bluuebunny/crossref_metadata_2025 huggingface dataset:
Alternate methods of project scheduling with limited resources
Authors: Patterson James H.
Published: May 2007

The 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

This 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

A 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.
Mathematical aspects of the 3 × n job‐shop sequencing problem
Authors: Szwarc Wlodzimierz
Published: May 2007

The 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

This 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

A 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

In 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

The 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

Suppose 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

In 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

Suppose 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.
On the optimality of the bayes prediction policy in two‐echelon multistation inventory models
Authors: Zacks S.
Published: May 2007

The present paper provides a proof that the Bayes prediction ordering policy developed in [3] is an optimal policy, in the sense that it minimizes the total expected discounted cost of ordering for any finite planning horizon.
Bayes adaptive control of two‐echelon inventory systems, II: The multistation case
Authors: Zacks S. , Fennell J.
Published: May 2007

The 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

In 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

The 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

In 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.
Upper and lower bounds for a pattern bombing problem
Authors: Washburn Alan R.
Published: May 2007

This paper includes two simple analytic formulas for kill probability that are applicable in circumstances where shots should be fired in a pattern. The two formulas bracket the maximum kill probability achievable with an optimal pattern. The upper bound corresponds to an optimal nonfeasible pattern, and the lower bound to a nonoptimal feasible pattern.
An iterative procedure for nondiscounted discrete‐time markov decisions
Authors: Koehler Gary J. , Whinston Andrew B. , Wright Gordon P.
Published: May 2007

This paper considers the problem of computing, by iterative methods, optimal policies for Markov decision processes. The policies computed are optimal for all sufficiently small interest rates.
Lower confidence limits for the impact probability within a circle in the normal case
Authors: Zacks S. , Solomon H.
Published: May 2007

Lower 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

For 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

This 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

A 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

The 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

We 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

A 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

This 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

Least 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

This 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

To 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.
Isoquants of continuous production correspondences
Authors: Bol G. , Moeschlin O.
Published: May 2007

Bol has discussed consequences of the continuity of production correspondences in connection with relations between efficient input and output vectors. Isoquants of continuous production correspondences are used here to extend this work. Simplifications to existing theory are discussed.
A note on control theory and attaining equilibrium
Authors: Tiplitz Charles
Published: May 2007

Most 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

Existing 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

A 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

We 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.
Stochastic duels with round‐dependent hit probabilities
Authors: Ancker C. J.
Published: May 2007

The effect of round dependent hit probabilities in the fundamental stochastic duel are examined. The general solution and several specific examples are derived where one side's hit probabilities are improved from round to round. For these specific cases the advantages of round to round improvement are explicitly displayed.
On the treatment of force‐level constraints in times‐equential combat problems
Authors: Taylor James G.
Published: May 2007

The 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

Empirical 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.
An analysis of the long range operating characteristics of the MIL‐STD‐105D sampling scheme and some suggested modifications
Authors: Brown Gerald G. , Rutemiller Herbert C.
Published: May 2007

An integral part of the MIL–STD–105D scheme for sampling inspection by attributes is the transfer from normal inspection to reduced or tightened inspection when the historical record of inspected lots suggests unusually good or bad quality. The switching rules in MIL–STD–105D have been criticized, especially by Japanese manufacturers, as being too severe when what is defined as acceptable quality material is submitted. This paper examines the long range fraction of lots rejected for several MIL–STD–105D sampling plans by using the MIL–STD–105D switching rules, using a modification suggested by the Japanese Standards Association, and by using a second modification developed by the authors.

The Japanese Standards Association switching rules are more complex than those in MIL–STD–105D. It is demonstrated that they lead to improved long–range properties for Normal–Tightened–Reduced schemes, but to poorer properties for Normal–Tightened schemes.

A simplified set of switching rules is suggested, wherein the “limit numbers” in MIL–STD–105D are eliminated. In comparison to MIL–STD–105D, the simpler rules lead to a lower probability of rejection for good lots and a comparable probability of rejection for bad lots.
Calculation of the cost of warranty policies as a function of estimated life distributions
Authors: Blischke Wallace R. , Scheuer Ernest M.
Published: May 2007

Two types of warranties are analyzed. These are the free‐replacement warranty, under which failed items are replaced free of charge until a specified total operating time has been achieved, and the pro rata warranty, under which items that fail prior to a specified time are replaced at pro rata cost to the buyer. Both the buyer's and seller's points of view are considered. The basis of the analysis is a comparison of warranted and unwarranted (otherwise identical) items with regard to long‐run cost to the buyer and long‐run profit to the seller.

Application of the results requires knowledge of certain characteristics of the life distribution of the items in question. Parametric and nonparametric methods of estimation of these characteristics from incomplete data are discussed. Single and multiple failure‐mode situations are considered.

Some solutions to the problem are illustrated using incomplete data on failure times of an aircraft component.
On scheduling with earliest starts and due dates on a group of identical machines
Authors: Tilquin Charles
Published: May 2007

This paper examines the (n, m) scheduling problem with n operations distributed among m machines. An algorithm for solving this problem is presented and, gives a good heuristic solution on a wide class of problems. Computational results are reported which demonstrate the efficiency of this approach.
A note on the optimal scheduling of two parallel processors
Authors: Zaloom Victor , Vatz David
Published: May 2007

The problem of minimizing mean flow time of two parallel processors is discussed. Prior results are briefly reviewed. A dynamic programming algorithm is presented which minimizes mean flow time for a set of n preordered jobs on two nonequivalent parallel processors. The algorithm is illustrated with an example problem. The computational experience is presented which illustrates the efficiency of the algorithm.
Explicit formulas for the order size and reorder point in certain inventory problems
Authors: Das Chandrasekhar
Published: May 2007

This study concentrates on distributions of leadtime demand that permit explicit solution to the lot‐size, reorder point model. The optimal order size for the general case is first expressed as a function of the economic order quantity and a quantity known as the “residual mean life” in reliability theory. The concept of “no aging” is then utilized to identify a broad class of distributions for which the optimal order size can be determined explicitly, independent of the reorder point.
On the equivalence of three approximate continuous review inventory models
Authors: Nahmias Steven
Published: May 2007

This paper considers the problem of computing reorder points and order quantities for continuous review inventory systems subject to either a service level constraint or a constraint on the average fraction of time out of stock. It is demonstrated that three apparently distinct models are equivalent under these circumstances. Using this equivalence, streamlined algorithms for computed lot sizes and recorder points are developed.
Multiperiod capacity expansion and shipment planning with linear costs
Authors: Fong C. O. , Srinivasan V.
Published: May 2007

In this paper we consider a multiperiod deterministic capacity expansion and shipment planning problem for a single product. The product can be manufactured in several producing regions and is required in a number of markets. The demands for each of the markets are non‐decreasing over time and must be met exactly during each time period (i.e., no backlogging or inventorying for future periods is permitted). Each region is assumed to have an initial production capacity, which may be increased at a given cost in any period. The demand in a market can be satisfied by production and shipment from any of the regions. The problem is to find a schedule of capacity expansions for the regions and a schedule of shipments from the regions to the markets so as to minimize the discounted capacity expansion and shipment costs. The problem is formulated as a linear programming model, and solved by an efficient algorithm using the operator theory of parametric programming for the transporation problem. Extensions to the infinite horizon case are also provided.
An algorithm for solving general fractional interval programming problems
Authors: Charnes A. , Granot Daniel , Granot Frieda
Published: May 2007

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two‐sided linear inequality constraints.

In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.
Solving fixed charge network problems with group theory‐based penalties
Authors: Rardin R. L. , Unger V. E.
Published: May 2007

Many well‐known transportation, communication, and facilities location problems in operations research can be formulated as fixed charge network problems, i.e. as minimum cost flow problems on a capacitated network in one commodity where some arcs have both fixed and variable costs. One approach to solving such problems is to use group theoretic concepts from the theory of integer programming to provide bounds for a branch‐and‐bound procedure. This paper presents such a group‐theory based algorithm for exact solution of fixed charge network problems which exploits the special structures of network problems. Computational results are reported for problems with as many as 100 fixed charge arcs.
The normal approximation to the multinomial with an increasing number of classes
Authors: Weiss Lionel
Published: May 2007

For a fixed number of classes and the number of trials increasing, the approach of the multinomial cumulative distribution function to a normal cumulative distribution function is familiar. In this paper we allow the number of classes to increase as the number of trials increases, and show that under certain circumstances the probabilities assigned to arbitrary regions by the multinomial distribution are all close to the probabilities assigned by the distribution of “rounded off” normal random variables. As the number of trials increases, the amount rounded off approaches zero. The result can be used to study the asymptotic distribution of functions of multinomial random variables.
A note on explicit solution in linear fractional programming
Authors: Charnes A. , Granot Daniel , Granot Frieda
Published: May 2007

In this note we analyze the fractional interval programming problem (FIP) and find, explicitly, all its optimal solutions.

Though our results are essentially the same as those in Charnes and Cooper [4], the proofs and analysis we provide here are considerably simpler.
A note on testing for exponentiality
Authors: Harris Carl M.
Published: May 2007

In this note some extensions are made to previous work by a number of authors on the development of tests for exponentiality. The most recent example is due to Fercho and Ringer in which they compare the small sample powers of a few well‐known test statistics for the hypothesis of a constant failure rate. It is the primary intent of this current work to extend Gnedenko's F test to situations with hypercensoring and to provide guidance for its use, particularly when a log‐normal distribution is the alternative.
Optimal flowshop schedules with no intermediate storage space
Authors: Gupta Jatinder N. D.
Published: May 2007

In this paper the problem of finding an optimal schedule for the n‐job, M‐machine flowshop scheduling problem is considered when there is no intermediate space to hold partially completed jobs and the objective function is to minimize the weighted sum of idle times on all machines. By assuming that jobs are processed as early as possible, the problem is modeled as a traveling salesman problem and solved by known solution techniques for the traveling salesman problem. A sample problem is solved and a special case, one involving only two machines, is discussed.
Multichannel queueing systems with heterogeneous classes of arrivals
Authors: Bhat U. Narayan , Fischer Martin J.
Published: May 2007

In an integrated telecommunications network, voice and data traffic compete for the same transmission facilities. Assuming Poisson arrivals and exponential service with different rates, analytic expressions are obtained for measures of performance such as blocking probability and average delay under the following operating rule: class 1 traffic behaves as a loss system while class 2 traffic is buffered when all channels are busy. In view of the inordinate amount of computational effort needed when the number of channels is large, simple approximations have been suggested.
An infiltration game with time dependent payoff
Authors: Thomas Marlin U. , Nisgav Yair
Published: May 2007

The problem of assigning patrol boats, subject to resource constraints, to capture or delay an infiltrator with perishable contraband attempting escape across a long, narrow strait is formulated as a two‐sided time sequential game. Optimal mixed strategies are derived for the situation of one patrol boat against one smuggler. Procedures for obtaining numerical solutions for R > 1 patrol boats are discussed.
Distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables
Authors: Malik Henrick John
Published: May 2007

In this paper the exact distribution of a linear function and the ratio of two independent linear functions of independent generalized gamma variables is given.
A survey of maintenance models: The control and surveillance of deteriorating systems
Authors: Pierskalla William P. , Voelker John A.
Published: May 2007

The literature on maintenance models is surveyed. The focus is on work appearing since the 1965 survey, “Maintenance Policies for Stochastically Failing Equipment: A Survey” by John McCall and the 1965 book,The Mathematical Theory of Reliability, by Richard Barlow and Frank Proschan. The survey includes models which involve an optimal decision to procure, inspect, and repair and/or replace a unit subject to deterioration in service.
OPTIMAL FACILITY LOCATION UNDER RANDOM DEMAND WITH GENERAL COST STRUCTURE
Authors: Balachandran V. , Jain Suresh
Published: May 2007

This paper investigates the problem of determining the optimal location of plants, and their respective production and distribution levels, in order to meet demand at a finite number of centers. The possible locations of plants are restricted to a finite set of sites, and the demands are allowed to be random. The cost structure of operating a plant is dependent on its location and is assumed to be a piecewise linear function of the production level, though not necessarily concave or convex. The paper is organized in three parts. In the first part, a branch and bound procedure for the general piecewise linear cost problem is presented, assuming that the demand is known. In the second part, a solution procedure is presented for the case when the demand is random, assuming a linear cost of production. Finally, in the third part, a solution procedure is presented for the general problem utilizing the results of the earlier parts. Certain extensions, such as capacity expansion or reduction at existing plants, and geopolitical configuration constraints can be easily incorporated within this framework.
Some comparative & design aspects of fixed cycle production systems
Authors: Soyster A. L. , Toof D. I.
Published: May 2007

A serial production line is defined wherein a unit is produced if, and only if, all machines are functioning. A single buffer stock with finite capacity is to be placed immediately after one of the first N‐1 machines in the N machine line. When all machines have equal probability of failure it is shown that the optimal buffer position is exactly in the middle of the line. This result is synthesized with the earlier work of Koenigsberg and Buzacott including an analysis of the covariance between transition states. An alternative model formulation is presented and integrated with previous results. Finally, a sufficient condition and solution procedure is derived for the installation of a buffer where there is a possible trade‐off between increasing the reliability of the line versus adding a buffer stock.
Estimation of strategies in a markov game
Authors: Filar Jerzy A.
Published: May 2007

In this paper a two‐person Markov game, in discrete time, and with perfect state information, is considered from the point of view of a single player (player A) only. It is assumed that A's opponent (player B) uses the same strategy every time the game is played. It is shown that A can obtain a consistent estimate of B's strategy on the basis of his past experience of playing the game with B. Two methods of deriving such an estimate are given. Further, it is shown that using one of these estimates A can construct a strategy for himself which is asymptotically optimal. A simple example of a game in which the above method may be useful is given.
Occupational structure in the military and civilian sectors of the economy
Authors: Haber Sheldon E.
Published: May 2007

This paper focuses on trends in the occupational structure of the military and civilian sectors of the economy. Some implications of these trends for manpower policies for the all‐volunteer military establishment are examined.
On multipopulation queuing systems with first‐come first‐served discipline
Authors: Truemper K.
Published: May 2007

Steady‐state probabilities for a multipopulation single channel multiserver queuing system with first‐come first‐served queue discipline are established. Special cases lead to simplified formulas which sometimes can be evaluated using existing statistical and/or queuing tables. Optimization aspects are considered involving control of service rates. Several applications are presented.
Algorithms for minimizing total cost, bottleneck time and bottleneck shipment in transportation problems
Authors: Srinivasan V. , Thompson G. L.
Published: May 2007

We consider the transportation problem of determining nonnegative shipments from a set of m warehouses with given availabilities to a set of n markets with given requirements. Three objectives are defined for each solution: (i) total cost, TC, (ii) bottleneck time, BT (i.e., maximum transportation time for a positive shipment), and (iii) bottleneck shipment, SB (i.e., total shipment over routes with bottleneck time). An algorithm is given for determining all efficient (pareto‐optimal or nondominated) (TC, BT) solution pairs. The special case of this algorithm when all the unit cost coefficients are zero is shown to be the same as the algorithms for minimizing BT. provided by Szwarc and Hammer. This algorithm for minimizing BT is shown to be computationally superior. Transportation or assignment problems with m=n=100 average about a second on the UNIVAC 1108 computer (FORTRAN V)) to the threshold algorithm for minimizing BT. The algorithm is then extended to provide not only all the efficient (TC, BT) solution pairs but also, for each such BT, all the efficient (TC, SB) solution pairs. The algorithms are based on the cost operator theory of parametric programming for the transportation problem developed by the authors.
On a constraint qualification in a nondifferentiable programming problem
Authors: Mond Bertram , Schechter Murray
Published: May 2007

A mathematical programming problem with an objective function containing the square root of a positive semidefinite quadratic form has been considered by Mond. In order to use a transposition theorem of Eisenberg, Mond introduces a complicated constraint qualification. In this note we give a simple geometric characterization to this constraint qualification and show that it is implied by the generalized Slater constraint qualification.
Zero‐sum games with multiple goals
Authors: Cook Wade D.
Published: May 2007

This paper investigates a class of two‐person zero‐sum multiple payoff games in which each component is deterministic. The problem of minimizing a player's total underachievement of a fixed set of goals is shown to reduce to a linear programming problem. Applications are discussed and illustrative examples are presented.
Multivariate tests of fit using asymptotically sufficient grouping
Authors: Weiss Lionel
Published: May 2007

A sample is taken from a continuous multivariate distribution. The problem is to test the hypothesis that the unknown joint cumulative distribution function is equal to a completely specified function. The observed data are transformed so that the hypothesis being tested is that the distribution is uniform over a unit hypercube. If only neighboring alternatives are considered, it is shown that the numbers of observations falling in a gradually increasing number of subcubes are asymptotically sufficient. It is shown that for all asymptotic probability calculations, we can assume that the joint distribution of the numbers of observations can be considered to be the distribution of slightly rounded off normal random variables. Tests based on these facts are constructed.
The effect of prior assumptions on the expected cost of m/m/1 queueing systems with unknown arrival rate
Authors: Barzily Zeev , Yadin Micha
Published: May 2007

In this study we deal with the determination of optimal service rate in an M/M/1 queue. The arrival rate is unknown and assumed to be a random variable with a known distribution function. Holding and operating costs are considered and service rate is determined to minimize total expected discounted costs for infinite horizon. The effects of the arrival rate's distribution properties on the characteristics of the system are examined.
Stochastic duels with bursts
Authors: Ancker C. J.
Published: May 2007

In this analysis we extend the theory of stochastic duels to include the situation where one of the contestants fires a single infinitely long burst at a fixed rate of fire and secondly where he fires fixed‐length, fixed‐rate of fire bursts randomly spaced. In both cases the opponent fires single rounds randomly spaced. Special cases and parameter effects are considered.
Elements of a theory in non‐convex programming
Authors: Burdet Claude‐Alain
Published: May 2007

The question of necessary and sufficient optimality conditions for non‐convex programs is analyzed in the general context of subadditivity. Several types of convex set extensions are investigated to generate valid inequalities from the corresponding gauge functions.