One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.     

On the theory of semi-infinite programming and a generalization of the kuhn-tucker saddle point theorem for arbitrary convex functions

We first present a survey on the theory of semi-infinite programming as a generalization of linear programming and convex duality theory. By the pairing of a finite dimensional vector space over an arbitrarily ordered field with a generalized finite sequence space, the major theorems of linear programming are generalized. When applied to Euclidean spaces, semi-infinite programming theory yields a dual theorem associating as dual problems minimization of an arbitrary convex function over an arbitrary convex set in n-space with maximization of a linear function in non-negative variables of a generalized finite sequence space subject to a finite system of linear equations. We then present a new generalization of the Kuhn-Tucker saddle-point equivalence theorem for arbitrary convex functions in n-space where differentiability is no longer assumed.     

What is the global landpower network and what value might it provide?

US national security guidance, as well as the US Army’s operational experiences since 2001, emphasizes the importance of working closely with partner countries to achieve US strategic objectives. The US Army has introduced the global landpower network (GLN) concept as a means to integrate, sustain and advance the Army’s considerable ongoing efforts to meet US national security guidance. This study develops the GLN concept further, and addresses three questions. What benefits can the GLN provide the Army? What are the essential components of the GLN? What options exist for implementing the GLN concept? By developing the GLN concept, the Army has the opportunity to transition the GLN from an often ad hoc and reactive set of relationships to one that the Army more self-consciously prioritizes and leverages as a resource to meet US strategic objectives.     

Remotely Piloted Aircraft,Risk, and Killing as Sacrifice: The Cost of Remote Warfare

In this paper I argue that a remotely piloted aircraft (RPA) pilot’s act of killing remotely, when it is done in the defense of another person, can be viewed as an act of sacrifice. This argument concludes from two premises. First, the RPA pilot faces psychological risk to self by carrying out such an action; second, the RPA pilot is motivated to some significant degree by something other than self-interest. Moreover, I challenge both the view that RPA represent merely an incremental development in technology yielding an incremental expansion of the distance between the war-fighter and the target and the view that RPA is revolutionary in some fundamental sense. I instead argue that, based upon the natural geometric boundary imposed by the earth’s shape, RPA have maximized the physical distance between the war-fighter and the target and, over time, this fact will change, not only the psychological effects on the RPA pilot, but also the way we view killing and distance in general. When taken together, these two broad claims, that other-defense can justify killing in war and that there is a psychological cost paid by remote killers, yield a conception of remote killing as an act of sacrifice that will inform the broader conversation about ethics, risk, killing, and RPA.     

A unified model incorporating yield,burn‐in,and reliability

The correlated improvement in yield and reliability has been observed in the case studies on integrated circuits and electronic assemblies. This paper presents a model that incorporates yield and reliability with the addition of a burn‐in step to explain their correlated improvement. The proposed model includes as special cases several yield and reliability models that have been previously published and thus provides a unifying framework. The model is used to derive a condition for which yield functions can be multiplied to obtain the overall yield. Yield and reliability are compared as a function of operation time, and an analytical condition for burn‐in to be effective is also obtained. Finally, Poisson and negative binomial defects models are further considered to investigate how reliability is based on yield. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Optimal machine capacity expansions with nested limitations under stochastic demand

This paper studies capacity expansions for a production facility that faces uncertain customer demand for a single product family. The capacity of the facility is modeled in three tiers, as follows. The first tier consists of a set of upper bounds on production that correspond to different resource types (e.g., machine types, categories of manpower, etc.). These upper bounds are augmented in increments of fixed size (e.g., by purchasing machines of standard types). There is a second‐tier resource that constrains the first‐tier bounds (e.g., clean room floor space). The third‐tier resource bounds the availability of the second‐tier resource (e.g., the total floor space enclosed by the building, land, etc.). The second and third‐tier resources are expanded at various times in various amounts. The cost of capacity expansion at each tier has both fixed and proportional elements. The lost sales cost is used as a measure for the level of customer service. The paper presents a polynomial time algorithm (FIFEX) to minimize the total cost by computing optimal expansion times and amounts for all three types of capacity jointly. It accommodates positive lead times for each type. Demand is assumed to be nondecreasing in a “weak” sense. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A general model of heterogeneous system lifetimes and conditions for system burn‐in

Burn‐in is a technique to enhance reliability by eliminating weak items from a population of items having heterogeneous lifetimes. System burn‐in can improve system reliability, but the conditions for system burn‐in to be performed after component burn‐in remain a little understood mathematical challenge. To derive such conditions, we first introduce a general model of heterogeneous system lifetimes, in which the component burn‐in information and assembly problems are related to the prediction of system burn‐in. Many existing system burn‐in models become special cases and two important results are identified. First, heterogeneous system lifetimes can be understood naturally as a consequence of heterogeneous component lifetimes and heterogeneous assembly quality. Second, system burn‐in is effective if assembly quality variation in the components and connections which are arranged in series is greater than a threshold, where the threshold depends on the system structure and component failure rates. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 364–380, 2003.     

Computerized scheduling of seagoing tankers

Computerized Scheduling of Seagoing Tankers The tanker scheduling problem considered in this paper is that of the Defense Fuel Supply Center (DFSC) and the Military Sealift Command (MSC) in the worldwide distribution of bulk petroleum products. Routes and cargoes which meet delivery schedule dates for a multiplicity of product requirements at minimum cost are to be determined for a fleet of tankers. A general mathematical programming model is presented, and then a mixed integer model is developed which attempts to reflect the true scheduling task of DFSC and MSC as closely as possible. The problem is kept to within a workable size by the systematic construction of a set of tanker routes which does not contain many possible routes that can be judged unacceptable from practical considerations alone.     

The fractional fixed-charge problem

Fractional fixed-charge problems arise in numerous applications, where the measure of economic performance is the time rate of earnings or profit (equivalent to an interest rate on capital investment). This paper treats the fractional objective function, after suitable transformation, as a linear parametric fixed-charge problem. It is proved, with wider generality than in the case of Hirsch and Dantzig, that some optimal solution to the generalized linear fixed-charge problem is an extreme point of the polyhedral set defined by the constraints. Furthermore, it is shown that the optimum of the generalized fractional fixed-charge problem is also a vertex of this set. The proof utilizes a suitable penalty function yielding an upper bound on the optimal value of the objective function; this is particularly useful when considering combinations of independent transportation-type networks. Finally, it is shown that the solution of a fractional fixed-charge problem is obtainable through that of a certain linear fixed-charge one.