bluuebunny/crossref_metadata_2025_split huggingface dataset:
Lanchester‐type models of warfare and optimal control
Authors: Taylor James G. 
Published: May 2007

AbstractThe optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester‐type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition‐rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.
An experimental comparison of solution algorithms for the single‐machine tardiness problem
Authors: Baker Kenneth R. , Martin James B. 
Published: May 2007

AbstractA basic problem in scheduling involves the sequencing of a set of independent tasks at a single facility with the objective of minimizing mean tardiness. Although the problem is relatively simple, the determination of an optimal sequence remains a challenging combinatorial problem. A number of algorithms have been developed for finding solutions, and this paper reports a comparative evaluation of these procedures. Computer programs for five separate algorithms were written and all were run on a data base designed to highlight computational differences. Optimizing algorithms developed by Emmons and by Srinivasan appeared to be particularly efficient in the comparative study.
A note on some series representations of the integral of a bivariate normal distribution over an offset circle
Authors: Gilliland Dennis C. , Hansen Eldon R. 
Published: May 2007

AbstractConsider the problem of computing an offset circle probability under a normal distribution. One approach is to utilize an infinite series representation in which case it is important to have rapid convergence and a good upper bound on the error introduced by consideration of only a finite number of terms of the series. We relate three seemingly different series representations. In particular we show how two series representations for the bivariate case can be obtained by specializing more general results of Harold Ruben.
A note on the costly surveillance of a stochastic system
Authors: Chitgopekar S. S. 
Published: May 2007

AbstractWe consider the costly surveillance of a stochastic system with a finite state space and a finite number of actions in each state. There is a positive cost of observing the system and the system earns at a rate depending on the state of the system and the action taken. A policy for controlling such a system specifies the action to be taken and the time to the next observation, both possibly random and depending on the past history of the system. A form of the long range average income is the criterion for comparing different policies. If RΔ denotes the class of policies for which the times between successive observations of the system are random variables with cumulative distribution functions on [0, Δ], Δ < ∞, we show that there exists a nonrandomized stationary policy that is optimal in RΔ. Furthermore, for sufficiently large Δ, this optimal policy is independent of Δ.
The mixed ordering policy in periodic review stochastic multi‐commodity inventory systems
Authors: Goswick T. E. , Sivazlian B. D. 
Published: May 2007

AbstractIn multi‐commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two‐commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K1, or K2, where max (K1, K2) ≤ K ≤ K1 + K2, This paper considers a two‐commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.
Maintenance policies when failure distribution of equipment is only partially known
Authors: Kander Z. , Raviv A. 
Published: May 2007

AbstractAn optimal schedule for checking an equipment subject to failure which can be detected by inspection only, is derived. Increasing failure rate and one percentile specify the otherwise unknown life distribution. Dynamic programming methodology yields the solution which minimizes the maximum expected cost. Numerical examples are presented and compared with models employing differing amounts of knowledge.
A general treatment of upper unbounded and bounded hitchcock problems
Authors: Dwyer P. S. 
Published: May 2007

AbstractThis paper is designed to treat (a) the problem of the determination of the absolute minimum cost, with the associated assignments, when there is no limit, N, on the number of parcels available for shipment in a modified Hitchcock problem. This is accomplished with the use of a transformed cost matrix. C*, to which the so‐called transportation paradox does not apply. The general Hitchcock solution using C* gives the cost T*, which is the absolute minimum cost of the original problem, as well as sets of assignments which are readily transformed to give the general assignments of the original problem. The sum of these latter assignments gives the value of Nu, the unbounded N for minimum cost. In addition, this paper is designed to show (b) how the method of reduced matrices may be used, (c) how a particular Hitchcock solution can be used to determine a general solution so that one solution using C* can provide the general answer, (d) how the results may be modified to apply to problems with fixed N, and hence (e) to determine the function of the decreasing T as N approaches Nu, and finally (f) to provide a treatment when the supplies at origin i and/or the demands at destination j, are bounded.
Pollution abatement and economic growth: An application of the von neumann model of an expanding economy
Authors: Cremeans John E. 
Published: May 2007

AbstractThe generalized von Neumann model of an expanding economy permits both joint products and alternative processes. Pollutants may be explicitly treated as the normal by‐products of certain economic processes and “clean” and “dirty” production alternatives may be simultaneously available. The paper describes some methods for incorporating pollutants in the model and several techniques that may be used to study the relationship between pollution abatement and economic growth. Numerical examples are used to illustrate cases of direct control of processes, consumer demand for “eliminated pollutant” and the limitation of total produced pollutants by exogenous constraint. In the last case an effluent charge is calculated.
Covariance of weibull order statistics
Authors: Lochner Robert H. , Basu A. P. , Diponzio Margaret 
Published: May 2007

AbstractLet X1 < X2 <… < Xn denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 ‐ exp (−xp), x > 0. Formulae for computing Cov (Xi, Xj) are well known, but they are difficult to use in practice. A simple approximation to Cov(Xi, Xj) is presented here, and its accuracy is discussed.
A note on a constrained replacement model for ships subject to degradations in utility
Authors: Kaplan Seymour 
Published: May 2007

AbstractIn a recent paper, Peter J. Kalman considers a stochastic constrained optimal replacement model using the case of ship replacement as an example. However, the development of the constrained model proposed is not pursued and the optimal interval between replacements is determined in the absence of constraints. Among other things, it is the purpose of the present paper to extend the previous results to develop explicit types of constraints for the case of ship replacement and to determine how the optimal replacement interval may change as a result of these constraints. The constraints are concerned with the state of readiness of each ship in a group of ships. Readiness is assumed to be measured on an ordinal valued utility scale. It is proposed that ordinal valued data on ship combat readiness ratings collected by the Navy may be a useful source of empirical information for a model of the type discussed.
Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case
Authors: Roodman Gary M. 
Published: May 2007

AbstractThis paper develops a method for doing postoptimality analysis on the mixed integer programming problem. The proposed procedures form a natural adjunct to enumerative I.P. algorithms that are linear programming based, and they are designed, in effect, to capitalize on insights generated as the problem is initially solved to do subsequent analysis upon it. In particular, limited ranging analysis is possible on selected parameters, as is the efficient resolving of the problem following parameter changes.
An efficient heuristic procedure for the capacitated warehouse location problem
Authors: Khumawala Basheer M. 
Published: May 2007

AbstractThis paper introduces an efficient heuristic procedure for solving a special class of mixed integer programming problem called the capacitated warehouse (plant) location problem. This procedure parallels the work reported earlier in [9] on the uncapacitated warehouse location problem. The procedure can be viewed as tracing a judiciously selected path of the branch and bound tree (from the initial node to the terminal node) to arrive at a candidate solution. A simple backtracking scheme is also incorporated in the procedure to investigate possible improvement in the solution. Computational results on problems found in the literature look quite encouraging.
On estimating the reliability of a component subject to several different stresses (strengths)
Authors: Chandra Satish , Owen Donald B. 
Published: May 2007

AbstractThis paper is concerned with estimating p = P(X1 < Y …, Xn < Y) or q =P (X < Y1, …, X < Yn) where the X's and Y's are all independent random variables. Applications to estimation of the reliability p from stress‐strength relationships are considered where a component is subject to several stresses X1, X2, …, XN whereas its strength, Y, is a single random variable. Similarly, the reliability q is of interest where a component is made of several parts all with their individual strengths Y1, Y2 …, YN and a single stress X is applied to the component. When the X's and Y's are independent and normal, maximum likelihood estimates of p and q have been obtained. For the case N = 2 and in some special cases, minimum variance unbiased estimates have been given. When the Y's are all exponential and the X is normal with known variance, but unknown mean (or uniform between 0 and θ, θ being unknown) the minimum variance unbiased estimate of q is established in this paper.
Exact first and second order moments of order statistics from the truncated exponential distribution
Authors: Saleh A. K. Md. Ehsanes , Scott Christine , Junkins D. Bruce 
Published: May 2007

AbstractExact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances‐covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.
Application of the fundamental theorem of games to an example concerning antiballistic missile defense
Authors: Croucher John S. 
Published: May 2007

AbstractThis paper considers a two sided resource allocation game in which both players initially have fixed resources which may be distributed over various targets. Their effectiveness depends on the manner of distribution and also on the strategy of the opponent, a natural payoff function for such a situation being used. The complete solution to the game is derived and a numerical example given.
Insurance type item provisioning guidelines
Authors: Burton Robert W. , Jaquette Stratton C. 
Published: May 2007

AbstractPolicy decisions for insurance type items, where zero or one unit is maintained at the depot, are more difficult and more critical than decisions for common supply items. This report presents results of developing initial provisioning guidelines for insurance type items. The guidelines are based on examination of lifetime costs and benefits. Costs of stocking an item as compared with not stocking are developed through a sinking fund annual payment formulation. Benefits of stocking are developed as stationary reduction in time weighted backorders experienced. A resource allocation formulation yields an optimal policy for allocating a fixed budget. The guideline is presented with refinements based on a sample of items. A figure of merit is calculated for each item, and if it is large the item is stocked while if small it is not stocked. Empirical definitions for large and small are developed based on sample data. Estimation techniques are discussed for deriving all of an item's parameters needed to compute its figure of merit. A Bayes procedure is suggested based on family group Experienced Demand Replacement Factors. This and other techniques are discussed.
A recursive branch and bound algorithm for the multidimensional knapsack problem
Authors: Thesen Arne 
Published: May 2007

AbstractThis paper presents an efficient branch and bound algorithm for the solution of certain multiconstrained knapsack problems. The key to this algorithm is a rigidly defined tree structure in which branching and bounding may be performed through recursive relationships. The algorithm is particularly useful when only limited amounts of core storage are available as only the current and one previous solution is saved at any one time. Execution speeds compare favorably with other algorithms. A numerical example and computational experience is given.
Parametric studies in transportation‐type problems
Authors: Fong C. O. , Rao M. R. 
Published: May 2007

AbstractIn this paper we present some results in parametric studies on several transportation‐type problems. Specifically, a characterization is obtained for the optimal values of the variables in the problem of determining an optimal growth path in a logistics system. We also derive an upper bound beyond which the optimal growth path remains the same. The results are then extended to the goal programming model and the prespecified market growth rate problem.
An efficient cyclic coordinate method for optimizing penalty functions
Authors: Bazaraa Mokhtar S. 
Published: May 2007

AbstractIn this study, a simple and efficient cyclic coordinate search procedure is used to optimize penalty functions. Since the contours of the penalty function are very ill‐behaved, an accurate line search is very difficult to achieve. Due to accumulated errors in line search, this makes “simple‐minded” search directions just as good as more sophisticated directions, and actually better since they require a smaller effort per iteration. Of course this is only true if the search procedure is able to “ride” along steep ridges, and meanwhile move an appreciable distance towards the optimal, if at all possible. Computational results on the cyclic coordinate method seems to support this point of view, and shows robustness, reliability, and efficiency of the method.
On fractional programming and equivalence
Authors: Craven B. D. , Mond B. 
Published: May 2007

AbstractUnder fairly general conditions, a nonlinear fractional program, where the function to be maximized has the form f(x)/g(x), is shown to be equivalent to a nonlinear program not involving fractions. The latter program is not generally a convex program, but there is often a convex program equivalent to it, to which the known algorithms for convex programming may be applied. An application to duality of a fractional program is discussed.
Extensions and reductions in the von neumann model of an expanding economy
Authors: Bauer Leonhard 
Published: May 2007

AbstractThis paper introduces an extension of the v. Neumann model of an expanding economy. In addition to the conventional nonnegative input and output matrices A1, B1 representing technology, two matrices A2, B2 represent socio‐political evaluations and show that there exist solutions to the 4‐matrix model. The proof is based on an extension of a constructive proof given by O. Morgenstern and G. L. Thompson. It is shown that this proof is valid only under an additional assumption. The transformation of v. Neumann models (taking consumption into account) into 1 or 2 games is shown and adds an additional condition to M. Morishima's model to guarantee a solution. The equivalence of the v. Neumann model to a maximization problem under a (efficiency) constraint is presented. It is shown that E. Malinvaud's maximality and efficiency criterion ‐ if based on the same assumptions (model) ‐ are equivalent and specify the assumptions which will make the MT‐model efficient. The economic evaluation is considered to be of utmost importance.
One machine sequencing to minimize mean flow time with minimum number tardy
Authors: Emmons Hamilton 
Published: May 2007

AbstractThe problem of sequencing n jobs on one machine is considered, under the multiple objective of minimizing mean flow time with the minimum number of tardy jobs. A simple procedure is first proposed to schedule for minimum flow time with a specified subset of jobs on time. This is used in conjunction with Moore's Algorithm in a simple heuristic producing good and often optimal schedules. A branch‐bound algorithm is presented to produce the optimal schedule efficiently with the help of several theorems which eliminate much branching.
Optimal production growth for the machine loading problem
Authors: Balachandran V. 
Published: May 2007

AbstractThis paper investigates a production growth logistics system for the machine loading problem (generalized transportation model), with a linear cost structure and minimum levels on total machine hours (resources) and product types (demands). An algorithm is provided for tracing the production growth path of this system, viz. in determining the optimal machine loading schedule of machines for product types, when the volumes of (i) total machine hours, and (ii) the total amount of product types are increased either individually for each total or simultaneously for both. Extensions of this methodology, when (i) the costs of production are convex and piecewise linear, and (ii) when the costs are nonconvex due to quantity discounts, and (iii) when there are upper bounds for productions are also discussed. Finally, a “goal‐programming” production growth model where the specified demands are treated as just goals and not as absolute quantities to be satisfied is also considered.
A game theoretic approach to a two firm bidding problem
Authors: Cook W. D. , Kirby M. J. L. , Mehndiratta S. L. 
Published: May 2007

AbstractIn this paper a model is developed for determining optimal strategies for two competing firms which are about to submit sealed tender bids on K contracts. A contract calls for the winning firm to supply a specific amount of a commodity at the bid price. By the same token, the production of that commodity involves various amounts of N different resources which each firm possesses in limited quantities. It is assumed that the same two firms bid on each contract and that each wants to determine a bidding strategy which will maximize its profits subject to the constraint that the firm must be able to produce the amount of products required to meet the contracts it wins. This bidding model is formulated as a sequence of bimatrix games coupled together by N resource constraints. Since the firms' strategy spaces are intertwined, the usual quadratic programming methods cannot be used to determine equilibrium strategies. In lieu of this a number of theorems are given which partially characterize such strategies. For the single resource problem techniques are developed for determining equilibrium strategies. In the multiple resource problem similar methods yield subequilibrium strategies or strategies that are equilibrium from at least one firm's point of view.
Transportation problems with some xij negative and transshipment problems
Authors: Dwyer Paul S. 
Published: May 2007

AbstractThe general solution process of the Hitchcock transportation problem resulting from the application of the method of reduced matrices may give solutions with some negative xij values. This paper is devoted to a review of the reduced matrices method, an examination of suitable interpretation of sets of xij which include some negative values, and ways of interpreting these values in useful modifications of the Hitchcock problem. Such modifications include a) the reshipment problem, b) the overshipment problem, and c) the transshipment problem. Techniques are developed for determining and eliminating cij which are not optimal. These techniques and results are useful in solving the problems indicated above. The natural applicability of the simple and general method of reduced matrices is emphasized.
Implicit enumeration based algorithms for postoptimizing zero‐one programs
Authors: Piper Christopher J. , Zoltners Andris A. 
Published: May 2007

AbstractIt has been shown by G. Roodman that useful postoptimization capabilities for the 0‐1 integer programming problem can be obtained from an implicit enumeration algorithm modified to classify and collect all fathomed partial solutions. This paper extends the the approach as follows: 1) Improved parameter ranging formulas are obtained by higher resolution classification criteria. 2) Parameters may be changed so as to tighten the original problem, in addition to relaxing it. 3) An efficient storage structure is presented to cope with difficult data collection task implicit in this approach. 4) Finally, computer implementation is facilitated by the elaboration of a unified set of algorithms.
A note on allocating jobs to two machines
Authors: Rothkopf Michael H. 
Published: May 2007

AbstractA recent article in this journal by Mehta, Chandrasekaran, and Emmons [1] described a dynamic programming algorithm for assigning jobs to two identical parallel processors in a way that minimizes the average delay of these jobs. Their problem has a constraint on the sequence of the jobs such that any group of jobs assigned to a processor must be processed in the order of the sequence. This note has two purposes. First, we wish to point out a relationship between this work and some prior work [2]. Second, we wish to point out that Mehta, Chandrasekaran, and Emmons formulation, slightly generalized, can be used to find the optimum assignment of jobs to two machines in a more general class of problems than they considered including a subclass in which the jobs are not constrained to be processed in a given sequence.
A modified block replacement policy
Authors: Berg Menachem , Epstein Benjamin 
Published: May 2007

AbstractA well known preventive replacement policy is the block replacement policy (BRP). In such a policy the item undergoes a planned replacement at a sequence of equally spaced time points independent of failure history. The main advantage of a BRP is its simplicity, because under this policy it is unnecessary to keep detailed records about times of failures or ages of items. The main drawback of a BRP is that at planned replacement times we may be replacing practically new items. In this paper we study a modified BRP which is free of this drawback. We calculate the expected cost of following a modified BRP for lifetime distributions possessing a special structure and illustrate it for the case of an Erlang distribution. A numerical comparison is made between a modified BRP and a standard BRP for the special case of a two stage Erlang distribution.