On the design of a tandem queue with blocking: Modeling,analysis, and gradient estimation

We demonstrate here how recent advances in the study of discrete-event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make-to-stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade-off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample-path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 1994 John Wiley & Sons, Inc.     

Energy-constrained pursuit in a fluid

A pursuer (P) pursues an evader(E), with each party choosing a speed in ignorance of the other's choice. Going extremely fast is not wise for either party because doing so would quickly exhaust available energy. The situation is modeled as a two-person zero-sum game. The game may or may not have a saddle point, depending on the energy ratio and tactical parameters. © 1994 John Wiley & Sons, Inc.     

Search techniques for a nonlinear multiprocessor scheduling problem

The problem of assigning computer program modules to functionally similar processors in a distributed computer network is investigated. The modules of a program must be assigned among processors in such a way as to minimize interprocessor communication while taking advantage of affinities of certain modules to particular processors. This problem is formulated as a zero-one quadratic programming problem, but is more conveniently modeled as a directed acyclic search graph. The model is developed and a backward shortest path labeling algorithm is given that produces an assignment of program modules to processors. A non-backtracking branch-and-bound algorithm is described that uses a local neighborhood search at each stage of the search graph.     

A note on cycling in the simplex method

Although cycling in the simplex method has long been known, a number of theoretical questions concerning cycling have not been fully answered. One of these, stated in [3], is to find the smallest example of cycling, and Beale's example with three equations and seven variables is conjectured to be the smallest one. The exact bounds on dimensions of cycling examples are established in this paper. We show that Beale's example is the smallest one which cycles at a non-optimal solution, that a smaller one can cycle at the optimum, and that, in general (including the completely degenerate case), a cycling example must have at least two equations, at least six variables, and at least three non-basic variables. Examples and geometries are given for the extreme cases, showing that the bounds are sharp.     

Branch and bound methods for a search problem

The problem of searching for randomly moving targets such as children and submarines is known to be fundamentally difficult, but finding efficient methods for generating optimal or near optimal solutions is nonetheless an important practical problem. This paper investigates the efficiency of Branch and Bound methods, with emphasis on the tradeoff between the accuracy of the bound employed and the time required to compute it. A variety of bounds are investigated, some of which are new. In most cases the best bounds turn out to be imprecise, but very easy to compute. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 243–257, 1998     

A novel method for determination of lethal radius for high-explosive artillery projectiles

A new model has been defined that enables the estimation of the lethal radius (radius of efficiency) of HE (High Explosive) artillery projectiles against human targets. The model is made of several modules: CAD (Computer Aided Design) modeling, fragment mass distribution estimation, fragment initial velocity prediction, fragment trajectory calculation, effective fragment density estimation, and high explosive projectile lethal radius estimation. The results were compared with the experimental results obtained based on tests in the arena used in our country, and the agreement of the results was good. This model can be used in any terminal-ballistics scenario for high explosive projectiles since it is general, para-metric, fast and relatively easy to implement.     

The optimal linear combination of control variates in the presence of asymptotically negligible bias

The optimal linear combination of control variates is well known when the controls are assumed to be unbiased. We derive here the optimal linear combination of controls in the situation where asymptotically negligible bias is present. The small-sample linear control which minimizes the mean square error (MSE) is derived. When the optimal asymptotic linear control is used rather than the optimal small-sample control, the degradation in MSE is c/n³, where n is the sample size and c is a known constant. This analysis is particulary relevant to the small-sample theory for control variates as applied to the steady-state estimation problem. Results for the method of multiple estimates are also given.