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.     

Incorporating learning curve costs in acquisition strategy optimization

Each year, the U.S. Army procures billions of dollars worth of weapons and equipment. The process of deciding what to buy, when to buy, and in what quantities is extremely complex, requiring extensive analysis. Two techniques used in this analysis are mathematical programming and cost estimation. Although they are related through constraints on available procurement funds, the use of nonlinear cost learning curves, which better represent system costs as a function of quantity produced, have not been incorporated into the mathematical programming formulations that compute the quantities of items to be procured. As a result, the solutions obtained could be either suboptimal, or even infeasible with respect to budgetary limitations. In this paper we present a piecewise linear approximation of the learning curve costs for a more accurate portrayal of budgetary constraints used in a mixed integer linear programming for acquisition strategy optimization. In addition, implementation issues are discussed, and performance results are given. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 255–271, 1999     

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.     

The individual station technique for the analysis of cyclic polling systems

Polling systems are used to model a wide variety of real-world applications, for example, telecommunication and material handling systems. Consequently, there is continued interest in developing efficient algorithms to analyze the performance of polling systems. Recent interest in the optimization of these systems has brought up the need for developing very efficient techniques for analyzing their waiting times. This article presents the Individual Station technique for cyclic polling systems. The technique possesses the following features: (a) it allows the user to compute the mean waiting time at a selected station independent of the mean waiting time computations at other stations, and (b) its complexity is low and independent of the system utilization. In addition the technique provides explicit closed-form expressions for (i) the mean waiting times in a system with 3 stations, and (ii) the second moment of the waiting times in a system with 2 stations, for an exhaustive service system. © 1996 John Wiley & Sons, Inc.     

Printed circuit board family grouping and component allocation for a multimachine,open-shop assembly cell

This article considers a particular printed circuit board (PCB) assembly system employing surface mount technology. Multiple, identical automatic placement machines, a variety of board types, and a large number of component types characterize the environment studied. The problem addressed is that of minimizing the makespan for assembling a batch of boards with a secondary objective of reducing the mean flow time. The approach adopted is that of grouping boards into production families, allocating component types to placement machines for each family, dividing of families into board groups with similar processing times, and the scheduling of groups. A complete setup is incurred only when changing over between board families. For the environment studied, precedence constraints on the order of component placement do not exist, and placement times are independent of feeder location. Heuristic solution procedures are proposed to create board subfamilies (groups) for which the component mounting times are nearly identical within a subfamily. Assignment of the same component type to multiple machines is avoided. The procedures use results from the theory of open-shop scheduling and parallel processor scheduling to sequence boards on machines. Note that we do not impose an open-shop environment but rather model the problem in the context of an open shop, because the order of component mountings is immaterial. Three procedures are proposed for allocating components to machines and subsequently scheduling boards on the machines. The first two procedures assign components to machines to balance total work load. For scheduling purposes, the first method groups boards into subfamilies to adhere to the assumptions of the open-shop model, and the second procedure assumes that each board is a subfamily and these are scheduled in order of shortest total processing time. The third procedure starts by forming board subfamilies based on total component similarity and then assigns components to validate the open-shop model. We compare the performance of the three procedures using estimated daily, two-day, and weekly production requirements by averaging quarterly production data for an actual cell consisting of five decoupled machines. © 1994 John Wiley & Sons, Inc.