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.     

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.     

Ambulance location for maximum survival

This article proposes new location models for emergency medical service stations. The models are generated by incorporating a survival function into existing covering models. A survival function is a monotonically decreasing function of the response time of an emergency medical service (EMS) vehicle to a patient that returns the probability of survival for the patient. The survival function allows for the calculation of tangible outcome measures—the expected number of survivors in case of cardiac arrests. The survival‐maximizing location models are better suited for EMS location than the covering models which do not adequately differentiate between consequences of different response times. We demonstrate empirically the superiority of the survival‐maximizing models using data from the Edmonton EMS system. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Threshold optimization for weighted voting classifiers

Weighted voting classifiers considered in this paper consist of N units each providing individual classification decisions. The entire system output is based on tallying the weighted votes for each decision and choosing the one which has total support weight exceeding a certain threshold. Each individual unit may abstain from voting. The entire system may also abstain from voting if no decision support weight exceeds the threshold. Existing methods of evaluating the reliability of weighted voting systems can be applied to limited special cases of these systems and impose some restrictions on their parameters. In this paper a universal generating function method is suggested which allows the reliability of weighted voting classifiers to be exactly evaluated without imposing constraints on unit weights. Based on this method, the classifier reliability is determined as a function of a threshold factor, and a procedure is suggested for finding the threshold which minimizes the cost of damage caused by classifier failures (misclassification and abstention may have different price.) Dynamic and static threshold voting rules are considered and compared. A method of analyzing the influence of units' availability on the entire classifier reliability is suggested, and illustrative examples are presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 322–344, 2003.     

On the polyhedral structure of two‐level lot‐sizing problems with supplier selection

In this article, we study a two‐level lot‐sizing problem with supplier selection (LSS), which is an NP‐hard problem arising in different production planning and supply chain management applications. After presenting various formulations for LSS, and computationally comparing their strengths, we explore the polyhedral structure of one of these formulations. For this formulation, we derive several families of strong valid inequalities, and provide conditions under which they are facet‐defining. We show numerically that incorporating these valid inequalities within a branch‐and‐cut framework leads to significant improvements in computation. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 647–666, 2017