bluuebunny/crossref_metadata_2025_split huggingface dataset:
An operator theory of parametric programming for the transportation problem‐II
Authors: Srinivasan V. , Thompson G. L. 
Published: May 2007

AbstractThis paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions‐i. e., the warehouse supplies and market demands‐, the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. Operators that effect the transformation of optimum solution associated with such data changes, are shown to be a product of basis preserving operators (described in the earlier paper) that operate on a sequence of adjacent basis structures. Algorithms are provided for both rim and cost operators. The paper concludes with a discussion of the economic and managerial interpretations of the operators.
Properties of a multifacility location problem involving euclidian distances
Authors: Francis Richard L. , Cabot A. Victor 
Published: May 2007

AbstractThis paper considers a problem of locating new facilities in the plane with respect to existing facilities, the locations of which are known. The problem consists of finding locations of new facilities which will minimize a total cost function which consists of a sum of costs directly proportional to the Euclidian distances among the new facilities, and costs directly proportional to the Euclidian distances between new and existing facilities. It is established that the total cost function has a minimum; necessary conditions for a mimumum are obtained; necessary and sufficient conditions are obtained for the function to be strictly convex (it is always convex); when the problem is “well structured,” it is established that for a minimum cost solution the locations of the new facilities will lie in the convex hull of the locations of the existing facilities. Also, a dual to the problem is obtained and interpreted; necessary and sufficient conditions for optimum solutions to the problem, and to its dual, are developed, as well as complementary slackness conditions. Many of the properties to be presented are motivated by, based on, and extend the results of Kuhn's study of the location problem known as the General Fermat Problem.
On the discrete‐time queue length distribution under markov‐dependent phases
Authors: Chaudhry M. L. 
Published: May 2007

AbstractThe technique of probability generating functions has been applied to solve the steady state behavior of a discrete‐time, single‐channel, queueing problem wherein the arrivals to the queue at consecutive time‐marks are statistically independent, but the service is accomplished in phases which are Markov‐dependent. Special cases of importance have been discussed. In the end, mean number of phases, its special cases, the mean queue lengths, and the variances have been ascertained.
Heuristic solution to a discrete collection model
Authors: Saipe Alan L. , Cunningham A. A. 
Published: May 2007

AbstractA discrete time Collection Model is formulated, involving the completion of a touring objective on a network with stochastic node states. Heuristic touring strategies are constructed, there being as yet inadequate analytic results for its optimal solution. Effectiveness of the heuristics is assessed by comparing expected tour times under the heuristics with expected tour times given perfect information. A branch and bound algorithm is presented for computing the perfect information tour times.
An economic model for planning strategic mobility posture
Authors: Bennington G. , Gsellman L. , Lubore S. 
Published: May 2007

AbstractThis paper describes a linear programming model used to perform cost‐effectiveness analysis to determine the requirements for military strategic mobility resources. Expenditures for three classes of economic alternatives are considered: purchase of transportation resources; prepositioning of material; and augmentation of port facilities. The mix of economic alternatives that maximizes the effectiveness of the resultant transportation system is determined for a given investment level. By repeating the analysis for several levels of investment, a cost‐effectiveness tradeoff curve can be developed.
A mixed optimization technique for the generalized machine replacement problem
Authors: Sethi S. P. , Morton T. E. 
Published: May 2007

AbstractA mixed optimization technique for optimal machine replacement is presented which allows much more flexibility than previous models. Optimal purchase, maintenance and sale of a given machine between any two given points in time is treated as a subproblem, which one may choose to solve via control theory, dynamic programming, or practical engineering considerations. (A control theory formulation is used in the paper as an illustration.) These subproblem solutions are then incorporated into a Wagner‐Whitin formulation for solution of the full problem. The technique is particularly useful for problems with such asymmetries as an existing initial machine or uneven technological change. A simple numerical example is solved in the Appendix.
A defense allocation problem with development costs
Authors: Shere Kenneth D. , Cohen Edgar A. 
Published: May 2007

AbstractIn this paper, the mathematical model for the allocation of resources among a general mix of percentage vulnerable and of numerically vulnerable weapon systems is presented and solved. Percentage vulnerable systems consist of mobile weapons which are difficult to locate, but relatively easy to destroy once located; numerically vulnerable systems comprise easily located fixed base weapons which are difficult to destroy. The distinguishing feature of this analysis is the inclusion of development costs. The theory of max‐min is extended as necessary to solve this problem. References are provided to a sequence of earlier versions of this problem.
On the isbell and marlow fire programming problem
Authors: Taylor James G. 
Published: May 2007

AbstractA complete solution is derived to the Isbell and Marlow fire programming problem. The original work of Isbell and Marlow has been extended by determining the regions of the initial state space from which optimal paths lead to each of the terminal states of combat. The solution process has involved determining the domain of controllability for each of the terminal states of combat and the determination of dispersal surfaces. This solution process suggests a solution procedure applicable to a wider class of tactical allocation problems, terminal control attrition differential games. The structure of optimal target engagement policies in “fights to the finish” is discussed.
Stationary (s, s) policies for a finite horizon
Authors: Wheeler Alan C. 
Published: May 2007

AbstractIn the finite‐horizon stochastic (s, S) inventory model with periodic review the parameters of the optimal policy generally vary with the length of the horizon. A stationary policy, however, is easier to implement and may be easier to calculate. This paper studies optimal stationary policies for a finite horizon and relates them to optimal policies through their relation to optimal stationary policies for an infinite horizon.
Scheduling data transmission under an {si; o} policy
Authors: Sahney Vinod K. 
Published: May 2007

AbstractThis paper discusses scheduling of data transmission when data can only be transmitted in one direction at a time. A common policy used is the so‐called alternating priority policy. In this paper we select a more general class of policies named the {Si; O} policy. We show how to determine the optimal parameters of the {Si; O} policy for given system parameters. We also give a simple example to show that {Si; O} policy is, in fact, better then alternating priority policy.
Productivity estimates of the strategic airlift system by the use of simulation
Authors: Nolan Richard L. , Mastroberti Rocci 
Published: May 2007

AbstractAlthough the strategic airlift system is under continuous analysis, C‐5A problems provided impetus to analyze the airlift system productivity function by using a large‐scale simulation model. Development of the simulation model (Simulation of Airlift Resources ‐ SOAR) was initiated by the Office of Secretary of Defense (Systems Analysis) in 1966. SOAR had barely become operational in time for the study in November 1968.Since limited verification and validation tests had been performed on the simulation model, the design of experiments was of critical importance. The experimental design had to be flexible enough to salvage the maximum amount of information possible upon the discovery of either a verification or validation error. In addition, the experimental design was required to accommodate the estimation of a large number of possibly changing independent variables.The experimental design developed for the analysis was full factorial design sets for a finite number of factors. Initial analysis began with aggregated sets of factors at two levels, and information gained from experiment execution was used to parse the sets. The process was sequential and parsing continued until the major explanatory independent variables were identified or enough information was obtained to eliminate the factor from further direct analysis. This design permitted the overlapping of simulation runs to fill out the factorial design sets.In addition to estimating the airlift productivity function, several other findings are reported which tended to disprove previous assumptions about the nature of the strategic airlift system.
Optimal location of public facilities
Authors: Dee Norbert , Liebman Jon C. 
Published: May 2007

AbstractLocation of both public and private facilities has become an important consideration in today's society. Progress in solution of location problems has been impeded by difficulty of the fixed charge problem and the lack of an efficient algorithm for large problems.In this paper a method is developed for solving large‐scale public location problems. An implicit enumeration scheme with an imbedded transportation algorithm forms the basis of the solution technique.
Structured markovian decision problems
Authors: Kalymon Basil A. 
Published: May 2007

AbstractStructured finite action‐finite state space discounted Markovian decision problems are analyzed. Any problem of a general class is shown to be equivalent to a “separated” problem with decomposable problem structure. A modified policy iteration approach is developed for this decomposable reformulation. Both analytic and computer evaluations of the decomposition algorithm's effectiveness are presented.
Polaroids: A new tool in non‐convex and in integer programming
Authors: Burdet Claude‐Alain 
Published: May 2007

AbstractThis paper presents a generalization, called polaroid, of the concept of polar setsA list of properties satisfied by polaroids is established indicating that the new concept nay be fruitfully used in an area of non‐convex (called here polar) programming as well as in integer programming, by means of polaroid cuts; this class of new cuts contains the ones defined by Tuy for concave programming (a special case of polar programming) and by Balas integer programming; it furthermore provides for new degrees of freedom in the construction of algorithms in the above‐mentioned areas of mathematical programming.
A squared‐variable transformation approach to nonlinear programming optimality conditions
Authors: Taylor James G. 
Published: May 2007

AbstractWe show that the well‐known necessary and sufficient conditions for a relative maximum of a nonlinear differentiable objective function with nonnegative variables constrained by nonlinear differentiable inequalities may be derived using the classical theory of equality constrained optimization problems with unrestricted variables. To do this we transform the original inequality‐constrained problem to an equivalent equality‐constrained problem by means of a well‐known squared‐variable transformation. Our major result is to show that second order conditions must be used to obtain the Kuhn‐Tucker conditions by this approach. Our nonlinear programming results are motivated by the development of some well‐known linear programming results by this approach.
Parametric analysis of linear programs with upper bounded variables
Authors: Panwalkar S. S. 
Published: May 2007

AbstractLinear programming problems with upper bounded variables can be solved by regular simplex method by considering upper bounding constraints as explicit constraints of the problem. However, more efficient methods exist which consider these upper bound constraints implicitly. When parametric analysis for problems with upper bounds is to be carried out, one can use the regular parameter analysis by considering the upper bound constraints explicitly. This paper develops formulas for parametric analysis where upper bound constraints are used implicitly, thus reducing the size of the basic matrix.
Requirements of an “optimizer” for computer simulations
Authors: Smith Dennis E. 
Published: May 2007

AbstractComputer simulation has many advantages. However, one major disadvantage is that, in all too many cases, the attempt to use computer simulation to find an optimum solution to a problem rapidly degenerates into a trial‐and‐error process. Techniques for overcoming this disadvantage, i. e., for making optimization and computer simulation more compatible, are applicable at two points in the development of the overall computer simulation. Techniques which are used within actual construction of the mathematical models comprising the simulation will be labeled as internal methods, while those which are used after the simulation has been completely developed will be termed external methodsBecause external methods appear to offer the largest potential payoff, discussion is restricted to these methods, which are essentially search techniques. In addition, the development of an “Optimizer” computer program based on these techniques is suggestedAlthough drawbacks to the use of search techniques in the computer simulation framework exist, these techniques do offer potential for “optimization.” The modification of these techniques to satisfy the requirements of an “Optimizer” is discussed.
Three ways of obtaining the average cost expression in a problem related to joint replenishment inventory control
Authors: Silver Edward A. 
Published: May 2007

AbstractThis paper does not present a new result, rather it is meant to illustrate the choice of modelling procedures available to an analyst in a typical inventory control problem. The same “average cost per unit time” expression is developed by three quite different procedures. This variety of approaches, as well as the recounting of the author's chronological efforts to solve the problem, should be of interest to the reader. The specific inventory problem studied is one where the controller of an item is faced with random opportunities for replenishment at a reduced setup cost; the problem is an integral component of the broader problem of inventory control of a group of items whose replenishments are coordinated to reduce the costs of production, procurement, and/or transportation.
An approach to the allocation of common costs of multi‐mission systems
Authors: Crow Robert Thomas 
Published: May 2007

AbstractMany Naval systems, as well as other military and civilian systems, generate multiple missions. An outstanding problem in cost analysis is how to allocate the costs of such missions so that their true costs can be determined and resource allocation optimized. This paper presents a simple approach to handling this problem for single systems. The approach is based on the theory of peak‐load pricing as developed by Marcel Boiteux. The basic principle is that the long‐run marginal cost of a mission must be equal to its “price.” The implication of this is that if missions can cover their own marginal costs, they should also be allocated some of the marginal common costs. The proportion of costs to be allocated is shown to a function of not only the mission‐specific marginal costs and the common marginal costs, but also of the “mission price.” Thus, it is shown that measures of effectiveness must be developed for rational cost allocation. The measurement of effectiveness has long been an intractable problem, however. Therefore, several possible means of getting around this problem are presented in the development of the concept of relative mission prices.
Min/max bounds for dynamic network flows
Authors: Wilkinson W. L. 
Published: May 2007

AbstractThis paper presents an algorithm for determining the upper and lower bounds for arc flows in a maximal dynamic flow solution. The procedure is basically an extended application of the Ford‐Fulkerson dynamic flow algorithm which also solves the minimal cost flow problem. A simple example is included. The presence of bounded optimal are flows entertains the notion that one can pick a particular solution which is preferable by secondary criteria.
Concave minimization over a convex polyhedron
Authors: Taha Hamdy A. 
Published: May 2007

AbstractA general algorithm is developed for minimizing a well defined concave function over a convex polyhedron. The algorithm is basically a branch and bound technique which utilizes a special cutting plane procedure to' identify the global minimum extreme point of the convex polyhedron. The indicated cutting plane method is based on Glover's general theory for constructing legitimate cuts to identify certain points in a given convex polyhedron. It is shown that the crux of the algorithm is the development of a linear undrestimator for the constrained concave objective function. Applications of the algorithm to the fixed‐charge problem, the separable concave programming problem, the quadratic problem, and the 0‐1 mixed integer problem are discussed. Computer results for the fixed‐charge problem are also presented.
Some experiments in global optimization
Authors: Hartman James K. 
Published: May 2007

AbstractWhen applied to a problem which has more than one local optimal solution, most nonlinear programming algorithms will terminate with the first local solution found. Several methods have been suggested for extending the search to find the global optimum of such a nonlinear program. In this report we present the results of some numerical experiments designed to compare the performance of various strategies for finding the global solution.
Generalized multicomponent systems under cannibalization
Authors: Hochberg Murray 
Published: May 2007

AbstractUsing the theory of Hirsch, Meisner, and Boll, we study the consequences of interchanging parts within a generalized coherent structure. This procedure has been termed “cannibalization.” The theory of cannibalization is extended to the case where each component can operate at several levels of partial performance and a representation theorem is derived, which expresses the state of a system as a function of the number of working parts at each level. The stochastic theory of these systems is then investigated.
A theory of ideal linear weights for heterogeneous combat forces
Authors: Howes David R. , Thrall Robert M. 
Published: May 2007

AbstractDetailed combat simulations can produce effectiveness tables which measure the effectiveness of each weapon class on one side of an engagement, battle, or campaign to each weapon class on the other. Effectiveness tables may also be constructed in other waysThis paper assumes that effectiveness tables are given and shows how to construct from them a system of weapon weights each of which is a weighted average of the effects of a given weapon against each of the enemy's weapons. These weights utilize the Perron‐ Frobenius theory of eigenvectors of nonnegative matrices. Methods of calculation are discussed and some interpretations are given for both the irreducible and reducible cases.
Further light on nonparametric selection efficiency
Authors: Dudewicz Edward J. , Fan Chung‐Lien 
Published: May 2007

AbstractA nonparametric selection procedure 𝒫bs was proposed by Bechhofer and Sobel (1958) and studied by Dudewicz (1971) in comparison with other procedures under normal and uniform alternatives. He found 𝒫BS always required larger sample sizes, sometimes substantially so. For 2‐point populations we find more extreme results. We also find that 𝒫BS may be substantially better than reasonable competitors designed specifically for 2‐point populations. Finally, a new nonparametric selection procedure (conjectured to be better than 𝒫BS) is proposed.
Simplified estimates of the parameters of the double exponential distribution based on optimum order statistics from a middle‐censored sample
Authors: Ahsanullah M. , Rahim M. A. 
Published: May 2007

AbstractIn an ordered sample from a given population, a few of the consecutive observations from somewhere in the middle may be missing Further, we may be constrained to use a few, and not all, of the remaining observations for purposes of estimation of population parameters. In this paper, such a situation is considered for the double exponential distribution and best linear unbiased estimates are obtained for its parameters, based on a choice of an optimum set of order statistics when the number of observations in the set are prefixed.
Alternate methods of project scheduling with limited resources
Authors: Patterson James H. 
Published: May 2007

AbstractThe applicability of critical path scheduling is limited by the inability of the algorithm to cope with conflicting resource demands. This paper is an assessment of the effectiveness of many of the heuristic extensions to the critical path method which resolve the conflicts that develop between the resources demanded by an activity and those available. These heuristic rules are evaluated on their ability to solve a large multiproject scheduling problem.
Scheduling with parallel processors and linear delay costs
Authors: Baker Kenneth R. , Merten Alan G. 
Published: May 2007

AbstractThis paper deals with the sequencing problem of minimizing linear delay costs with parallel identical processors. The theoretical properties of this m‐machine problem are explored, and the problem of determining an optimum scheduling procedure is examined. Properties of the optimum schedule are given as well as the corresponding reductions in the number of schedules that must be evaluated in the search for an optimum. An experimental comparison of scheduling rules is reported; this indicates that although a class of effective heuristics can be identified, their relative behavior is difficult to characterize.
A partitioning technique for obtaining solutions to the modularization problem
Authors: Caponecchi A. J. , Jensen P. A. 
Published: May 2007

AbstractA significant problem in electronic system design is that of partitioning the functional elements of an equipment schematic into subsets which may be regarded as modules. The collection of all such subsets generated by a particular partitioning forms a potential modular design. The specific problem is to determine that partitioning of the schematic that minimizes a cost function defined on the subsets subject to specified hardware, design, packaging, and inventory constraints. This problem is termed the modularization problem. This paper presents a method for obtaining restricted solutions to the modularization problem by employing some recent developments in linear graph theory obtained by one of the coauthors. Numerical results from the solution of several typical problems are presented.