bluuebunny/crossref_metadata_2025 huggingface dataset:
An automatic addressing device
Authors: Fennell J. P.
Published: May 2007

In many computations the identification of an item or items requires several decimal digits, an index which cannot be accommodated readily as a machine address. It is characteristic of these indices that the cardinality of the actual range is within the limits determined by conventional high‐speed storage. This fact is exploited by means of the system under discussion.

The device1 to be discussed consists chiefly of a magnetic drum with a capacity of about 400,000 decimal digits with variable word lengths of 4 to 64 digits, a register (FR) with capacity varying from 4 to 64 digits, and an address register (FADR). Upon the execution of a SEARCH command, the entire surface (about 30,000 words at WL=12) is scanned in 32 ms, and, if the contents of FR are found anywhere, this information is made available in the form of an output which can be used to cause a transfer—similarly, if this number is not present. When the number is found its location is entered into FADR. This system may be employed as a conventional storage device with the usual READ, WRITE instructions. The various commands and logical elements of the FDS are discussed.
Comments on interindustry economics
Authors: Manne Alan S.
Published: May 2007

In writing “INTERINDUSTRY ECONOMICS” [1], Hollis Chenery and Paul Clark have furnished the profession with a uniquely useful work. Within the same covers, they have succeeded in providing both a readable textbook for the beginner, and at the same time a systematic treatise for the input‐output practitioner. Two chapters are to be singled out for special mention: Chapter 6, “Testing the Validity of Input‐Output Assumptions” and Chapter 7, “A survey of Interindustry Research.” Together, these chapters provide a long‐overdue survey of the literature on empirical implementation of Leontief's model of the economy. Much of this Literature has appeared only in mimeographed form, and has not hitherto been generally accessible.
General simulation model for logistics operation in a randomly damaged system
Authors: Walsh John E.
Published: May 2007

The logistics operation considered is imbedded in a system that is subject to damage. Natural attrition and induced attrition can both occur. This system is concerned with the availability and/or use of several different types of items during a specified period of time. The purpose of logistics is to furnish transportation, reduce natural attrition through maintenance, and return damaged items to operational condition. The capability of the logistics operation is examined by simulating the operation of the entire system for the specified time period. The damage received by the various parts of the system depends on the situation at the start of the time period, the use made of the items, the nature of the induced attrition, and the maintenance procedures, etc. Attrition occurs on a probability distribution basis and is introduced by a Monte Carlo procedure. The time required to return a damaged item to operational condition depends on the type of damage, the damage received by other items, the characteristics of the logistics operation, the damage received by the logistics part of the system, etc. To obtain the simulation model, the over‐all system is divided into subsystems on the basis of the use and location of the items, the properties of the logistics operation, etc. The time scale used is discrete; i.e., all important effects are considered to occur during one of a specified finite set of time intervals. The same form of simulation model is used for representing the operation of each subsystem for each time interval. That is, the mathematical model has the same functional form, but the variables in this functional form can differ with the subsystem and time interval. These subsystems can interact in many ways, e.g., items can be transferred between subsystems, damage received in one subsystem can affect the logistics operations in other subsystems, etc. By using time as the basis for coordination among subsystems, the mathematical model and random assignments for attrition can be programmed on a high‐speed computer. The simulation is performed by obtaining first the operational results for all subsystems at the first time considered; then, by using the first‐time results, the second‐time results are obtained, etc. Examination of the subsystem results for each time interval should furnish a good indication of the capabilities of the logistics operation. Repetitions of this simulation furnish an indication of the effects of statistical variation.
Priority ratings in more than one dimension
Authors: Mellon W. G.
Published: May 2007

This paper presents certain theoretical and empirical results for problems which involve the assignment of priority ratings or indicators of military worth, where either several of these ratings must be aggregated or the outcome is to be evaluated by a multi‐valued criterion. The first portion of the paper contains a discussion of the logic of the problem and the axiomatic structure of a desirable solution. The second section includes the results of an experiment in which random demands were processed by running them through a model supply system using several alternative systems of priorities.
Determining merchant shipping requirements in integrated military planning
Authors: Hunt Ralph B. , Rosholdt Erling F.
Published: May 2007

To establish a perspective, a discussion is made of the over‐all planning process involved in the determination of military requirements for the merchant shipping needed to support a prescribed military plan. Three of the principal parts of the planning process, namely: the determination of “pure” pipeline requirements, ship repair loads, and repair replacement ships, under convoy and nonconvoy conditions, are examined. After this, the newly developed models, assumptions, and methodologies for these are dissected and illustrated by means of figures.

Typical characteristics and behavior of both the nonconvoy and convoy‐type pipelines and the effect of the repair policies upon them are presented. Additional logistics problems, which were generated in the planning process and which require further research, are outlined.
An alternative solution to the “lost at sea” problem
Authors: Gluss Brian
Published: May 2007

A problem posed by Bellman and considered by Isbell is as follows: Suppose one is a mile from a straight shore with no means whatsoever of ascertaining its direction. What is the optimum path to follow so as to (a) minimize the maximum distance travelled in reaching shore, (b) minimize the statistical expectation of the distance travelled, or (c) maximize the probability of reaching shore within a given distance travelled? Isbell found the solution to (a); in the present paper a sequence of approximations to the optimal policy for (b) is considered.
Replacement when constant failure rate precedes wearout
Authors: Hunter Larry , Proschan Frank
Published: May 2007

Assume a component has a constant failure rate during the first τ unit of time following installation. After that, wearout sets in so that failure rate begins to increase sharply. Assume further that replacement is made at the time of component failure or at τ units of time following installation, whichever occurs first. Under these assumptions, we obtain explicit formulas for the distribution and expected value of the number of planned replacements, the number of failures, and the total number of removals due to either planned replacement or failure replacement, corresponding to any specified length of time. Examples are worked to show the application of these formulas. The results obtained in this article are of use in determining the number of spares to stock or the budget required to maintain the equipment.
Constraint qualifications in maximization problems
Authors: Arrow Kenneth J. , Hurwicz Leonid , Uzawa Hirofumi
Published: May 2007

Many problems arising in logistics and in the application of mathematics to industrial planning are in the form of constrained maximizations with nonlinear maximands or constraint functions or both. Thus a depot facing random demands for several items may wish to place orders for each in such a way as to maximize the expected number of demands which are fulfilled; the total of orders placed is limited by a budget constraint. In this case, the maximand is certainly nonlinear. The constraint would also be nonlinear if, for example, the marginal cost of storage of the goods were increasing. Practical methods for solving such problems in nonlinear programming almost invariably depends on some use of Lagrange multipliers, either by direct solution of the resulting system of equations or by a gradient method of successive approximations (see [5], Part II). This article discusses a part of the sufficient conditions for the validity of the multiplier method.
Optimal disposal policies
Authors: Fukuda Yoichiro
Published: May 2007

In this paper we analyze the inventory model in which the disposal of surplus items is taken into consideration as well as the purchase of stock in anticipation of future demand. Our main concern is to formulate the optimal ordering and disposal policy in a simple form, and it is assumed that the decision to be made at the beginning of each period is always one of the following: (1) ordering, (2) disposal, (3) no ordering and no disposal. The multiple installation model is treated by the method of implied penalty described by Clark and Scarf. The simple optimal policies are explicitly determined under various sets of assumptions on the cost structure of the inventory model.
A transportation algorithm and code
Authors: Flood Merrill M.
Published: May 2007

A FORTRAN II transportation code, using Kuhn's Hungarian Method, was reported upon at the RAND Symposium on Mathematical Programming in March 1959. The algorithm was based upon a proof of the König‐Egervary theorem, presented by the present author at the 1958 Symposium on Combinatorial Problems sponsored by the American Mathematical Society. The code was entirely rewritten (in FORTRAN II), during the 1959 IBM Summer Institute on Combinatorial Problems, and several problems were run at the IBM Research Center to obtain data regarding computing times and frequencies of various internal loops. A CLOCK Subroutine yields readings, in hundredths of minutes, for each time through selected portions of the computing run. The version reported upon at RAND solved a 29 × 116 pseudorandom transportation problem in 8.01 min, as compared with 3.17 min using the fastest competing code (SHARE 464) then available. The present version solved this same problem in 2.87 min, and another 29 × 116 problem in 1.89 min. This paper presents the algorithm and reports upon computing experience.
Approximately optimal one‐dimensional search policies in which search costs vary through time
Authors: Gluss Brian
Published: May 2007

Consider a model in which there are N neighboring cells in one of which there is an object that it is required to find. The a priori probabilities of the object being in cells 1, …, N are p1, …, pN respectively, and the costs of examination of these cells are tl, …, tN respectively; the search policy is considered to be optimal when the statistical expectation of the total cost of the search is minimized. For the case in which the ti†s are constant throughout the search, an optimal policy solution has previously been found by Bellman and by Smith. In the present paper it is assumed that the costs comprise a travel cost dependent upon the distance from the last cell examined, in addition to a fixed examination cost: initially, assuming that the searcher is next to cell 1, ti = i + t, where t is constant; and from then onwards, assuming that the jth cell has just been examined, ti = | i ‐ j | + t. An optimal search strategy is found in the case where the pi† s are all equal, and approximately optimal strategies in the case where pi is proportional to i. The latter case has application to defense situations where complete searches occur at successive intervals of time, and hence the enemy objects are thinned out the nearer they come to the defense base.
An approximative algorithm for the fixed‐charges transportation problem
Authors: Kuhn Harold W. , Baumol William J.
Published: May 2007

A computationally simple method for approximating the optimal solution to transportation problems is described. Also, a method to deal with fixed charges is proposed. The computational algorithms have been designed primarily to handle very large numbers of transportation problems each involving a small number of origins and destinations as is frequently the situation in the Navy supply system. The results of empirical tests of the effectiveness of the methods are summarized.
On the asymptotic distribution of an estimate of a scale parameter
Authors: Weiss Lionel
Published: May 2007

In an earlier paper, an estimate of an unknown scale parameter was proposed and shown to have certain desirable properties. The asymptotic distribution of a modified version of the estimate is found.
Toward a study of bidding processes some constant‐sum games
Authors: Griesmer James H. , Shubik Martin , Watson Thomas J.
Published: May 2007

The study of bidding has presented both economics and psychology with a host of as yet unresolved problems. The lack of understanding of these problems has been manifested in the difficulties confronting policy‐makers in the framing of laws to deal with collusive or restrictive practices in bidding under various market mechanisms. On the one hand, a theory of competitive behavior may call for all competitors to charge the same price for the same product, yet the submission of identical bids may, in fact, be a criterion of collusion.

This paper, the first of a series on bidding, gives a general and preliminary discussion of several of the factors entering into the construction of models of the bidding process.

Following this discussion, a number of bidding situations, formulated as two‐person constant‐sum games are examined. A number of open questions, suggested during the investigation of such games. are mentioned.

Succeeding papers will be devoted to the more important cases of bidding models formulated as non‐constant‐sum games, both for single‐shot bids and for sequences of bids.
Simulation and the logistics systems laboratory
Authors: Geisler M. A. , Haythorn W. W. , Steger W. A.
Published: May 2007

Systems analysis is the term used to describe the study of large and complex systems. An example would be the problem involved in the employment and support of new weapon systems and the selection among alternative weapon systems for achieving given strategic or tactical objectives. Several techniques have been used in systems analysis, ranging in degree of abstraction from collection and statistical analysis of data gathered in field tests to highly abstract mathematical models and analysis.

An intermediate approach in this spectrum of abstraction is called simulation. Its use has been bettered significantly by the availability of electronic computers, which permit the specification of the environment in sufficient detail to obtain good correspondence between the characteristics of the simulated system and the system under study, and by the rapid calculation of the simulated system to study its characteristics.

Simulation itself consists of a variety of alternative and complementary techniques for simulating systems. One such method is “game‐simulation” — the principal topic of this paper. The joint and integrated use of people and computers to simulate complex man‐machine systems characterizes game‐simulation. This paper compares game‐simulation with other simulation techniques; describes its use inlogistics research; explains the results obtained in analyzing logistics systems; and gives the advantages and disadvantages of the technique at its present state of development.
Optimum allocation of a spares budget
Authors: Blitz M. , Wnltham
Published: May 2007

An algorithm is derived for allocating finite resources in discrete amounts to a number of activities subject to a set of nonlinear constraints. The algorithm differs from those previously described in that the amount of the resource consumed for an additional unit of any one activity need not be constant. The algorithm is then applied to the problem of allocating a spares budget when repair of failed subsystems is allowed and the cost of unit subsystems is a function of the number to be spared. Two models are presented: one with an unrestricted repair facility, exponential failure distributions, and general repair distributions; and another with more limited repair and exponential failure and repair distributions.
Scheduling general production systems using schedule algebra
Authors: Ciffler B.
Published: May 2007

The objective of this work is to demonstrate the use of schedule algebra to define and solve problems to generate and evaluate production schedules and, in the process, to describe a recently completed computer program, SCHEDULER I, which solves this problem for a wide class of products and production systems. The problem formulation requires that the program user describe each system output in terms of its constituent tasks and state, for each task, all restraints which will or may affect either the time it is performed or the choice of a particular facility to perform it. The user must also specify the numbers and types of facilities which are available to perform the tasks and all restraints affecting these availabilities. The problem is, given restraints of the preceding character, to determine when each task starts and ends, the specific facility which performs it, how long the task had to wait for the facility to become available (or, if the facility was previously idle, how long it was idle) and how long the task's scheduled start could be postponed without automatically forcing the postponement of the scheduled start of any other task. Novel features of the problem formulation permit the user to specify, with considerable latitude, the decision rules to be used in selecting tasks to be started on a vacated facility, to freely dovetail successive tasks to produce a same output and successive tasks performed by a same facility, and to change the capacity of the production system at any point in time. The program automatically readjusts the time‐phasing of a task if its processing must be interrupted in order to reduce the capacity of the production system.
A pitfall in accelerated life testing
Authors: Allen W. R.
Published: May 2007

The Managing Editor invites communications which are consistent with the objectives of the Naval Research Logistics Quarterly. No communication will be printed without the expressed consent of the author. All views represented are those of the author and are not to be regarded as the opinion of the Naval Research Logistics Quarterly or any elements of the Department of Defense.
N‐person games in partition function form
Authors: Thrall R. M. , Lucas W. F.
Published: May 2007

This paper gives a formulation of a theory of n‐person cooperative games with side payments in terms of a partition function which is defined on the set of all partitions of the set of players. The results for all games with n ≤ 3 are presented. This development generalizes the von Neumann‐Morgenstern theory of games in characteristic function form.
Some factors that affect the overhaul cost of ships: An exercise in statistical cost analysis
Authors: Farrar Donald E. , Apple Robert E.
Published: May 2007

Cross sectional data on 85 U.S. Atlantic Fleet warships is collected and analyzed. Multivariate statistical techniques are employed in an attempt to relate thorough overhaul repair expenditures to factors such as age, size, complexity, power plant, and usage level. Several variables are found to be statistically significant and quantitatively important. Parameter estimates, measures of statistical and predictive importance for individual variables, and examples of the model's use are included.
Analysis of A time‐shared processor
Authors: Kleinrock Leonard
Published: May 2007

This paper analyzes a queueing structure for a time‐shared service facility (or processor) and compares these results with a straightforward first‐come first‐served discipline. The assumption is that the processing time for each job is chosen from a geometric distribution. This time‐shared discipline shares the desirable features of a first‐come first‐served principle, as well as that of a discipline which services short jobs first. It is shown that those jobs with shorter than average processing requirements, spend less time in the queue than they would in a strict first‐come first‐served system, and conversely for longer than average jobs.
On estimating location and scale parameters from truncated samples
Authors: Weiss Lionel
Published: May 2007

Asymptotically efficient estimators are developed for the problem of estimating a location and a scale parameter, using only the observations between the pth and qth sample quantiles.
Decomposition of linear programs by dynamic programming
Authors: Nemhauser George L.
Published: May 2007

The decomposition principle of Dantzig and Wolfe is a method for breaking large linear programs with a block diagonal structure into a set of smaller subprograms. An alternative decomposition scheme derived from a dynamic programming approach is proposed here. This results in a series of parametric linear subprograms whose recursive solution yields the solution to the original linear program.
On the direct sum and tensor product of matrix games
Authors: Mond Bertram
Published: May 2007

A direct sum and tensor product of matrix games and of their equivalent linear programs are defined. The relationship of a “composed” game to the corresponding “composed” linear program is derived. Conditions are obtained for the solution of the direct sum or tensor product game to be determined from the solutions of the component games. Examples are given to show how many actual conflicts can be represented by direct sum or tensor product games.
Simplicial methods for quadratic programming
Authors: van de Panne C. , Whinston Andrew
Published: May 2007

The article is concerned with two closely related quadratic programming methods, the Simplex and the dual method for quadratic programming. Though a self‐contained exposition of both methods is given, the article is concentrated on proofs of convergence of these methods and the properties of the Simplex tableaux.
A delay dependent queue discipline
Authors: Kleinrock L.
Published: May 2007

Queue disciplines studied in the past have not given the system designer sufficient freedom with which to alter the relative waiting times of the various priority groups. In this paper, results are derived for a delay dependent priority system in which a unit's priority is increased, from zero, linearly with time in proportion to a rate assigned to the unit's priority group. The utility of this new priority structure is that it provides a number of degrees of freedom with which to manipulate the relative waiting times for each priority group.
Team decision models of an inventory supply organization
Authors: Kriebel Charles H.
Published: May 2007

When uncertainty is a consideration in the normative analysis of decisions and information within organizations, “best” programs of decision rules depend on the information structure which pertains to the organization. Under different information structures, different decision rule programs are optimal relative to the prevailing criteria of organization performance.

Propositions from team decision theory may be employed advantageously to resolve behavioral issues in the formal description of organizational decision processes. In specifying the information structure of an organization within the analysis of team problems it becomes useful to distinguish between components of the data generating process and the information system. An information system can be described completely in terms of (1) the space of states of the world, {Xi} = X; (2) the space of information, {Zk} = Z; and (3) the system likelihood function or conditional probability of each item of information, Zk, given the state, Xi, for each Zk ε Z and Xi ε X. The framework of applied statistical decision theory provides an operational procedure for the normative analysis of alternative decision rule programs and information systems.

These considerations are illustrated for a simple logistics organization with operating costs given by a constrained asymmetric linear function of inventory and demand. In particular, both normal and extensive form analyses of the team decision problem are detailed under several logistics information systems.
The bounded variable problem‐an application of the dual method for quadratic programming
Authors: Whinston Andrew
Published: May 2007

The paper presents an algorithm to solve the bounded variable quadratic programming problem. The algorithm is a direct extension of an earlier algorithm of H. Wagner (N.R.L.Q. 1958) for the case of a bounded variable linear programming problem.
The kernel of a cooperative game
Authors: Davis Morton , Maschler Michael
Published: May 2007

The kernel of a cooperative n‐person game is defined. It is a subset of the bargaining set 𝔐(i). Its existence and some of its properties are studied. We apply it to the 3‐person games, to the 4‐person constant‐sum games, to the symmetric and n‐quota games and to games in which only the n and the (n‐1)‐person coalitions are allowed to be non‐flat.

In order to illustrate its merits and demerits as a predictor of an actual outcome in a real‐life situation, we exhibit an example in which the kernel prediction seems frustrating. The opinions of other authors are quoted in order to throw some light on this interesting example.
A note on systems of simultaneous linear difference equations with constant coefficients
Authors: Pfouts Ralph W.
Published: May 2007

General solutions of systems of simultaneous linear difference equations with constant coefficients are developed and specific solution methods are discussed. A matric form of difference equations is demonstrated. A theorem on the separation of variables is proved as are two theorems on the possible paths of a system. A brief statement on the underlying mathematical theory is included.
Minimum‐cost flows in convex‐cost networks
Authors: Hu T. C.
Published: May 2007

An algorithm is given for solving minimum‐cost flow problems where the shipping cost over an arc is a convex function of the number of units shipped along that arc. This provides a unified way of looking at many seemingly unrelated problems in different areas. In particular, it is shown how problems associated with electrical networks, with increasing the capacity of a network under a fixed budget, with Laplace equations, and with the Max‐Flow Min‐Cut Theorem may all be formulated into minimum‐cost flow problems in convex‐cost networks.
A price leadership method for solving the inspector's non‐constant‐sum game
Authors: Maschler Michael
Published: May 2007

An inspector's game is a non‐constant‐sum two‐person game in which one player has promised to perform a certain duty and the other player is allowed to inspect and verify occasionally that the duty has indeed been performed.

A solution to a variant of such a game is given in this paper, based on the assumption that the inspector can announce his mixed strategy in advance, if he so wishes, whereas the other player, who has already given his promise, cannot threaten by explicitly saying that he will not keep his word.
One‐person games of economic survival
Authors: Morrill John E.
Published: May 2007

This paper discusses the one‐person economic survival game model with a discrete probability distribution for the contribution to surplus variable. The general game model and strategies in these games are examined, and necessary conditions which an undominated, stationary strategy must satisfy are obtained. For a special class of these games a mathematical formulation of the value of the game is given, and examples and theorems which relate to undominated strategies in this class are presented. This paper, in some sense, is a sequel to a portion of a paper by Shubik and Thompson [7] which appeared in this journal.
Vessel allocation by linear programming
Authors: Laderman J. , Gleiberman L. , Egan J. F.
Published: May 2007

This paper presents a linear programming model of a fleet of vessels which is required to transport quantities of cargo, such as coal, iron ore, limestone, and salt from certain producing ports to specific destination ports. This model has been implemented and is currently being used both for planning purposes and as an aid in scheduling the trips to be made by each vessel.
A method for solving the transportation problem
Authors: Lagemann J. J.
Published: May 2007

A new method has been developed f o r solving the transportation problem. This method is a modification and a generalization of the method for solving the multiple assignment problem developed by Dr. A. J. Hoffman and Dr. H. M. Markowitz.

This method is of interest for several reasons. In the first place it is significantly different from all other methods for solving the trans ‐portation problem known to the author. Secondly, it is moderately simple touse and understand. Thirdly, and perhaps most important, it has proved to be very adaptable tri high‐speed computer operations. It is now being used by several branches of the armed services.
An approximate solution method for the fixed charge problem
Authors: Cooper L. , Drebes C.
Published: May 2007

In the absence, to date, of an exact method for solving the linear programming problem with fixed charges, two heuristic methods have been proposed and extensively investigated, computationally, for moderate sized problems. The results indicate that the heuristic methods produce optimal solutions in well over 90 percent of the several hundred problems investigated and very close to optimal (a few percent) in the remaining cases. Hence it should be of practical significance to practitioners in the field.
Linear estimation of the location and scale parameters from type 11 censored samples from symmetric unimodal distributions
Authors: Chan Lai Kow
Published: May 2007

Estimates of the location and scale parameters, linear in the order statistics of a Type II censored or complete sample, from a continuous symmetric unimodal distribution satisfying certain conditions are obtained. Their coefficients are explicit functions of the expectations of the order statistics or population quantiles from the known parameter‐free standardized distribution. Linear estimates with simpler coefficients are also obtained. The theorems state the complete sample case, and the singly and doubly censored cases. The more general case, the multiple censoring, is an extension of these cases and is indicated. All the estimates obtained are asymptotically efficient in the strict sense.
Simple stability of general n‐ person games
Authors: Marchi Ezio
Published: May 2007

Herein are introduced noncooperative points of n‐person games defined on compact and convex sets in a Euclidean space and continuous payoff functions, which are natural extensions of the respective concepts of maximin, minimax strategies and saddle points of two‐person games. The conc:ept of equilibrium point appears as a special of one of those.

As a particular case, we examine such points for the mixed extension of finite n‐person games; finally, a related topic is illustrated.

These results represent the first installment of a collection which will be continued in subsequent publications.
A two‐station stochastic inventory model with exact methods of computing optimal policies
Authors: Love Robert F.
Published: May 2007

A method is presented for calculating optimal inventory levels in a two‐station transactions reporting inventory system. The criterion of optimality is the minimization of expected cost. The computational properties of the model are stressed and the solution method is precise.

It is shown that when the model represents a central warehouse which supplies several retail outlets, stocks carried at the central location affect the capacity of the system to handle orders. Stocks carried at the retail level affect only the size of the retail order backlog.
Queues with stochastic service rates
Authors: Harris Carl M.
Published: May 2007

The purpose of this paper is to explore an extension of the output discipline for the Poisson input, general output, single channel, first‐come, first‐served queueing system. The service time parameter, μ, is instead considered a random variable, M. In other words, the service time random variable, T, is to be conditioned by a parameter random variable, M. Therefore, if the distribution function of M is denoted by FM(μ) and the known conditional service time distribution as B(t |μ), then the unconditional service distribution is given by B(t) = Pr {T ≤ t}. = ∫‐∞∞ B(t |μ) dFM(μ).

Results are obtained that characterize queue size and waiting time using the imbedded Markov chain approach. Expressions are derived for the expected queue length and Laplace‐Stieltjes transforms of the steady‐state waiting time when conditional service times are exponential. More specific results are found for three special distributions of M: (1) uniform on [1.2]; (2) two‐point; and (3) gamma.
Some constraints on shipping in linear programming models
Authors: Whiton Justin C.
Published: May 2007

This note describes some constraints that may be applied to shipping models structured as linear programming problems. These constraints defining port‐throughput capability have proven useful in applications of linear programming by the author and provide additional realism in problems of vessel allocation and ship design selection. Increase in model size through the use of the constraints is in general mode rate.
Maximum matching in a convex bipartite graph
Authors: Glover Fred
Published: May 2007

A special matching problem arising in industry is shown to be solvable by an algorithm of the form: match objects ai and bj if they satisfy a local optirnality criterion based on a ranking of currently unmatched objects. When no ai and bi remain that can be matched, the largest number of acceptable matches has been found.
Toward a study of bidding processes part IV ‐ games with unknown costs
Authors: Criesmer James H. , Levitan Richard E. , Shubikt Martin
Published: May 2007

This paper represents a continuation of three previous papers [1‐.3] in the study of competitive bidding processes. It treats the case where a bidder's knowledge of his competitor's cost i s given by a probability distribution over a certain interval. The results obtained extend the work of Vickrey [4] to the case where the cost intervals a r e not necessarily symmetric.
The truck assignment problem
Authors: Szwarc Wlodzimierz
Published: May 2007

Let us consider the following problem: A group of cement factories produces several types of cement, but each factory produces only one type. There is also a group of purchasers and each purchaser may need several types of cement. The amounts supplied and the demands are assumed to be known for each cement factory and each purchaser. Each cement factory has several trucks, but there is only one dispatcher for ail of the trucks from all of the factories. It is assumed that the entire lcad of each truck is for one purchaser only. A truck begins its workday by leaving its base depot loaded and ends its day by returning to it empty. During the day it may be required to transport cement from any of the cement factories. The distances from various factories to individual purchasers are known. The problem to be solved is that of finding a truck schedule such that cement in the needed quantities is delivered daily to the individual purchasers and in such a manner that the total truck‐kilometers traveled will be as small as possible. This paper presents the method of solution, though the assumption of an 8‐hour workday may not be met. On the other hand, there are methods developed for effecting a variety of cyclic routings which can be used to lend considerable flexibility to the schedules.
Markov chain analysis of a situation where cannibalization is the only repair activity
Authors: Rolfe Alan J.
Published: May 2007

This paper considers a group of S identical aircraft, each of which is partitioned into K parts which fail exponentially. The only way in which a failed aircraft can be repaired is by cannibalizing its out‐of‐commission parts from other failed aircraft. The evolution of the number of good aircraft over time is governed by the transient behavior of an absorbing Markov chain. We can therefore study this behavior by matrix multiplication although the computational problem grows large for K ≥ 3. Some numerical results and some approximations are also provided.
Some estimates of reliability using interference theory
Authors: Mazumdar M.
Published: May 2007

According to “interference theory” of reliability, a component fails if the maximum stress exceeds the component's strength. Assuming that both these quantities are random and their distributions are normal, we obtain in this paper some point and interval estimates of reliability when the stress distribution is known and a few observations exist on component strengths.
The optimal burn‐in testing of repairable equipment
Authors: Cozzolino John M.
Published: May 2007

The subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn‐in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn‐in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repairable device.
Production and employment scheduling in multistage production systems
Authors: von Lanzenauer Christoph Haehling
Published: May 2007

A model is developed for planning optimal production and employment levels in multi‐product, multistage production systems. The market requirements for each product over the planning period are given. Backorders and/or shortages are permitted. Backorders and shortages must be considered in order to determine the amount of each product's demand that should be filled, backlogged, or go unsatisfied if the production capacity is insufficient to fill all market requirements. Backorders and shortages, on the other hand, are desirable under certain dynamic market conditions.
A mutual primal‐dual linear programming algorithm
Authors: Harris Milton Y.
Published: May 2007

A new primal‐dual linear programming algorithm is exhibited. A proof is given that optimal solutions to both primal and dual problems (when such solutions exist) are found in a finite number of steps by this algorithm. A numerical example is included to illustrate the method.
Interception in a network
Authors: Wollmer R. D.
Published: May 2007

This paper presents an algorithm for determining where to place intercepting units in order to maximize the probability of preventing an opposing force from proceeding from one particular node in an undirected network to another.

The usual gaming assumptions are invoked; namely, the strategy for placing the units is known to the opponent and he will choose a path through the network which, based on this knowledge, maximizes his probability of successful traverse. As given quantities, the model requires a list of the arcs and nodes of the network, the number of intercepting units available to stop the opposing force, and the probabilities for stopping the opposition at the arcs and nodes as functions of the number of intercepting units placed there. From these quantities, the algorithm calculates the probabilities for placing the unit at the arcs and nodes when one intercepting unit is available, and the expected numbers of units to place at the arcs and nodes when multiple intercepting units are available.
Cooperation pattern
Authors: Jones Victor
Published: May 2007

Voluntary association of local units called step to ‘federalism’ of metropolitan areas.
Program for citizens
Authors: Galligan David J.
Published: May 2007

New Jersey State Chamber of Commerce numerous action courses in practical conducts politics.
Taming urban giant
Authors: Loeks C. David
Published: May 2007

Metropolitan planning needs to be a working partnership of various levels of government.
Mermaid with a broom
Authors: Poling James
Published: May 2007

She finds ways to let nature's own sanitary engineers living in streams keep water pure.
The ‘people problem’
Authors: Thompson Wayne E.
Published: May 2007

Oakland gets $2 million grant to find pattern resolving social, economic puzzles of cities.
Home rule appraised
Authors: Lee Eugene C.
Published: May 2007

Today our task is to create cities capable of meeting responsibilities of self‐government.
Partition of unity for localization in implicit a posteriori finite element error control for linear elasticity
Authors: Carstensen Carsten , Thiele Jan
Published: May 2007

The partition of unity for localization in adaptive finite element method (FEM) for elliptic partial differential equations has been proposed in Carstensen and Funken (SIAM J. Sci. Comput. 2000; 21: 1465–1484) and is applied therein to the Laplace problem. A direct adaptation to linear elasticity in this paper yields a first estimator ηL based on patch‐oriented local‐weighted interface problems. The global Korn inequality with a constant CKorn yields reliability for any finite element approximation uh to the exact displacement u. In order to localize this inequality further and so to involve the global constant CKorn directly in the local computations, we deduce a new error estimator µL. The latter estimator is based on local‐weighted interface problems with rigid body motions (RBM) as a kernel and so leads to effective estimates only if RBM are included in the local FE test functions. Therefore, the excluded first‐order FEM has to be enlarged by RBM, which leads to a partition of unit method (PUM) with RBM, called P1+RBM or to second‐order FEMs, called P2 FEM. For P1+RBM and P2 FEM (or even higher‐order schemes) one obtains the sharper reliability estimate . Efficiency holds in the strict sense of .

The local‐weighted interface problems behind the implicit error estimators ηL and µL are usually not exactly solvable and are rather approximated by some FEM on a refined mesh and/or with a higher‐order FEM. The computable approximations are shown to be reliable in the sense of . The oscillations are known functions of the given data and higher‐order terms if the data are smooth for first‐order FEM.

The mathematical proofs are based on weighted Korn inequalities and inverse estimates combined with standard arguments. The numerical experiments for uniform and adapted FEM on benchmarks such as an L‐shape problem, Cook's membrane, or a slit problem validate the theoretical estimates and also concern numerical bounds for CKorn and the locking phenomena. Copyright © 2007 John Wiley & Sons, Ltd.
Stochastic convergence acceleration through basis enrichment of polynomial chaos expansions
Authors: Ghosh Debraj , Ghanem Roger
Published: May 2007

Given their mathematical structure, methods for computational stochastic analysis based on orthogonal approximations and projection schemes are well positioned to draw on developments from deterministic approximation theory. This is demonstrated in the present paper by extending basis enrichment from deterministic analysis to stochastic procedures involving the polynomial chaos decomposition. This enrichment is observed to have a significant effect on the efficiency and performance of these stochastic approximations in the presence of non‐continuous dependence of the solution on the stochastic parameters. In particular, given the polynomial structure of these approximations, the severe degradation in performance observed in the neighbourhood of such discontinuities is effectively mitigated. An enrichment of the polynomial chaos decomposition is proposed in this paper that can capture the behaviour of such non‐smooth functions by integrating a priori knowledge about their behaviour. The proposed enrichment scheme is applied to a random eigenvalue problem where the smoothness of the functional dependence between the random eigenvalues and the random system parameters is controlled by the spacing between the eigenvalues. It is observed that through judicious selection of enrichment functions, the spectrum of such a random system can be more efficiently characterized, even for systems with closely spaced eigenvalues. Copyright © 2007 John Wiley & Sons, Ltd.
An FMM for periodic boundary value problems for cracks for Helmholtz' equation in 2D
Authors: Otani Yoshihiro , Nishimura Naoshi
Published: May 2007

This paper presents an FMM (fast multipole method) for periodic boundary value problems for Helmholtz' equation in 2D. The periodic Green function is an important ingredient in our formulation, which is computed efficiently with the help of the Fourier analysis. We validate the proposed method by comparing the obtained numerical results with those computed with the conventional approach. We then apply the proposed method to the analysis of scattering problems for periodic array of cracks and plot the energy transmittance vs wave numbers. The stopband and related phenomena are observed clearly. Copyright © 2007 John Wiley & Sons, Ltd.
On the computation of steady‐state compressible flows using a discontinuous Galerkin method
Authors: Luo Hong , Baum Joseph D. , Löhner Rainald
Published: May 2007

Computation of compressible steady‐state flows using a high‐order discontinuous Galerkin finite element method is presented in this paper. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing solid wall boundary conditions for curved geometries. Particular attention is given to the impact and importance of slope limiters on the solution accuracy for flows with strong discontinuities. A physics‐based shock detector is introduced to effectively make a distinction between a smooth extremum and a shock wave. A recently developed, fast, low‐storage p‐multigrid method is used for solving the governing compressible Euler equations to obtain steady‐state solutions. The method is applied to compute a variety of compressible flow problems on unstructured grids. Numerical experiments for a wide range of flow conditions in both 2D and 3D configurations are presented to demonstrate the accuracy of the developed discontinuous Galerkin method for computing compressible steady‐state flows. Copyright © 2007 John Wiley & Sons, Ltd.