bluuebunny/crossref_metadata_2025_split huggingface dataset:
Mathematical aspects of the 3 × n job‐shop sequencing problem
Authors: Szwarc Wlodzimierz 
Published: May 2007

AbstractThe paper discusses mathematical properties of the well‐known Bellman‐Johnson 3 × n sequencing problem. Optimal rules for some special cases are developed. For the case min Bi ≥ maxAj we find an optimal sequence of the 2 × n problem for machines B and C and move one item to the front of the sequence to minimize (7); when min Bi ≥ max Cj we solve a 2 × n problem for machines A and B and move one item to the end of the optimal sequence so as to minimize (9).There is also given a sufficient optimality condition for a solution obtained by Johnson's approximate method. This explains why this method so often produces an optimal solution.
A problem of restricted partitions
Authors: Uppuluri V. R. R. , Carpenter J. A. 
Published: May 2007

AbstractThis paper presents a simple algorithm for finding the number of restricted k‐partitions of a natural number n. The unrestricted k‐partitions of n are expressed as the sum of these restricted k‐partitions, called inadmissible, and the admissible k‐partitions. The simplicity of the algorithm is striking, though all the implications are unclear.
Variations on a cutting plane method for solving concave minimization problems with linear constraints
Authors: Cabot A. Victor 
Published: May 2007

AbstractA cutting plane method for solving concave minimization problems with linear constraints has been advanced by Tui. The principle behind this cutting plane has been applied to integer programming by Balas, Young, Glover, and others under the name of convexity cuts.This paper relates the question of finiteness of Tui's method to the so‐called generalized lattice point problem of mathematical programming and gives a sufficient condition for terminating Tui's method.The paper then presents several branch‐and‐bound algorithms for solving concave minimization problems with linear constraints with the Tui cut as the basis for the algorithm. Finally, some computational experience is reported for the fixed‐charge transportation problem.
A saddle‐point theorem for a class of infinite games
Authors: Wingate John W. 
Published: May 2007

AbstractIn this paper, the existence of a saddle point for two‐person zero‐sum infinite games of a special type is proved. The games have continuous bilinear payoff functions and strategy sets which are convex, noncompact subsets of an infinite‐dimensional vector space. The closures of the strategy sets are, however, compact. The payoff functions satisfy conditions which allow the use of dominance arguments to show that points in the closure of a strategy set are dominated by or are strategically equivalent to points in the strategy set itself. Combining the dominance arguments with a well‐known existence theorem produces the main result of the paper.The class of games treated is an extension of a class studied by J. D. Matheson, who obtained explicit solutions for the saddle points by using necessary conditions.
The optimal size of a storage facility
Authors: Levy Joel 
Published: May 2007

AbstractThe appropriate size for a piece of fixed capital equipment (measured in units of capacity) depends on the anticipated demand for its services and on its cost. Using several models developed in the study of optimal inventory policy we derive the contribution to cost reduction that additional storage space makes under each of these models. Comparison of the sum of the discounted benefits (ie., reduced operating cost) with construction costs for additional storage space then yields the optimal size of the storage facility.
Maximization of long‐run average rate‐of‐return by stochastic approximation
Authors: Agnew Robert A. 
Published: May 2007

AbstractSuppose that an individual has a surplus stock of wealth and a fixed set of risky investment opportunities over a sequence of time periods. Assuming the criterion of maximal long‐run average rate‐of‐return, the individual may select portfolios sequentially via a modified stochastic approximation procedure. This approach yields optimal asymptotic investment results under minimal assumptions.
Order‐preserving allocation of jobs to two machines
Authors: Mehta S. , Chandraseharan R. , Emmons H. 
Published: May 2007

AbstractIn this paper, we consider the problem of minimizing the mean flow time of jobs to be processed on two machines. The jobs have a predetermined order, perhaps reflecting the order of arrival, and each job has a known processing time. We wish to assign the jobs to machines so as to minimize the mean flow time, with the constraint that the original order must be preserved within the subset of jobs assigned to each machine. An efficient algorithm based on dynamic programming is developed.
Stochastic control of queueing systems
Authors: Prabhu N. U. 
Published: May 2007

AbstractSuppose that the state of a queueing system is described by a Markov process { Yt, t ≥ 0}, and the profit from operating it up to a time t is given by the function f(Yt). We operate the system up to a time T, where the random variable T is a stopping time for the process Yt. Optimal stochastic control is achieved by choosing the stopping time T that maximizes Ef(YT) over a given class of stopping times. In this paper a theory of stochastic control is developed for a single server queue with Poisson arrivals and general service times.
Bayes adaptive control of two‐echelon inventory systems, II: The multistation case
Authors: Zacks S. , Fennell J. 
Published: May 2007

AbstractThe present paper extends the results of [7] to cases of multistation lower echelon. For this purpose an algorithm for the optimal allocation of the upper echelon stock among the lower echelon stations is developed. The policy of ordering for the upper echelon is an extension of the Bayes prediction policy developed in [7]. Explicit formulae are presented for the execution of this policy. Several simulation runs are presented and analyzed for the purpose of obtaining information on the behavior of the system, under the above control policy, over short and long periods.
An algorithm for the solution of a location problem with metric constraints
Authors: Schaefer Margaret K. , Hurter Arthur P. 
Published: May 2007

AbstractIn many location problems, the solution is constrained to lie within a closed set. In this paper, optimal solutions to a special type of constrained location problem are characterized. In particular, the location problem with the solution constrained to be within a maximum distance of each demand point is considered, and an algorithm for its solution is developed and discussed.
A basically poisson queue with nonpoisson output
Authors: Hadidi Nasser 
Published: May 2007

AbstractThe output of the queueing system M/M/1 is well known to be Poisson. This has also been shown to be true for other more general models inclusive of M/Mn/1; the system in which arrivals and epochs of service completion are elements of a birth and death process with parameters Λ and nμ, respectively, when the system contains n ≥ 1 customers. We shall here show that this result is not true in MnM/1; a system where arrival parameter is state dependent quantity Λ/n+1. Expressions will be given for the steady state joint density of two consecutive output intervals as well as the coefficient of correlation between them.
Comparison of stochastic processes used in sonar detection models
Authors: McCabe Bernard J. 
Published: May 2007

AbstractIn any model for a sonar detection process, some assumption must be made about the nature of the acoustic fluctuation process. Two processes that are widely used in this role are the jump process and the Gauss‐Markov process. These processes are similar in that they are both stationer) Markov processes and have autocovariance functions of the form s̀2exp(—γt). For these reasons, it might be believed that one could use either of these processes and get comparable results if all one is interested in is computing cumulative detection probabilities or mean time to gain or lose contact. However, such is not the case in that vastly different results can be obtained in some applications. An application of this sort is presented. We also present necessary and sufficient conditions for a threshold to have the property that it is almost surely crossed by the jump process, or by the Gauss‐Markov process. This affords another method of comparison.
Lower confidence limits for the impact probability within a circle in the normal case
Authors: Zacks S. , Solomon H. 
Published: May 2007

AbstractLower confidence limits are derived for the impact probability within a circle of fixed radius. The bivariate normal distribution with zero means, unequal variances, and zero correlation is the probability model for impacts. A new representation of the impact probability function is offered. This presentation is valid also for the dependent case, where the eigenvalues of the covariance matrix replace the variances. When the ratio of variances is known the lower confidence limits are uniformly most accurate (UMA). A few alternative approaches are compared by simulation when the ratio of variances is unknown.
Testing fit with nuisance location and scale parameters
Authors: Weiss Lionel 
Published: May 2007

AbstractFor each n, X1(n),…, Xn(n) are independent and identically distributed random variables, each with cumulative distribution function F(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that \documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution function Gx is completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2 are unknown and unspecified, except that the scale parameter θ2, is positive. Y1 (n) ≦ Y2 (n) ≦ … ≦ Yn (n)are the ordered values of X1(n),…, Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regularity condition.
An operator theory of parametric programming for the generalized transportation problem: II Rim, cost and bound operators
Authors: Balachandran V. , Thompson G. L. 
Published: May 2007

AbstractThis paper investigates the effect on the optimum solution of a capacitated generalized transportation problem when certain data of the problem are continuously varied as a linear function of a single parameter. First the rim conditions, then the cost coefficients, and finally the cell upper bounds are varied parametrically and the effect on the optimal solution, the associated change in costs and the dual changes are derived. Finally the effect of simultaneous changes in both cost coefficients and rim conditions are investigated. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum bases are preserved.
Generalized programming by linear approximation of the dual gradient: Equality constraints
Authors: Sharp J. Franklin , Wagner Michael H. 
Published: May 2007

AbstractA modified generalized programming procedure is presented for solving concave programming problems with equality constraints. The procedure constructs convenient linear approximations of the gradient of the dual and finds points where the approximating functions vanish. In the quadratic programming case, the procedure is finitely convergent. Global convergence is established for the non‐quadratic case. Illustrative numerical examples are included.
A linear programming solution to the generalized rectangular distance weber problem
Authors: Morris James G. 
Published: May 2007

AbstractThe Weber Problem generalized to the location of several new points with respect to existing points is formulated as a linear programming problem under the assumption that distances are rectangular. The dual problem is then formulated and subsequently reduced to a problem with substantially fewer variables and constraints than required by an existent alternative linear programming formulation.Flows may exist between new as well as between new and existing points. Linear constraints can be imposed to restrict the location of new points. Pairwise constraints limiting distances between new points and between new and existing points can also be accommodated.
Scheduling with earliest start and due date constraints on multiple machines
Authors: Bratley Paul , Florian Michael , Robillard Pierre 
Published: May 2007

AbstractWe consider the scheduling of n jobs on m identical machines when the jobs become available for processing at ready times ai, ai, ⩾ 0, require di time units for processing and must be completed by times bi for i = 1, 2, … n. The objective chosen is that of minimizing the total elapsed time to complete all jobs subject to the ready time and due date constraints, preemption is not allowed. We present a multi‐stage solution algorithm for this problem that is based on an implicit enumeration procedure and also uses the labelling type algorithm which solves the problem when preemption is allowed.
On a supplementary time variable approach to battle analysis
Authors: Mjelde Kare M. 
Published: May 2007

AbstractA supplementary time variable approach is used to analyze a battle where attackers search for defended logistical targets and the future actions of an attacker depend on its activities in the whole time interval since arrival at the operating area. As compared with the method discussed in this paper a corresponding Markov chain analysis of the problem requires a considerably greater number of mathematical relations for state transition probabilities with less possibilities in obtaining numerical solutions effectively and with less para‐metrical insight. A supplementary time variable is introduced to describe the arrival instants of attackers at the operating area, and is then used to express the probability generating functions of the losses at an arbitrarily selected time instant in terms of a general description of the capabilities of an individual attacker in the time interval since arrival. These capabilities are then related to a selected set of lower level parameters describing a specific battle situation by using a small set of integral relations of the multiple convolution type with solutions expressed as Laplace transforms.
Dynamic multiattribute models for mixed manpower systems
Authors: Charnes A. , Cooper W. W. , Niehaus R. J. 
Published: May 2007

AbstractThis paper reviews a wide variety of manpower and personnel models of the goal programming variety. This is done from a strategy‐oriented point of view addressing the problems of interest for immediate implementation as well as basic problems of manpower model research development. Particular emphasis in this paper is concerned with how analytical models can be brought to bear on the problems of combining military and civilian manpower into one management system. This includes a discussion of the computer support arrangements necessary to implement the models. First, we discuss an extension of multilevel models to provide an integrated approach to program planning which includes the dynamics of the manpower requirements‐inventory relationships of mixed military‐civilian manpower systems. Then, focus is given to some of the potential Navy applications particularly in terms of ways the outputs from the global multilevel model might be interfaced with assignment models for operational planning. The paper concludes with a discussion of static and dynamic multiattribute assignment models which operate on the individual man‐job matching level. It is at this level of detail that dynamic mixed manpower systems might be constructed for use in equal employment opportunity planning and for local organization design studies.
Inference from accelerated life tests using eyring type re‐parameterizations
Authors: Singpurwalla Nozer D. , Castellino Victor C. , Goldschen Donald Y. 
Published: May 2007

AbstractLeast squares estimators of the parameters of the generalized Eyring Model are obtained by using data from censored life tests conducted at several accelerated environments. These estimators are obtained after establishing that the Gauss‐Markov conditions for least squares estimation are satisfied. Confidence intervals for the hazard rate at use conditions are obtained after empirically showing that the logarithm of the estimate of the hazard rate at use conditions is approximately normally distributed. The coverage probabilities of the confidence intervals are also verified by a Monte Carlo experiment. The techniques are illustrated by an application to some real data.
An operator theory of parametric programming for the generalized transportation problem—IV—global operators
Authors: Balachandran V. , Thompson G. L. 
Published: May 2007

AbstractThis paper investigates the effect of the optimal solution of a (capacitated) generalized transportation problem when the data of the problem (the rim conditions—i.e., the available time of machine types and demands of product types, the per unit production costs, the per unit production time and the upper bounds) are continuously varied as a linear function of a single parameter. Operators that effect the transformation of optimal solution associated with such data changes, are shown to be a product of basis preserving operators (described in our earlier papers) that operate on a sequence of adjacent basis structures. Algorithms are furnished for the three types of operators—rim, cost, and weight. The paper concludes with a discussion of the production and managerial interpretations of the operators and a comment on the “production paradox”.
Adjacent vertices on transportation polytopes
Authors: McKeown Patrick G. , Rubin David S. 
Published: May 2007

AbstractTo solve linear fixed charge problems with Murty's vertex ranking algorithm, one uses a simplex algorithm and a procedure to determine the vertices adjacent to a given vertex. In solving fixed charge transportation problems, the simplex algorithm simplifies to the stepping‐stone algorithm. To find adjacent vertices on transportation polytopes, we present a procedure which is a simplification of a more general procedure for arbitrary polytopes.
A note on control theory and attaining equilibrium
Authors: Tiplitz Charles 
Published: May 2007

AbstractMost researchers have not recognized that the main problem of an economic system is the excessive time it requires to reach equilibrium (and consequent inadequate control). An extension of control theory is applied to the Competitive Equilibrium Model. The calculation shows, in contrast to previous results, full employment, if attained, may be maintained for nonzero periods. However, ill condition and other factors cause a very slow approach to optimum. Consequently, constant social and other changes keep a complex economy far from optimum.
On ordering perishable inventory under erlang demand
Authors: Nahmias Steven 
Published: May 2007

AbstractExisting models for describing optimal ordering policies for perishable inventory cast the problem as a multidimensional dynamic program, the dimensionality being one less than the product lifetime in periods. An approach developed in previous work takes explicit account of outdating in the single period model. Formulas for the expected quantity of any new order which will outdate are developed for the case where the demand has a stationary Erlang distribution. A modified version of the one period model is shown to yield a reasonable approximation to the stationary optimal policy.
Solving a (0, 1) hyperbolic program by branch and bound
Authors: Saipe Alan L. 
Published: May 2007

AbstractA problem in (0, 1) hyperbolic programming is formulated and solved by the use of branch and bound methods. Computational results are presented including a comparison among several branching rules. Heuristic methods for quickly finding relatively good feasible solutions are presented and tested. The problem finds application in the scheduling of common carriers.In the solution of the main problem, a subproblem is identified and solved. A geometric analogue is presented, which allows an interesting interpretation of the subproblem. The subproblem itself finds application in the design of gambles.
Denumerable state markovian sequential control processes: On randomizations of optimal policies
Authors: Chitgopekar S. S. 
Published: May 2007

AbstractWe consider a denumerable state Markovian sequential control process. It is well known that when we consider the expected total discounted income as a criterion, there exists a nonrandomized stationary policy that is optimal. It is also well known that when we consider the expected average income as a criterion, an optimal nonrandomized stationary policy exists when a certain system of equations has a solution. The problem considered here is: if there exist two optimal nonrandomized stationary policies, will a randomization of these two policies be optimal? It is shown that in the discounted case the answer is always yes, but in the average income case, the answer is yes only under certain additional conditions.
On the treatment of force‐level constraints in times‐equential combat problems
Authors: Taylor James G. 
Published: May 2007

AbstractThe treatment of force‐level constraints in time‐sequential combat optimization problems is illustrated by further studying the fire‐programming problem of Isbell and Marlow. By using the theory of state variable inequality constraints from modern optimal control theory, sharper results are obtained on necessary conditions of optimality for an optimal fire‐distribution policy (in several cases justifying conjectures made in previous analysis). This leads to simplification of the determination of the domains of controllability for extremals leading to the various terminal states of combat. (Additionally, some new results for the determination of boundary conditions for the adjoint variables in optimal control problems with state variable inequality constraints have arisen from this work.) Some further extensions of previous analysis of the fire‐programming problem are also given. These clarify some key points in the solution synthesis. Some important military principles for target selection and the valuation of combat resources are deduced from the solution. As a result of this work, more general time‐sequential combat optimization problems can be handled, and a more systematic solution procedure is developed.
Empirical bayes single sampling plans for specified posterior consumer and producer risks
Authors: Martz Harry F. 
Published: May 2007

AbstractEmpirical Bayes single‐sample acceptance sampling procedures are derived. These procedures assume that the lot fraction defective varies randomly according to a completely unknown and unspecified prior distribution. The unknown prior density function is estimated based on sampling results from previous lots. A procedure is developed for obtaining single‐sampling plans that achieve specified posterior consumer and producer risks. The procedures are illustrated for a real‐data example.