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     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

Scheduling of depalletizing and truck loading operations in a food distribution system

This paper studies a scheduling problem arising in a beef distribution system where pallets of various types of beef products in the warehouse are first depalletized and then individual cases are loaded via conveyors to the trucks which deliver beef products to various customers. Given each customer's demand for each type of beef, the problem is to find a depalletizing and truck loading schedule that fills all the demands at a minimum total cost. We first show that the general problem where there are multiple trucks and each truck covers multiple customers is strongly NP‐hard. Then we propose polynomial‐time algorithms for the case where there are multiple trucks, each covering only one customer, and the case where there is only one truck covering multiple customers. We also develop an optimal dynamic programming algorithm and a heuristic for solving the general problem. By comparing to the optimal solutions generated by the dynamic programming algorithm, the heuristic is shown to be capable of generating near optimal solutions quickly. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Mimetic and normative isomorphism in the establishment and maintenance of independent air forces

Why do countries have air forces? Organizational alternatives, such as maintaining separate air arms for the army and navy, have become quite rare. The conventional narrative advanced by advocates of independent air forces stress that the primacy of airpower in modern warfare mandates centralized control of most military aviation. In this view, political–military uncertainty has driven mimetic isomorphism – pressure on national governments to organize as others organize so as to fight or deter war just as effectively. However, working from a set of 56 countries that were politically independent within a few years of the establishment of the first ever independent air force (the Royal Air Force) in 1918, and continuing through nearly the present, there is no clear pattern of external military pressure prompting this particular reorganization. Rather, from anecdotal evidence, the cause has more likely been normative isomorphism – a professional craving to look as others look to foster political or personal legitimacy. For whatever reason, though, choices of structures tend to lead to specific choices of policies. Thus, the result suggests that defense ministries looking for more effective or less costly organizational schemas may reasonably consider alternatives to the tripartite army–navy–air force structure.