study, and we perform tests on the performance of the ATCF rule using a real data set from a large hospital in China. We further compare its performance with that of the classical ATC rule. We also compare the schedules improved by the ATCF rule with what we believe are Near Optimal schedules generated by a general search procedure. The computational results show that especially with a low due date tightness, the ATCF rule performs significantly better than the well‐known ATC rule generating much improved schedules that are close to the Near Optimal schedules. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 249–267, 2017     

Mixture selection for maximal stochastic performance

Methodology for the optimal selection of a mixture of components for the attainment of a required performance level is developed. This accommodates both cost and stochastic variation and is applied to gasoline blending. © 1994 John Wiley & Sons, Inc.     

Properties of a three-dimensional estimator

A large-scale simulation was conducted to investigate the statistical properties and the suitability of an estimator that estimates the coordinates of a three-dimensional source, according to the angles at which several observers view the source. The estimator uses a heuristical averaging method of estimates obtained from the solution of six two-dimensional problems that utilize line-to-point transformations. The estimator was found to be approximately unbiased with low standard deviations for normal error distributions. An effective and easy-to-use forecasting formula was developed to forecast the parameters of the distributions of the estimates. © 1994 John Wiley & Sons, Inc.     

Country survey XI: Defence and the Israeli economy

The literature on economic aspects of defence in Israel is critically reviewed by subject: measuring the defence burden, the determinants of defence spending, the effects of defence spending on the economy, and the military‐industrial complex. An overview of the Israeli economy is provided, and some new econometric findings on the determinants of defence spending are presented. The paper concludes by addressing policy issues in the context of Israel's jubilee.