bluuebunny/crossref_metadata_2025 huggingface dataset:
On Two Commodity Network Flows
Authors: Rothschild B. , Whinston A.
Published: November 2008

The paper considers the problem of two-commodity network flows and generalizes a result of Hu on integral flows in networks with integral capacities. The main result of the paper is a max-flow min-cut theorem for two commodity networks. The method of proof involves a particular type of separation process. This leads to an algorithm for finding the maximal flows. Several counterexamples to certain possible generalizations are given at the end of the paper.
On the Problem of Batch Arrivals and its Application to a Scheduling System
Authors: Soriano A.
Published: November 2008

The single-server queuing problem where customers arrive in batches is considered with general types of service time and batch interarrival time distributions. Following an argument similar to that of Lindley, transient and steady-state time distribution functions are obtained for the two processes: (i) a random batch size, and (ii) a periodic batch size. It is shown how to apply the general solution of the process with a random batch size in obtaining particular solutions for the cases with p2 = 1, q1 = 1, and (1) M/G/1 or (2) D/E/1. The latter solution has been used in a comparison of two scheduling systems.
A Stochastic Model of Supermarket Traffic Flow
Authors: Farley John U. , Ring L. Winston
Published: November 2008

A model is developed to predict area-to-area transition probabilities for traffic in supermarkets. The independent variables involve physical measures of store layout and transaction volumes at various locations. The model is fitted to data on traffic patterns in five Pittsburgh stores. The results indicate that the model is useful for traffic analysis both in a given store and for analysis of hypothetical store layouts.
The Intersection Delay Problem with Correlated Gap Acceptance
Authors: Weiss George H.
Published: November 2008

This paper considers a modification of the single-car intersection delay problem in which the waiting driver, upon finding a suitable gap for crossing also examines the succeeding one, and uses it if it is larger. It is shown that the additional delay time caused by this method of gap acceptance is generally quite small.
A “Universal” Attrition Model
Authors: Helmbold Robert L.
Published: November 2008

Starting with a basic model of volley fire against a group of homogeneous passive targets, a series of discrete approximations to the expected number of surviving targets is proposed. Some of these yield quite good approximations over a reasonably wide range of parameter values. Continuous analogues of these approximations are described, and it is shown how various Lanchester-type equations arise in a natural way from these continuous analogues.
An Approach to Some Structured Linear Programming Problems
Authors: Bennett John M.
Published: November 2008

The work describes a computational approach, which is alternative to that of Dantzig and Wolfe, for handling structured linear programming problems that would break up into a number of subproblems except for some restrictions on groups of variables occurring in more than one subproblem.
Optimum Policy Regions for Markov Processes with Discounting
Authors: Smallwood Richard D.
Published: November 2008

In many practical situations the discount factor for future rewards and costs is not known precisely. In the modeling of such situations, this is often reflected in a dependence of the optimum policy on the discount factor. We discuss this dependence of the optimum policy on discount factor for the class of finite-state, time-invariant, Markov models. A procedure is developed for finding the value of the discount factor for which we are indifferent between two policies. This is then extended to a discussion of how we can find the complete description of the optimum policy regions over any range of the discount factor. Two examples are presented.
The Queue M/G/1 with the Shortest Remaining Processing Time Discipline
Authors: Schrage Linus E. , Miller Louis W.
Published: November 2008

A priority queuing model in which the processing times of jobs are known upon arrival and preemption without loss of time or processing already accomplished is studied. Priority is assigned to jobs according to the length of processing remaining with highest priority going to the job with least processing left. A preemption will occur whenever the processing time of a newly arriving job is less than the remaining processing time of the job then in service. The Laplace-Stieltjes transforms of the waiting time and time-in-system distributions are obtained and comparisons with other queuing disciplines are made.
Probability Bounds on the Size of Storage Areas
Authors: Weiss Irving
Published: November 2008

Through the use of generating functions upper and lower bounds are obtained for the probability that at least n units are in storage at any given time. The inputs to the storage area are assumed to be independent and of the Poisson type and the outputs are also independent and follow the negative exponential law. The storage area is assumed to be infinite. A numerical example is included.
An Infeasibility-Pricing Decomposition Method for Linear Programs
Authors: Balas Egon
Published: November 2008

This paper presents two versions of a method for solving large linear programs through decomposition. In both versions the problem is decomposed into subprograms as in the Dantzig-Wolfe model, but each version uses a different type of linking program. The subprograms are first solved, and then the infeasibility of the resulting solution for the linking program is used to generate a price-adjustment process (much like a market mechanism), which gradually corrects the objective functions of the subprograms, until either some optimal solutions to the latter yield a feasible solution to the linking program (then the problem is solved), or evidence is obtained that the problem has no feasible solution.
A Hierarchy of Deterministic Procurement—Inventory Systems
Authors: Fabrycky W. J. , Banks Jerry
Published: November 2008

The research results reported in this paper present a higher level generalization about deterministic procurement-inventory systems embracing multi-item and multisource characteristics. Lower ordered deterministic systems embracing single-item or single-source characteristics are also presented. Dynamic programming is used to find the optimal procurement and inventory policy for each system in the hierarchy.
Letter to the Editor—Comments on the Preceding Note
Authors: Balas Egon
Published: November 2008

Some comments on James Willard D. 1966. Some Remarks on a Numerical Example of Balas and on the Note by Glover and Zionts, Operations Research 14(5) 941.
Letter to the Editor—On a Duality Principle in the Theory of Queues
Authors: Shanbhag D. N.
Published: November 2008

This note establishes a connection between the queue sizes of a queuing system with Poisson arrivals, batch service and general service times, and its dual. It also shows that the knowledge of this relation is useful in the simultaneous study of the busy periods of these systems with infinite waiting space.
The Effect of Standby Redundancy in System’s Failure with Repair Maintenance
Authors: Srinivasan V. S.
Published: November 2008

Two models are considered in this paper with a view to make a theoretical study of the effect of standby redundancy on the time to failure of a system that is used intermittently and the units of which are subject to breakdowns and repairs. The models described in this paper differ only in the definition we make on system's failure. In the first model a system's failure is defined without taking the demand pattern of the system into account, whereas in the second the demand pattern of the system is included in the definition. The Laplace transforms of the probability density functions of system's failure defined under Model I and Model II are derived. The expressions for expected times to failures under these models are also derived.
Letter to the Editor—Winning Probability in an Ambush Engagement
Authors: Kisi Takasi , Hirose Tadasi
Published: November 2008

The combat model of Lanchester type given by S. J. Deitchman in investigating guerrilla-counterguerrilla warfare is reformulated in stochastic form. The situation is such that the guerrillas, having been preparing an ambush for the approaching regular force, start firing; they fire on the regulars, who are in full view, while the latter are forced to return fire blindly into the area supposedly occupied by the guerrillas. A formula for the winning probability is derived, and its simple approximating expression in terms of Poisson probabilities is also given.
Time Dependent Priority Queues
Authors: Kleinrock Leonard , Finkelstein Roy P.
Published: November 2008

Considered is a class of rth order delay-dependent priority queuing disciplines in which a customer from the pth priority group, who arrives at time T, has a priority qp(t) at time t given by qp(t) = bp(t − T)r. The main result states that the expected wait on queue for p-type customers in an rth order system with parameter set [bp] is identical to the wait in any other such system, say one of order r′ with parameter set [bp′] if these parameters are chosen in the proper manner. From this, using the results due to Kleinrock for the first order systems, we obtain the expected wait on queue, conditioned on the priority groups, for any rth order system. This class of queuing disciplines ranges from Cobham's fixed priority system (for r → 0) to the first-come-first-served system (for r → ∞). For the case of two priority groups the set {bp} is chosen so as to minimize a class of delay-dependent cost functions. Results from a computer simulation are given to display the behavior of the waiting time variance.
An Attrition Game
Authors: Appelgren Leif
Published: November 2008

This paper describes a two-person zero-sum game in function space concerning the optimal allocation of a homogenous defense force on different levels of readiness. The second player, the attacker, wants to determine the time for the attack such that the cost is minimized. As the defense is subject to attrition, a delay is preferable for the attacker. This is balanced, however, by a delay cost which increases with time. The existence of a solution consisting of a pure defense strategy and a mixed strategy for the attack time is proved elsewhere. This paper mainly treats an approximation of the game with a time-discrete version for which an algorithm is derived. Arbitrarily close upper and lower bounds of the value of the original game can be obtained by the algorithm, as well as feasible defense and attacker strategies that realize these value estimates. Computational results are given for two simple problems, one of which is also solved analytically.
Comparing a Scheduled Process with an Analogous Poisson Process
Authors: Parker Rodger D.
Published: November 2008

The generating function of a queue in which n arrivals occur at fixed times, of equal intervals apart, and in which the service times are independently and identically distributed exponentially is derived in recursive form. The state probabilities are calculated explicitly for n = 1. An analogous recursion formula for the generating function of a related Poisson process is used to estimate whether the scheduled process may be approximated by a Poisson one. In no instance is the approximation a good one.
Two-Dimensional Collision in Parallel Paths
Authors: de Renna e Souza Celso
Published: November 2008

A particular case of “blind approach” is considered: that in which two vehicles travel with different speeds along parallel mean paths in a two-dimensional region. It is shown that the problem of calculating the probability of safe passage can be put in the form of equivalent zero-crossing problems for stationary, nonzero mean random processes, within a relatively long record. A lower bound for the probability of absence of zero-crossings is given in the form of a finite sum and some arguments on convergence are discussed.
A General Algorithm for Solution of the n-Job, M-Machine Sequencing Problem of the Flow Shop
Authors: Smith Richard D. , Dudek Richard A.
Published: November 2008

This paper describes an algorithm that will yield the minimum make-span sequence for n-jobs requiring processing through M-machines when no passing is allowed. Theoretical development utilizing combinatorial analysis and proof of sequence optimality precedes the algorithm and an example problem.
A Damage-Limiting Shelter-Allocation Strategy
Authors: Kelleher Grace J.
Published: November 2008

A damage-limiting strategy for allocating blast and fallout shelter protection is described in this report. The features that combine to make this strategy unique are its relatively fine-grained local orientation and its ability to meet a survival percentage criterion irrespective of the actual ground zero within the area considered. Shelter postures are tailored to the needs of individual cities or local areas, examined in one-square-kilometer detail. All potential ground zeros are evaluated in the shelter allocation process and least-cost decision rules are applied.
The Lanchester Attrition-Rate Coefficient
Authors: Bonder Seth
Published: November 2008

Since Lanchester's original efforts to describe the dynamics of combat mathematically, many analysts have extended the theory to include additional factors. Current literature suggests that the use of these models for prediction of battle results has been hampered by the inability to predict the Lanchester attrition-rate coefficients. In this paper a probability distribution for the attrition rate is developed for weapon systems that adjust fire based on results of the previous round fired. Parameters of the distribution are measurable capabilities of weapon systems and, accordingly, the attrition-rate coefficients can be predicted prior to inception of an engagement.
Optimal Linear Inventory Control and First Order Exponential Smoothing
Authors: Landi Dale M. , Johnson B. McK.
Published: November 2008

A linear, fixed-interval stock replenishment policy that achieves an optimal cost balance between inventory and order-level variances is derived in this paper. The reorder rule relies on an exponentially weighted moving average to smooth random components of the demand sequence, which are assumed to be pairwise uncorrelated with mean zero and variance that either grows or decays geometrically, or remains constant in time.
Letter to the Editor—Analysis of Dominance with Inequality Sets
Authors: Abramson Lee R.
Published: November 2008

This note describes a simpler method than that used by Fishburn to analyze a set of strategies for dominance when the decision maker's probability distribution satisfies a certain set of inequalities.
The Costs and Effectiveness of Reenlistment Incentives in the Navy
Authors: Fisher Franklin M. , Morton Anton S.
Published: November 2008

A nonlinear dynamic model was developed to investigate trade-off between costs and effectiveness of raising the first-term reenlistment rate. Costs per longevity year were determined for the Navy with present incentives and reenlistment rates. Survey responses were used to estimate reenlistment rates for additional incentives, and added costs were determined. In order to measure the operational effectiveness of the Navy, relative impact factors for four usefulness classes were derived from weighted average estimates made by experienced supervisors. A Cobb-Douglas utility function expressed operational effectiveness, both actual and required, as a multiplicative function of the number of men in each usefulness class. Effectiveness requirements that could be achieved by a Navy of specified characteristics were set up for a 30-year time frame. For each incentive situation, the model, using an iterative convergence solution, derived the optimal pattern of annual recruit inputs—the pattern that would at least achieve effectiveness goals, at minimal present discounted cost. The sensitivity of results to assumptions was tested. The optima were compared, indicating which incentives would at least achieve the effectiveness requirements at minimum cost.
A Principal Pivoting Simplex Algorithm for Linear and Quadratic Programming
Authors: Graves Robert L.
Published: November 2008

This paper presents a simplex algorithm for finding a nonnegative solution (or demonstrating the inconsistency) of y = a + Ax where A is positive semi-definite. Linear and quadratic programming problems are of this form. The function exhibited in the proof of finiteness does not appear in other algorithms. If a primal feasible solution is available in the linear programming case, the actual choice of pivot rows is exactly that made in the usual lexicographic simplex method.
Initial Provisioning with Spare Deterioration
Authors: Schweitzer Paul J.
Published: November 2008

Initial provisioning is analyzed for the case where parts in use and spares have exponential failure distributions with different failure rates. Expressions are given for system reliability and its asymptotic expansions for small time, large time, large numbers of spares, and small spare failure rate. The incremental reliability associated with each additional spare part is analyzed. Graphs are presented that yield, for arbitrary failure rates of spares and parts in use, the minimum number of spare parts needed to achieve system reliabilities of 90, 95, and 99 per cent.
Letter to the Editor—Note on the Letter by Morávek and Vlach
Authors: Haley K. B.
Published: November 2008

A note about Morávek, J., M. Vlach. 1967. On the necessary conditions for the existence of the solution of the multi-index transportation problem. Oper. Res. 15 542–545.
Letter to the Editor—Polar vs. Rectangular Road Networks
Authors: Einhorn Sheldon J.
Published: November 2008

In “Road Networks in an Expanding Circular City,” Opns. Res. 14 607–613 (1966). T. Tan discusses five alternative basic road systems for an idealized expanding circular city. Additional remarks presented here lead to considerably different qualitative results.
Letter to the Editor—Quality Improvement by Operational Testing
Authors: Bhattacharya S. K.
Published: November 2008

The familiar concept of burn-in for items with decreasing failure rate has been utilized here to achieve quality improvement by operational testing of lots that are mixtures of exponentially failing items, and a measure of improvement has been provided.
Letter to the Editor—A Note on a Graph Theoretic Game of Hakimi's
Authors: Frank H.
Published: November 2008

Hakimi's algorithm to find the absolute center of a graph is modified to solve a more general version of the same problem.
Letter to the Editor—Duality of Finite Markovian Queues
Authors: Harris Terrell J.
Published: November 2008

The purpose of this paper is to show the dual relation of the queue-size distribution of dual finite queuing systems in which one of the distributions (service or interarrival times) is negative exponential. Hence it is shown that the distribution of queue size at instances of arrival of the GI/M/1/N queuing system is the dual distribution of queue size at instances of service of the dual system.
Heuristic Approach to Nonstandard Form Assignment Problems
Authors: Joseph J. A.
Published: November 2008

Many problems of the practicing operations analyst do not fit the standard forms of analytic OR procedures and do not lend themselves to precise optimization methods. The voracious appetite of the computer demands numerical algorithms in order to give answers. Very often an optimum is not absolutely essential to management, as long as the answer is efficient or superior to guesswork. So heuristic approaches are adapted to the problem. This paper presents a heuristic approach to a nonstandard, practical assignment problem. It concerns a problem that the analyst had to solve “in the field” at Cape Canaveral (now Cape Kennedy) wherein 74 telemetry channels for 19 missiles had to be assigned to 28 available frequency bands. A conflict for a channel occurs if (a) time for use of the range by the missile channels is demanded and (b) another channel on another missile has the same frequency assignment and also wishes the same time. A conflict means one or more missiles must be denied time on the range, which causes costly delay. It is desirable to assign channels to frequencies (which is done at the time the missile is designed) so as to minimize the total expected amount of conflict (or cost of conflict). This paper shows a general, heuristic (not-necessarily optimum) procedure for handling typical, nonstandard assignment problems and gives details of the Cape Kennedy application. This is an example of what can happen “in the field” when standard mathematical forms are not available.
A Multivariate Statistical Model for Indirect Bomb Damage Assessment
Authors: Orr M. , Spohn R. H.
Published: November 2008

This paper describes a multivariate statistical model for obtaining the best estimate of the point of detonation of a long-range nuclear weapon. It extends previous work by permitting greater generality in the dimensional characterization of such problems. It also introduces a new concept of weapon-system error based upon covariance matrices of the model and exhibits simple algorithms for error computation based upon this concept. Specifically, the model provides a technique for combining the a priori knowledge of weapon-system accuracy with the post-burst reports of sensory devices deployed within measuring range of the target. Formulas are derived for several configurations and an example is given illustrating application of the model to Indirect Bomb Damage Assessment.
Evaluating Aircraft Requirements in the Light of Varying or Uncertain Mission Mixes
Authors: Abert James G. , Kamrass Murray , Navarro Joseph A.
Published: November 2008

It is often assumed that an extreme sacrifice in efficiency is made when utility or multi-purpose weapons systems are substituted for systems specifically designed to meet a particular requirement. In this paper the authors attempt to quantify the expected differences in the costs of providing a capability with either specialized or utility type aircraft to meet aircraft requirements in a counterinsurgency environment, where requirements are either uncertain or are known to change from time to time. Because little is known about the actual costs of aircraft operation in a primitive logistics environment, particularly the question of the difference in logistics costs as a result of operating more than one type of aircraft rather than only one type of aircraft, the analysis deals solely with average costs. Unless significant savings are likely to be achieved by providing a mix of specialized aircraft for a given level of operational requirements, an a priori case is considered made for the procurement of the utility aircraft.
A General Dynamic Model for Air Defense
Authors: Brodheim Eric , Herzer Ivo , Russ Laurence M.
Published: November 2008

A general model of air defense/offense interaction is developed on the basis of a dynamic program. Each particular air defense mission against aircraft, tactical ballistic missiles, or ICBM's is treated as a special case of the general functional equation. Several types of measures of effectiveness are generated, either as expectations or as probability distributions, and examples of each type are given. Particular applications of the model to problems of tradeoff, optimal strategies against defense control centers, and cost-effectiveness are discussed.
Note on “The Sequential Maximization Technique”
Authors: Danskin John M.
Published: November 2008

This note presents a generalization of the main theorem of the sequential maximization technique given in Fiacco and McCormick's paper just preceding this note.
Geometric Distribution in Some Two-Dimensional Queuing Systems
Authors: Evans Richard V.
Published: November 2008

The state of the system is a two dimensional random variable N = (N1, N2) with N1 ≧ 0, 1 ≦ N2 ≦ m. Transitions require negative exponential times. The vector Pn of probabilities of being in states for which N1 = n satisfy the general condition λIPn−1 + BPn + CPn+1 = 0. Two arguments are given showing Pn = RPn−1 and an iterative scheme for finding R is constructed.
Existence of a Stationary Control for a Markov Chain Maximizing the Average Reward
Authors: Martin-Löf Anders
Published: November 2008

The problem of optimal control of a discrete time stationary Markov chain with complete state information has been considered by many authors. The case with finitely many states and controls has been thoroughly investigated. Chains with infinitely many states or controls have also been considered with various assumptions concerning the reward function. In this paper the existence of a control maximizing the average reward is established for Markov chains with a finite number of states and an arbitrary compact set of possible actions in each state. It is assumed that there is only one ergodic class and no transient states in the chain for every control. The method of proof uses methods from convex programming, and is analogous to the linear programming approach used by Wolfe and Danzig.
Letter to the Editor—A Note on Some Classical Methods in Constrained Optimization and Positively Bounded Jacobians
Authors: Kortanek K. , Jeroslow R.
Published: November 2008

Using a variation of the classical Implicit Function Theorem and the Chain Rule, Cottle in “Nonlinear Programs with Positively Bounded Jacobians,” SIAM 14, 147–158 (1966) considers the problem [Formula: see text] where W is a continuously differentiable vector function defined on N-space, and proves that if W has a positively bounded Jacobian, then (I) has a solution z̄ satisfying z̄TW(z̄) = 0, when the problem is nondegenerate. The authors here point out by geometric interpretations and examples that: (1) there exist nondegenerate problems having optimal solutions that have no equivalent positively bounded representations, (2) degeneracy may be a common occurrence for problems of this form, and (3) the class of problems of the above form has yet to be studied for the general case where the infimum is finite, not necessarily assumed, and not necessarily zero.
Letter to the Editor—The Use of Branching in Dynamic Programming for Parametric Analysis
Authors: Greenberg Harvey J.
Published: November 2008

After solving a dynamic program, it is supposed that the analyst wishes to study stage characteristics (such as the return function) to note its effects on the total optimal return. This paper presents a methodology that consumes less computer time than the present approach.
Letter to the Editor—Choosing Among Investment Possibilities with Stochastic Pay-Off Minus Expenditure
Authors: Seppälä Yrjö
Published: November 2008

A multiperiod investment problem with stochastic pay-off minus expenditure is described. This problem can be solved by the method for solving discrete optimization problems of Lawler and Bell.
Algorithms for Optimal Production Scheduling and Employment Smoothing
Authors: Lippman Steven A. , Rolfe Alan J. , Wagner Harvey M. , Yuan John S. C.
Published: November 2008

This paper seeks here a minimum cost production plan over a finite number of time periods. There is a known demand requirement (stated in production hours) to be met in each period from current and previous hours of production (stored as inventory). A production policy consists of scheduled amounts of hours, some of which are costed at regular-time wage rates, the remainder costed at overtime rates. Expansion or contraction of the work force (stated in production hours) is charged against the period-to-period variations in regular-time employment. The fluctuations in overtime production do not incur such hiring and firing costs. The amount of overtime used, however, is constrained not to exceed a specified fraction of regular-time utilized in any period. We describe algorithms for rinding an optimal policy under the assumption that all costs are described by linear functions and where demands are either monotonic increasing or decreasing in time. In addition to presenting the algorithms, we also examine certain planning horizon results implied by these algorithms. Specifically, we ascertain when optimal first period decisions can be made without knowing the precise values of all future demands and costs.
Mathematical Models in Marketing
Authors: Gupta Shiv K. , Krishnan K. S.
Published: November 2008

For a marketing situation, mathematical models are developed expressing the relation between net revenue and the variables that affect it. These models are extensions of the ones discussed by Mills, and Krishnan and Gupta. Mills assumed that each competitor has only one controllable variable, viz., promotional effort. Krishnan and Gupta obtained equilibrium solutions for two competitors, each having two controllable variables. This paper deals with multicompetitors and discusses four models when the market potential is independent of both price and promotional effort and when it is dependent on either or both of the controllable variables.
On the Distribution of Stock Price Differences
Authors: Mandelbrot Benoit , Taylor Howard M.
Published: November 2008

Price changes over a fixed number of transactions may have a Gaussian distribution. Price changes over a fixed time period may follow a stable Paretian distribution, whose variance is infinite. Since the number of transactions in any time period is random, the above statements are not necessarily in disagreement. A possible explanation is proposed by Taylob, and then shown by Mandelbrot to be intimately related to an earlier discussion of the specialists' function of ensuring the continuity of the market.
A Decomposable Nonlinear Programming Approach
Authors: Zangwill Willard I.
Published: November 2008

Nonlinear, i.e., pseudo-concave, programming algorithms attempt to maximize an objective function f(x) subject to x in a feasible set. Large step algorithms seek this maximum by recursively generating both a sequence of points {xk} and a sequence of directions {sk}. Given a point xk and a direction sk the next point xk+1 is the feasible point that gives the largest value to the objective function along the ray emanating from xk in the direction sk. The key difference among large step procedures is in the choice of sk. This paper explores several means for selecting the direction sk. Some of these methods are particularly suited for large scale systems with a large number of constraints, as they decompose the problem and require the solution of only a finite number of subproblems. These algorithms have an interesting interpretation in terms of management by exception. They also lead naturally into a discussion of jamming or zigzagging; that phenomenon which plagues all large step methods and can lead to non-convergence. Jamming is studied for its cause and curve via an example and counter-example. For linear constraints a special large step method which proceeds by suboptimization in manifolds is proposed that avoids jamming. It is then shown that the Dantzig quadratic programming algorithm is a special case of this method. A straightforward geometric proof of the Dantzig method is then possible.
The Use of Uncertainty in a Simultaneous Search
Authors: Converse A. O.
Published: November 2008

Shannon's measure of uncertainty (entropy) is used to plan a simultaneous search for the extreme of a unimodal function of one variable. A general expression is developed to express the expected uncertainty about the location of the extreme of the function after the N-point function has been evaluated at H points. The optimum locations of these H evaluations are then found by choosing them so as to minimize the expected uncertainty. The method requires that the user assign values to the probability that the extremum lies at each of the N locations. In so doing it enables him to develop a search policy that reflects his prior partial knowledge about the location of the extremum. It is shown that the entropy policy is identical to the min-max policy for the special case of equal initial probabilities.
An Analytical Technique for Urban Casualty Estimation from Multiple Nuclear Weapons
Authors: Hunter Jeffrey J.
Published: November 2008

A model has been developed that estimates the total number of direct effects casualties due to a multiple weapon attack on a city whose population has a circular normal distribution. The only specifications required are the coordinates of the ground zeros in relation to the center of population, the population parameters, the weapon parameters, and the aiming error for each weapon. Further generalizations involving extension of the model to consider elliptical normal population distributions, elliptical normal aiming error distributions, and modified casualty functions are also discussed.
Queuing Systems with Enforced Idle Time
Authors: Powell B. A. , Avi-Itzhak B.
Published: November 2008

Enforced idle time occurs in any queuing system in which it is possible for the server to be idle and the queue length to be nonzero simultaneously. This paper examines queuing systems in which the server is constrained to start service only at fixed intervals of time, with arrivals of customers and service completions occurring continuously. The GI/M/N, GI/D/N, M/D/N, and GI/G/1 queuing systems with enforced idle time are studied and some closed form steady-state results are presented. An application to railroad car pool systems is suggested.
Letter to the Editor—Allocation of Launch Vehicles to Space Missions: A Fixed-Cost Transportation Problem
Authors: Stroup John William
Published: November 2008

The problem of assigning launch vehicles to space missions can be formulated as the fixed cost transportation problem treated by Croes and Healy in which there are unlimited supplies and fixed costs incurred for positive flow from the sources. The branch-and-bound technique of Little, et al., is used to obtain minimum cost solutions. The application to the space transportation problem is discussed and an example is worked out.
Acknowledgment
Authors: Gordon William J. , Newell Gordon F.
Published: November 2008

The authors would like to point out that the formula for the joint equilibrium probability distribution in their paper “Closed Queuing Systems with Exponential Servers,” Opns. Res. 15 254–265 (1967), may be obtained by specializing the parameters of the more general model studied by J. R. Jackson in “ Jobshop-Like Queuing Systems,” Management Sci. 10 131–142 (1963).
An Experimental Comparison of Techniques for the Assignment of Facilities to Locations
Authors: Nugent Christopher E. , Vollmann Thomas E. , Ruml John
Published: November 2008

The optimal assignment of facilities to locations is a combinatorial problem that remains unsolved. None of the several optimal-producing procedures is computationally feasible for any but small problems. Three previously proposed heuristic techniques (craft, one by Hillier, one by Hillier and Connors) and one new one (Biased Sampling) are examined and experimentally compared for problems of from five departments to 30 departments. The new Biased Sampling procedure is seen to produce the best solutions but at relatively high computational cost. The Hillier-Connors procedure is especially interesting because it is considerably faster than craft and Biased Sampling and its solutions are only 2–6 per cent worse than Biased Sampling and only slightly worse than craft.
Reliability Applications of a Bivariate Exponential Distribution
Authors: Harris Robert
Published: November 2008

This paper examines some two-unit systems in which the lifetimes of the two units in service are not independent but depend upon one another in a particular way. This dependence is characterized by the bivariate exponential distribution of Marshall and Olkin, which has exponential marginal distributions and other physically motivating properties. Two measures of reliability are determined: the first is the distribution and mean of the time to system failure (i.e., when all units are failed) and the second gives steady-state probabilities of the number of working units. Some graphical results are given to illustrate the deviation of these quantities from the values obtained under the classical assumption of independent lifetimes.
Letter to the Editor—An Extension of the Algorithm of Driebeek for Solving Mixed Integer Programming Problems
Authors: Rebelein Paul R.
Published: November 2008

A modification of the branch-and-bound algorithm due to Norman Driebeek for the solution of mixed integer programming problems is discussed. This modification increases the over-all efficiency of the algorithm. In addition, the modified algorithm is capable of solving, without reformulation, the more general problem in which i the allowable values for the restricted variables are not integers or are not evenly spaced. The algorithm has been coded in FORTRAN and tested on a Honeywell H-1800 computer.
Letter to the Editor—Remarks on “Linear Programming Under Uncertainty”
Authors: Williams A. C. , Avriel M.
Published: November 2008

In a recent article in this Journal, R. Wilson developed duality relations and certainty equivalent formulas for a linear programming problem with normally distributed random demands. The purpose of the present letter is to establish such relations and formulas for quite general continuous probability distributions. In addition, our analysis reveals more clearly the role of the means and variances as they affect the certainty equivalents.
Letter to the Editor—A Note on Radial Distributions
Authors: McNolty Frank
Published: November 2008

The paper considers some distribution functions associated with two-dimensional kill probability, target evacuation, and distribution of populations. A general radial distribution is postulated and from it the probability density functions for the random phase angle and the x, y components are derived. The generalized radial distribution is then specialized to several useful functions that occur in kill probability problems and the corresponding special cases for the phase and component distributions are obtained. The results include a broad range of situations extending from uniform phase, Gaussian components and Rayleigh distance to generalized nonuniform phase and non-Gaussian component distributions where the latter functions are of particular interest.
Erratum
Authors: Kumar Santosh
Published: November 2008

Corrections to the author's paper “The Routing Problem with ‘k’ Specified Nodes” Opns. Res. 14: 909–913 (1966).
On the Capacity of Tandem Server, Finite Queue, Service Systems
Authors: Hildebrand David K.
Published: November 2008

A queuing model incorporating major features of ‘assembly-line’ systems is developed. Some simple algebraic consequences of the structural properties of the model are set forth. The intuitive construction of the capacity of the system is given, and the capacity is calculated for some relatively simple exponential-service cases. A general method for exponential-service is outlined, and completed in some simple cases.
An Additional Special Channel, Limited Space Queuing Problem with Service in Batches of Variable Size
Authors: Murari K.
Published: November 2008

This paper studies the transient behavior of a first-come-first-served queuing problem with service in batches of variable size, Poisson input, and exponential service time distribution. Further, when the queue length increases to N, a fixed pre-assigned positive number, a special service channel capable of serving a group of N units and possessing exponential service time distribution is made available and is canceled at the termination of service if the queue length becomes less than N. Also a limited waiting space K is assumed for the waiting line. The Laplace transforms of various probability generating functions are obtained and the corresponding results for the steady state are derived. Finally, some particular cases are discussed.
The Pareto Distribution as a Queue Service Discipline
Authors: Harris Carl M.
Published: November 2008

A queuing system is described in which service times are conditioned upon a random parameter μ, such that the conditional service distribution is exponential and μ has a gamma density. It is shown that the resultant unconditional distribution of service times is Paretian. Several measures of effectiveness are discussed and the question of statistical estimation of service parameters is also explored.
Minimum Change-Over Scheduling of Several Products on One Machine
Authors: Glassey C. R.
Published: November 2008

Given a finite horizon delivery schedule for n products we wish to schedule production on a single machine to meet deliveries and minimize the number of change-overs of the machine from one product to another. A state space is defined and in it a network is constructed such that the shortest distance through the network corresponds to the minimum number of production change-overs. Certain properties of the optimal path are deduced from the dynamic programming formulation of the shortest route problem, and these properties are utilized in the construction of an algorithm that finds the optimal path. A numerical example illustrates the method.
Optimal Operating Policies for M/G/1 Queuing Systems
Authors: Heyman Daniel P.
Published: November 2008

We consider the economic behavior of a M/G/1 queuing system operating with the following cost structure: a server start-up cost, a server shut-down cost, a cost per unit time when the server is turned on, and a holding cost per unit time spent in the system for each customer. We prove that for the single server queue there is a stationary optimal policy of the form: Turn the server on when n customers are present, and turn it off when the system is empty. For the undiscounted, infinite horizon problem, an exact expression for the cost rate as a function of n and a closed form expression for the optimal value of n are derived. When future costs are discounted, we obtain an equation for the expected discounted cost as a function of n and the interest rate, and prove that for small interest rates the optimal discounted policy is approximately the optimal undiscounted policy. We conclude by establishing the recursion relation to find the optimal (nonstationary) policy for finite horizon problems.
Nonpreemptive Priority Queue with Binomial Input
Authors: Rajeswari A. R.
Published: November 2008

In our queue model of nonpreemptive priority discipline, we assume that arrivals occur at discrete time points, follow binomial distribution, and have a discrete time service distribution. In the limit, it is shown that all the parameters of the resulting queue, with the above arrival and service pattern, agree with those derived already by various authors, except for different notations used for service and arrival rates. At the end of this paper, this discipline is compared with that of the “first-come-first-served” discipline and the effect of priorities on average waiting time is obtained.
Letter to the Editor—Computing Two-Commodity Flows
Authors: Rothschild B. , Whinston A. , Kent J.
Published: November 2008

In Opns. Res. 14, 377–387 (1966) a max-flow min-cut theorem for two-commodity flows in Euler networks with integer capacities is proved. In this paper we describe an algorithm for constructing maximal two-commodity integer flows based on the proof in the reference cited, and we give computation times for some examples on a Burroughs B-5000 computer.
Interception Strategy Based on Intermittent Information
Authors: Lindsey George R.
Published: November 2008

A penetrator, p, attempts to cross a linear barrier patrolled by a searcher, S. S receives intermittent reports of P's position, P1, P2, …, but P knows only that S is somewhere on the barrier. After receiving report P1, a time τ can elapse before the next report P2 may reveal that S may be unable to intercept P even if he received continuous information thereafter. S attempts to select a position S (P1) that maximizes τ, while P attempts to choose a course α that minimizes τ. If the searcher is faster than the penetrator (speed ratio λ > 1), values of α and S(P1) that produce maximin τ are deduced. However, maximin τ < minimax τ, and P is obliged to use a mixed strategy in order to obtain the maximin. If the barrier is finite, contours of constant maximin τ are segments of conic sections. If λ < 1, S should modify the maximin τ strategy when P is close to the barrier. An indication is given of the frequency with which reports are needed as P approaches the barrier.
Queues with Feedback for Time-Sharing Computer System Analysis
Authors: Chang Wei
Published: November 2008

A time-sharing computer system brings the man with a problem much closer to the computer power he needs. The priority processing problems associated with time-sharing computer system are described. A mathematical model was developed based on queues with feedback. The queue size and its variability within the computer can be determined with the enclosed formulation. Other important system design parameters such as the system response time, etc., can also be obtained. The mathematical model complements standard simulation techniques for time-sharing computer analysis. Although the problems discussed in this paper arose in the computer systems, the queuing model developed is quite general and may be useful for other industrial applications.
Dynamic Programming with Linear Uncertainty
Authors: Greenberg H. J.
Published: November 2008

If a dynamic program has uncertainties of linear form in the constraint or objective function, a problem may be formulated to take this into account. This new problem, under certain assumptions, will be solvable by dynamic programming with a larger state space.
Letter to the Editor—On Suboptimization: An Example
Authors: Danskin John M.
Published: November 2008

This note proves that the “Principle of Suboptimization” cannot be applied to Max-Min problems when Max-Min < Min-Max.
Letter to the Editor—-A Closed Form Solution of Certain Programming Problems
Authors: Pincus Martin
Published: November 2008

A formula is given for the coordinates of the point that maximizes a given function F(x1, …, xn) over the closure of a bounded domain S in n-dimensional Euclidean space. The principal assumption made in deriving the formula is that F attains a global maximum at exactly one point of S. In certain cases the formula may be used to discuss the maximization problem as a function of the parameters involved. Some simple examples are given.
A Lagrangian Application to Production Models
Authors: Eppen Gary D. , Gould F. J.
Published: November 2008

This paper presents algorithms for finding solutions and planning horizons to two related T period, one product, deterministic production problems with capacity constraints and penalty costs for unsatisfied demand. The algorithms are derived from an application of Lagrangian techniques to problems with inequality constraints.
Asymptotic Lagrange Regularity for Pseudoconcave Programming with Weak Constraint Qualification
Authors: Kortanek K. O. , Evans J. P.
Published: November 2008

In a previous paper we obtained characterizations of constraint sets determined by a finite number of differentiate pseudoconcave constraint functions possessing an interior point, and showed that they are convex Lagrange regular. In this paper we introduce a weaker type of constraint qualification and obtain asymptotic Lagrange regularity conditions from the constructs of semi-infinite programming. We impose the constraint qualification that each constraint function possess an interior point, possibly different for different constraint functions. Computationally speaking, it is relatively easy to verify since each constraint function is examined individually for interior points in consistent problems. Artificial vectors are adjoined to the dual problem and within the constructs of this problem involving no new data, convergence is assured asymptotically to Lagrangian type conditions. In this case the dual objective value tends to the optimal primal value in the limit. In case the constraint functions are differentiable concave, then asymptotic Lagrange regularity is obtained without any constraint qualification whatever.