Solutions for a class of n-person games in partition function form

A unique polyhedral solution is given for most n-person games in partition function form when only partitions into coalitions with 1, n-1, and n players have large payoffs.     

A (Q,R) inventory model with lost sales and erlang-distributed lead times

The exact expression is derived for the average stationary cost of a (Q,R) inventory system with lost sales, unit Poisson demands, Erlang-distributed lead times, fixed order cost, fixed cost per unit lost sale, linear holding cost per unit time, and a maximum of one order outstanding. Explicit expressions for the state probabilities and a fast method of calculating them are obtained for the case of Q greater than R. Exponential lead times are analyzed as a special case. A simple cyclic coordinate search procedure is used to locate the minimum cost policy. Examples of the effect of lead time variability on costs are given.     

Cyclic preference scheduling for nurses using branch and price

This paper presents a new methodology to solve the cyclic preference scheduling problem for hourly workers. The focus is on nurse rostering but is applicable to any organization in which the midterm scheduling decision must take into account a complex of legal, institutional, and preferential constraints. The objective is to strike a balance between satisfying individual preferences and minimizing personnel costs. The common practice is to consider each planning period independently and to generate new rosters at the beginning of each. To reduce some of the instability in the process, there is a growing trend toward cyclic schedules, which are easier to manage and are generally perceived to be more equitable. To address this problem, a new integer programming model is presented that combines the elements of both cyclic and preference scheduling. To find solutions, a branch‐and‐price algorithm is developed that makes use of several branching rules and an extremely effective rounding heuristic. A unique feature of the formulation is that the master problem contains integer rather than binary variables. Computational results are reported for problem instances with up to 200 nurses. Most were solved within 10 minutes and many within 3 minutes when a double aggregation approach was applicable. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Combining standardized time series area and Cramér–von Mises variance estimators

We propose three related estimators for the variance parameter arising from a steady‐state simulation process. All are based on combinations of standardized‐time‐series area and Cramér–von Mises (CvM) estimators. The first is a straightforward linear combination of the area and CvM estimators; the second resembles a Durbin–Watson statistic; and the third is related to a jackknifed version of the first. The main derivations yield analytical expressions for the bias and variance of the new estimators. These results show that the new estimators often perform better than the pure area, pure CvM, and benchmark nonoverlapping and overlapping batch means estimators, especially in terms of variance and mean squared error. We also give exact and Monte Carlo examples illustrating our findings.© 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

气动剥离液滴的附面层分析方法

本文根据附面层理论,对高速气流中的液滴,因气流和液滴表面相互作用而产生的气动剥离现象进行了分析,建立了气液两相附面层耦合问题的理论分析模型,得到了发生气动剥离时的最小气流速度的计算公式,为液体燃料在高速气流申雾化机理研究提供参考。     

Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem. © 1996 John Wiley & Sons, Inc.     

Multilinear extensions and quotients of simple games

Studied here is the problem of evaluating the formation of coalitions in cooperative games by considering its internal and external effects. Our analysis is based upon a formal theory of the quotient game and the use of multilinear extensions to compute the Shapley value and the coalitional value. When it applies to simple games, a series of interesting results is obtained. © 1996 John Wiley & Sons, Inc.     

Optimal number of minimal repairs before replacement of a system subject to shocks

A system is subject to shocks that arrive according to a nonhomogeneous Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, whereas type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the times of type 2 failure or at the nth type 1 failure, whichever comes first. The optimal policy is to select n* to minimize the expected cost per unit time for an infinite time span. A numerical example is given to illustrate the method. © 1996 John Wiley & Sons, Inc.     

Intellectual spring cleaning: it’s time for a military “Do Not Read” list; and some sources that should be on that list

Military reading lists, intended to promote professional reading and in turn enhance education and develop critical thinking skills and sound judgement, recommend key texts to military personnel. This is a noble intent but the lists themselves, while generally good, are not flawless. Critiques of military reading lists often focus on what sources they are missing. This article offers its own critique but from a different perspective. It does so by analysing why some sources, which have become outdated, are based on faulty or incomplete research, have been thoroughly disproven, or some combination of the above, nevertheless linger on military reading lists. It then offers a short list of such sources, which it recommends be either removed from existing reading lists or accompanied by other sources that place the original source in appropriate historical context. Where applicable, it also recommends alternative sources that provide insights into the same subject matter. In so doing, this article is intended generate debate and to assist militaries to achieve a better balance between evaluation, induction and retention of valid knowledge on one hand, and rejection of outdated or flawed knowledge on the other.     

Cost analysis and extension of a simple maintenance-scheduling heuristic

Practitioners of maintenance scheduling sometimes use a simple analytic formula, derived based on inspection scheduling, as a heuristic to determine the length of the preventive maintenance period. The sensitivity of this heuristic solution is analyzed and the cost penalties are calculated compared to the exact solution that utilizes the lifetime distribution in the derivation of the optimal preventive maintenance period. A simple extension of the heuristic is suggested to improve the approximation with a slightly increased computational effort. The sensitivity and cost analysis of the improved heuristic are discussed as well. © 1994 John Wiley & Sons, Inc.