bluuebunny/crossref_metadata_2025 huggingface dataset:
A Study of the Logical Basis of Combat Simulation
Authors: Koopman Bernard O.
Published: November 2008

The object of this study is the analytic or computer-simulation model, used increasingly in analyses of combat, tactical and weapon-systems evaluation, etc. The thesis is that whenever the method yields quantitative results, it achieves these by setting the computer (or the analytic formulation) in states supposed to correspond to those in the combat, and programming a rule of transitions from state to state—picturing what is occurring in the combat. The transition rule may be deterministic or probabilistic, the latter usually by Monte Carlo selection; but the probabilities are always treated as known. This shows that the combat is assumed (explicitly or implicitly) to act as a stochastic process of the changes of state of a system. The computational procedure used implies further assumptions, which imply, in turn, that it is Markovian (directly, or after a transformation). After bringing out these facts, the necessary conditions for their validity are explored. One is the removal, by conventionalization, of the otherwise statistically indeterminate human decisions. Then the use of the full strength of the stochastic assumptions by more powerful mathematics than the conventional simulations is examined. The generalities are exemplified by endgames and a detection-destruction duel, studied in detail.
A Simple Model of Search for a Moving Target
Authors: Pollock Stephen M.
Published: November 2008

A target moves between two regions in a Markovian fashion, the parameters of which are known to the searcher. Discrete amounts of search effort (“looks”) may be allocated to one region at a time. This paper gives equations that characterize (a) the minimum expected number of looks to detect the target, and (b) the maximum probability of detecting the target within a given number of looks. These are solved completely for special cases, and numerical approximate solutions are described for general cases.
Surrogate Mathematical Programming
Authors: Greenberg Harvey J. , Pierskalla William P.
Published: November 2008

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach.
On the Unlimited Number of Faces in Integer Hulls of Linear Programs with a Single Constraint
Authors: Rubin David S.
Published: November 2008

The convex hull of the feasible integer points to a given integer program is a convex polytope I. The feasible set obtained by relaxing the integrality requirements is another convex polytope L. Cutting-plane algorithms essentially try to remove part of L − I. Hence the more complicated the relationship between L and I, the more difficult (in some sense) the integer program. This paper shows one such complexity: specifically, we construct a series of programs such that I has arbitrarily many faces even though L is a triangle. We also indicate the existence of a large class of problems that exhibit the same behavior.
The Value of Information and Stochastic Programming
Authors: Avriel M. , Williams A. C.
Published: November 2008

The problem of planning under uncertainty has many aspects; in this paper we consider the aspect that has to do with evaluating the state of information. We address ourselves to the question of how much better (i.e., how much more profitable) we could expect our plans to be if somehow we could know at planning time what the outcomes of the uncertain events will turn out to be. This expected increase in profitability is the “expected value of perfect information” and represents an upper bound to the amount of money that it would be worthwhile to spend in any survey or other investigation designed to provide that information beforehand. In many cases, the amount of calculation to compute an exact value is prohibitive. However, we derive bounds (estimates) for the value. Moreover, in the case of operations planning by linear or convex programming, we show how to evaluate these bounds as part of a post-optimal analysis.
An Evaluation of Blood-Inventory Policies: A Markov Chain Application
Authors: Pegels C. Carl , Jelmert Andrew E.
Published: November 2008

A theoretical model using mainly the theory of absorbing Markov chains is applied to several human-blood-issuing policies. The objective of the model applications is to determine the effects of the issuing policies on average inventory levels, which determine blood shortage probabilities, and on the average age of blood at the time it is transfused. Issuing policies that issue (transfuse) fresher blood with a higher probability than older blood are defined as modified fifo policies, and issuing policies that issue older blood with a higher probability than fresher blood are defined as modified fifo policies. Application of the theoretical model to the various issuing policies allows complete evaluation of the policies, and a policy choice can be made on the basis of the evaluation.
Social and Rehabilitation Services: A Challenge to Operations Research
Authors: Spindler Arthur
Published: November 2008

This paper examines the characteristics of our social and rehabilitation programs, and discusses some of the more pronounced factors affecting their susceptibility to quantification, measurement, and analysis. As an illustration of the potential role of OR, it describes the child-welfare-services program, a small but influential one having many of the attributes and characteristics prototypal of the social and rehabilitation field. The paper describes the program comprehensively: its legal authority, objectives, funding arrangements, state-plan requirements, Federal and state organizations, private service agencies, staffing of state agencies, juvenile facilities, the nature of child and family services, the characteristics of the clientele, unmet program needs, information requirements, evaluative research efforts and unresolved program questions for OR study. Finally, the paper discusses the analytical methods and problems in model building, program data collection, and costs-and-benefits analysis. The challenge to the operations-research profession is to contribute effectively to solving problems in this field, and, to this end, to succeed in convincing policy officials and administrators of the social- and rehabilitation-service programs that OR has the capability and desire to participate meaningfully in this sphere of American life.
A Theorem on Symmetric Traveling Salesman Problems
Authors: Steckhan Helmut
Published: November 2008

This paper shows how to eliminate arcs from a complete directed finite graph so that a maximum number of hamiltonian circuits is destroyed while their reverses are preserved. For all complete directed finite graphs containing more than two nodes, this effect is achieved by eliminating just three arcs that form an elementary circuit. This result can be used in calculating branch-and-bound solutions for symmetric traveling salesman problems.
Optimal Design of Offshore Natural-Gas Pipeline Systems
Authors: Rothfarb B. , Frank H. , Rosenbaum D. M. , Steiglitz K. , Kleitman D. J.
Published: November 2008

The exploitation of offshore natural gas reserves involves several phases, including production from reservoirs, separation of byproducts, and transportation to markets. The gas, which may originate as far as 100 miles from land, must be transported through pipelines to onshore delivery points. This paper develops techniques for solving the following problems: (1) selection of pipe diameters in a specified pipeline network to minimize the sum of investment and operation costs; (2) selection of minimum-cost network structures, given gas-field location and flow requirements; (3) optimal expansion of existing pipeline networks to include newly discovered gas fields. The techniques incorporate procedures for globally optimizing pipeline diameters for fixed tree structures and heuristic procedures for generating low-cost structures.
Technical Note—A Flexible Tree-Search Method for Integer Programming Problems
Authors: Tuan Nghiem Ph.
Published: November 2008

This paper presents an enumerative method for solving integer programming problems. In the enumerative methods so far available, the variables are ranked in a rigid order by the choices in the forward steps, and backtracking always takes place on the last variable in this order. The proposed method allows a greater flexibility in the backtracking step that makes it possible to devise suitable rules of choice to improve the efficiency of the searching process. A numerical example is devised to illustrate the enumerative method in the direct-search case.
Characterization and Computation of Optimal Policies for Operating an M/G/1 Queuing System with Removable Server
Authors: Bell Colin E.
Published: November 2008

This paper studies the optimal operation of an M/G/1 queuing system with removable server and the following cost structure: a holding cost per customer in the system per unit time, a cost per unit time of keeping the server running, and fixed charges for turning the server on or off. The server can be turned on at arrival epochs or off at service-completion epochs. The paper characterizes an optimal policy for the infinite-horizon discounted problem, offers an optimality proof, and presents a computational algorithm.
The Remaining Busy Period of a Finite Queue
Authors: Harris Terrell J.
Published: November 2008

In the M/G/1/N queuing system where no more than N < ∞ customers are allowed in the system, define the remaining busy period from state i = 0, 1, …, N as the time spent in transition from state i to state 0, i.e., until the server becomes idle for the first time. The purpose of this paper is to derive the Laplace-Stieltjes transform of the distribution of this time and the generating function of the number of customers served in this time.
Technical Note—On the Asymptotic Convergence Rate of Cost Differences for Markovian Decision Processes
Authors: Morton Thomas E.
Published: November 2008

The modified method of successive approximations for solving Markovian decision problems as formulated by White, Schweitzer, MacQueen, and Odoni, concentrates attention on cost differences either between successive stages in the same state, or relative to a base state in the same stage, rather than on the total cost function. The former bound the (discounted) gain of the optimal policy, while the latter relative-cost function determines the policy to be chosen at each stage. While these authors have demonstrated that these modified constructs converge to the gain and the optimal relative-cost function under rather general circumstances (undiscounted, single-chain, aperiodic processes), little is known about the rates of convergence. [Note that convergence of the relative-cost function guarantees optimality of a currently repeating policy, as noted by Howard.) A great deal of insight into this mathematically difficult question may be gained by working out the actual asymptotic convergence rates of these constructs for the special case of a single fixed policy. This is an easy exercise via Howward's methods, but very suggestive, since the policy will be asymptotically constant for a well-behaved problem. (In particular, if there is a unique optimal policy it will eventually repeat.) Convergence for both constructs for the fixed-policy case is very powerful even for discount rates greater than 1.0, depending principally on the dominant eigenvalue of the transition matrix. This note discusses the intuitive implications of this fact for the relative efficiencies of modified value iteration, policy iteration, policy iteration via successive approximations, or possible hybrids.
A Class of Fractional Programming Problems
Authors: Almogy Y. , Levin O.
Published: November 2008

The paper deals with problems of maximizing a sum of linear or concave-convex fractional functions on closed and bounded polyhedral sets. It shows that, under certain assumptions, problems of this type can be transformed into equivalent ones of maximizing multiparameter linear or concave functions subject to additional feasibility constraints. The problems are transformed into those finding roots of monotone-decreasing convex functions. Where the objective function is separable, such a root is unique, and any local optimum is a global one, i.e., the objective function is quasi-concave. In problems involving separable linear fractional functions, under some additional assumptions, the parametric presentation results in a combinational property. Where the number of terms in the objective function is equal or less than three, this property leads to an efficient algorithm.
Vector-Valued Criteria in Geometric Programming
Authors: Pascual Luis D. , Ben-Israel Adi
Published: November 2008

This paper derives, as optimal solutions of ordinary geometric programs, efficient and properly efficient solutions of geometric programming problems with vector-valued criteria.
Pathology of Traveling-Salesman Subtour-Elimination Algorithms
Authors: Bellmore Mandell , Malone John C.
Published: November 2008

The traveling-salesman problem has been the target of a substantial number of computational algorithms over the last two decades. Reported computational experience with these algorithms varies widely; authors, however, have generally failed to explain this variation adequately, or to offer predictive theories for their approaches. This paper (a) develops an underlying theory for the problem, (b) predicts pathological performance of some existing techniques, and (c) presents two algorithms, based upon the theory, with predictable polynomial growth in expected computation time and resistence to pathological problems.
An Analysis of the M/G/1 Queue Under Round-Robin Scheduling
Authors: Sakata M. , Noguchi S. , Oizumi J.
Published: November 2008

In order to discuss scheduling algorithms for time-sharing computer systems, this paper analyzes the M/G/1 queue under the well known round-robin (RR) discipline. Three models are considered: the constant-quantum RR model, the processor-shared (or zero-quantum RR) model, and the variable-quantum RR model. The paper proposes an effective calculating method for obtaining the expected response time under an arbitrary processing-time distribution with overhead. By the theoretical analysis, one can show how the response time is affected by the scheduling and processing-time distributions, as is demonstrated by some typical examples.
On the Growth of the Maximum Queue Length in a Stable Queue
Authors: Heyde C. C.
Published: November 2008

Even for a stable one-server queue with relative traffic intensity less than unity, the maximum queue length observed will tend to infinity in probability as the length of time for which the system has been observed becomes large. It is important to have information on the behavior of the maximum queue length to enable estimation of the congestion likely to be encountered in a system operating over a long period. The present paper studies the stable GI/M/1 system, and, interpreting the results obtained rather loosely, one can say that the maximum queue length attained by the time the nth customer has arrived (n large) can be expected to be of the order of log n.
Priority Queues with Random Order of Service
Authors: Durr L.
Published: November 2008

Calls of two priorities arrive at a single server in accordance with a Poisson process. The calls are served in order of priority and for each priority in a random manner. This paper considers cases of preemptive-resume and nonpreemptive priorities, and derives the moments of the stationary distribution of the waiting time for each priority class. The variance of the waiting time, when the order of service is random, is shown to be greater than the corresponding variance when the order of service is first-in, first-out, and smaller than the corresponding variance when the order of service is last-in, first-out.
On a Two-Unit Standby Redundant System with Standby Failure
Authors: Osaki Shunji , Nakagawa Toshio
Published: November 2008

This paper derives the mean time and the Laplace-Stieltjes transform of the distribution of the first time to system-down for a two-unit standby redundant system when failure of the unit in standby is allowed. Further, it shows that special cases of the results obtained here coincide with earlier results for the two-unit standby redundant system and the two-unit parallel redundant system. Finally, it discusses numerical examples and some interesting models.
Computing the Expected End-Product Service Time Using Stochastic Item Delays
Authors: Rose Marshall
Published: November 2008

This paper derives an expression for the expected completion time of a repair project, such as the servicing of end products, when the servicing is composed of a sequence of repair activities on parts of the end product. These parts are subject to repair with a specified probability and, at first, it is assumed that the completion time of each activity is constant. Subsequently, this assumption is relaxed so that an arbitrary probability distribution can be specified for the activity completion times. The concluding parts of the paper show how to compute the expected end-product service time for a particular class of activity-time probability distributions.
Technical Note—Operations Research on Football
Authors: Carter Virgil , Machol Robert E.
Published: November 2008

Based on a census of 8,373 plays from the first 56 games of the 1969 schedule of the National Football League, this note calculates, for various field positions, the expected point values of possession of the football with first down and ten yards to go, and discusses the strategic implications of these values.
An Evaluator for the Number of Operationally Ready Aircraft in a Multilevel Supply System
Authors: Sherbrooke Craig C.
Published: November 2008

This paper develops an analytic model that evaluates the expected number of aircraft not operationally ready at a random point in time because of supply (NORS). The model was developed for application to the F-111 aircraft for a multilevel problem, where demand on a first-level line replaceable unit (LRU) eventually causes second-level demands for one or more modules that are components of the LRU. The model is for a single base. Since it is evaluative in nature, the inputs include item stock levels as well as item demand rates, average repair times, and resupply times. An optimization model to determine stock levels that minimize the number of NORS aircraft subject to a budget constraint would be preferable to the evaluation model. The paper shows, however, that an optimization model is not mathematically tractable because the criterion function is not separable into independent item calculations. But an example using F-111 data indicates that if the METRIC model [see Opns. Res. 16, 122–141 (1968)] is used to optimize stock levels, the resulting number of aircraft NORS is within 1 percent of the minimum number of aircraft achievable with the same budget. Finally, the well-known formula of Erlang for the M/G/s service system with no queue allowed is generalized to the case where demand rates and repair rates may be a function of the number of units already in repair. This enables us to examine the sensitivity of the optimal allocation of budget across a group of items when expediting may take place. Though expediting improves system performance, the conclusion is that the optimal allocation is virtually the same as the METRIC allocation.
A Computational Procedure for a Class of Coverage Problems for Multiple Shots
Authors: Breaux Harold J. , Mohler Lynn S.
Published: November 2008

This paper considers certain computational difficulties associated with a class of coverage problems for multiple shots, including the situation where N rounds of a salvo are delivered onto a diffused target, where the single-round damage function, the distribution of impacts about the aim point, and the distribution of aim point about the target center are elliptical normal. The computational procedure employs Jacobi polynomials and results in better convergence properties of the resulting series than for series heretofore employed.
Approximation Procedures and Some Key Results for Estimating Expected Target Damage
Authors: Grubbs Frank E. , Breaux Harold J. , Coon Helen J.
Published: November 2008

This paper summarizes some suggested computational procedures for, and further progress on, estimating expected target damage for individual rounds, and for battery or battalion volley-type fire. In particular, it recommends the computational procedures that are best followed for suitably accurate estimation of target damage. Some other useful results relating to the target-damage analysis problem, and possibly to other applied studies, are also recorded.
Optimal Sequential Aim Corrections for Attacking a Stationary Point Target
Authors: Nadler Jack , Eilbott Joan
Published: November 2008

A battery of weapons is directed one at a time at a stationary point target. The impact points of each weapon have a common circular normal distribution centered an unknown distance from the target; however, the centering of this distribution can be altered by a known amount between one shot and the next, if desired. We derive the optimal corrections among all unbiasing corrections that are linear functions of earlier impact-point components, and give the corresponding maximum probability of target destruction for any number of weapons for two target destruction functions. Also, we determine how large the offset need be in order that the optimal scheme be less costly than a strategy that makes no adjustment to aim. Three other schemes that do adjust aim are compared to the optimal one for various battery sizes.
Technical Note—A Note on the Solution to Lanchester-Type Equations with Variable Coefficients
Authors: Taylor James G.
Published: November 2008

This note shows how to obtain a solution to Lanchester-type equations for combat between two homogeneous forces when the attrition rates are variable, provided that their quotient is a constant. Solutions are developed for either time or force separation as the independent variable.
On One-For-One-Ordering Inventory Policies with State-Dependent Leadtimes
Authors: Gross Donald , Harris Carl M.
Published: November 2008

This paper describes several one-for-one-ordering [continuous-review (s, S) policies, where s = S − 1] inventory models in which the time required for order replenishment, or leadtime, depends on the number of orders outstanding. Demand is assumed to be a Poisson random variable with a constant mean λ, and leadtime is assumed to be state dependent in either one of two ways: (1) the portion of the leadtime that corresponds to the actual filling of orders (i.e., the service time) is an exponentially-distributed random variable with distribution function BTm(t) = 1 − e−μ(m)t, where m is the number of outstanding orders just after the previous order has been filled (viz., an imbedded-Markov-chain approach); and (2) the instantaneous probability at an arbitrary point in time of an order being filled (i.e., a service completed) in an infinitesimal interval of time Δt is μ(n)Δt + 0(Δt), where n is the number of outstanding orders (viz., a birth-death approach). Several models are investigated for each type. The orders placed are assumed to go into a single-server queue, and queuing theory results are used to obtain the expected inventory costs as a function of S in order to obtain an optimal value of S. Some of the models are expanded to include costs dependent on a service-rate parameter and are then optimized with respect to both S and the service-rate parameter.
Stationary Properties of a Two-Echelon Inventory Model for Low Demand Items
Authors: Simon R. M.
Published: November 2008

This paper considers a two-echelon inventory model for consumable or repairable parts in which the first-echelon facilities use one-for-one replenishment policies and the second-echelon facility uses a continuous-review (s, S) policy. Repair may be accomplished at all facilities. Repair and transportation times are assumed to be deterministic, and the failure processes that generate demands are assumed to be Poisson. The paper derives exact expressions for the stationary distributions of stock on hand, stock in repair, and backlogged demand at each facility, and indicates how these expressions may be utilized for optimization purposes.
Cost Minimization in Networks with Discrete Stochastic Requirements
Authors: Connors Michael M. , Zangwill Willard I.
Published: November 2008

Multistage minimum-cost network-flow analysis solves many practical problems in production-inventory-distribution, marketing, personnel, and finance. Unlike previous network papers, which generally restricted themselves to a deterministic situation, this paper investigates the stochastic environment. Starting from the standard multistage network-flow problem, we create a stochastic network by permitting the node requirements to be discrete random variables with known conditional probability distributions. Our goal is to determine the minimum-expected-cost flow and thereby solve the problem. Although linear programming under uncertainty can determine this flow, it would ignore the special structure of network-flow problems that allows development of computationally efficient algorithms. In this paper, we instead exploit the underlying network structure to produce both a new structure that is not a network but maintains many of the properties of a network, and a new node that replicates flows instead of conserving them. The new nodes, called replication nodes, together with the new structure, allow the development of an efficient computational algorithm that is capable of solving problems much larger than those solvable by linear programming under uncertainty.
Optimal Advertising-Expenditure Implications of a Simultaneous-Equation Regression Analysis
Authors: Parsons Leonard J. , Bass Frank M.
Published: November 2008

This paper builds upon an empirical study of advertising and sales relations by developing a simultaneous-equation regression model, testing it against aggregative time-series data, and exploring the resulting managerial implications. Since the statistical model is dynamic, the optimization plan is multi-period in character. The implied optimal strategy is compared with the strategy used by an actual firm.
A Modified Linear Program for Columnar Methods in Mathematical Programming
Authors: Nemhauser G. L. , Widhelm W. B.
Published: November 2008

This paper develops a modified linear programming algorithm for columnar methods in mathematical programming that is applicable to the decomposition principle of linear programming, to concave maximization problems over compact and convex sets, and to searching generalized Lagrange multipliers. It derives the linear program from linear inequalities in the multiplier space and compares it with the well-known linear program of Dantzig and Wolfe for solving such problems.
Comments on Integer Hulls of Two Linear Constraints
Authors: Jeroslow R. G.
Published: November 2008

This paper establishes an intrinsic complexity for the integer-programming problem that goes well beyond the computational complexities of linear programming. To this end, it describes a procedure with the following property: given any two independent linear constraints in two dimensions and any number N however large, the procedure determines two other linear constraints (with integer coefficients) arbitrarily “close” to the given constraints such that the two new constraints have at least N faces in their integer hull. It is possible for the integer-programming optimum to occur at any extreme point of this hull, and the number of extreme points is one less than the number of faces. In contrast, the linear-programming problem consisting of two inequalities in the plane is a triviality. The paper has an expository style and illustrates its highly geometrical arguments with figures.
Utility Independence and Preferences for Multiattributed Consequences
Authors: Keeney Ralph L.
Published: November 2008

This paper introduces and defines the concept of utility independence, and derives general expressions for simplifying the assessment of multiattribute utility functions, given that certain utility independence assumptions hold. These results are more general than the commonly used additive utility function, which is shown to be a special case. Finally, the paper discusses the relevance of this work as an approximation technique when requisite assumptions are not satisfied.
Capacity of a Network with Increasing Demands and Arcs Subject to Failure
Authors: Doulliez P. J. , Rao M. R.
Published: November 2008

This paper considers a multiple-sink network with demand at some nodes of the network being an increasing function of time. It gives, for source-sink planar networks, an algorithm for finding the maximum time up to which all demands can be satisfied. This algorithm is applicable even if any set of a specified number of arcs of the network has the arc capacities reduced to given lower values. The method presented is based upon the properties of the dual network. Finally, the paper works out a numerical example and discusses an application of the method to the optimal-capacity planning of a network.
Toward an Integrated Methodology for the Analysis of Health-Care Systems
Authors: Smallwood Richard D. , Sondik Edward J. , Offensend Fred L.
Published: November 2008

This paper introduces patient state and physician state of information as two unifying concepts for the analysis of health-care systems. The concepts are presented in the context of four specific problem areas. As a demonstration of the utility of these concepts, a technique for evaluating alternative facility macroplans is described and some results from an actual application are presented and reviewed.
A Search Model for Evaluating Combinatorially Explosive Problems
Authors: McRoberts Keith L.
Published: November 2008

Heuristic algorithms have frequently been developed in the attempt to solve combinatorial problems such as those that frequently exist in plant-layout planning, sequencing, scheduling, and routing situations. In these algorithms there has been no basis available to evaluate the progress of the heuristic results in relation to an optimum. This paper outlines and provides examples of the application of extreme value distributions and, more particularly, the Weibull distribution as mechanisms for estimating optimum limits. Given such estimates, the paper further illustrates the development of decision rules applicable to the decision of continuing or halting the heuristic analysis.
Stronger Inequalities for 0, 1 Integer Programming Using Knapsack Functions
Authors: Kianfar Ferydoon
Published: November 2008

In deriving the well known cuts for cutting-plane methods in 0, 1 integer programming, the integer points outside the 0,1 space can limit the parallel movement of the hyperplane of the cut toward the solution set. Furthermore it is unnecessarily restrictive to limit the movement of this hyperplane to parallel translations. This paper removes these two limitations in order to derive stronger cuts and reduce the total number of cuts required. Thus, it describes a method based on a special case of the knapsack function that replaces each cut or original constraint by a new inequality whose hyperplane passes through as many integer points in 0, 1 space as possible.
The Solution of an Optimal Control Problem in Financial Modeling
Authors: Davis Blaine E. , Elzinga D. Jack
Published: November 2008

This paper solves a financial decision-making model in investment activity. Although highly simplified, it leads to a very complicated nonlinear optimal control problem whose complete feedback control solution is obtained by means of a reverse-time construction technique. A dispersal surface with nonunique solutions is present in the optimal solution because of the non-concavity of the problem.
A Multi-Item Inventory Model with Joint Backorder Criterion
Authors: Miller Bruce L.
Published: November 2008

This paper considers a one-period multi-item inventory model where the objective is to minimize a function of item backorders subject to a budget constraint. Two functions are considered: the sum of expected item backorders and an expected joint backorder criterion. A main result is a proof that the joint backorder criterion is convex for arbitrary, twice-differentiable demand distributions. The rest of the paper is devoted to comparing the solutions one obtains with the two criterion functions.
A Review of Quasi-Convex Functions
Authors: Greenberg Harvey J. , Pierskalla William P.
Published: November 2008

Many theorems involving convex functions have appeared in the literature since the pioneering work of Jensen. Recently some results have been obtained for a larger class of functions: quasi-convex. This review summarizes in condensed form results known to date, providing some refinements to gain further generality. An additional objective of this review is to clarify the structure underlying quasi-convex functions by presenting analogues to properties of convex functions, and by illustrating where analogues do not exist.
Bounding Distributions for a Stochastic Acyclic Network
Authors: Kleindorfer George B.
Published: November 2008

Where the durations of the activities in an acyclic scheduling network are random variables, this paper obtains upper and lower bounding distributions for the activity starting- and finishing-time probability distributions, as well as upper and lower bounds for the expected starting and finishing time of each network activity, and for expected network resource flows. The tightness of the bounds for various networks is examined, and a computational experience with the methods is reported.
Parameterizing an Activity Vector in Linear Programming
Authors: Kim Chaiho
Published: November 2008

This paper presents an algorithm that will parameterize an activity vector for a linear programming problem in the following manner. Assume that an optimum feasible basis for a parametric linear programming problem has been obtained for the low-bound value of the parameter θ, set to zero. The algorithm then determines a sequence of critical values θ1, …, θk, …, θT, where θk ≧ θk−1, and a series of bases B1, …, Bk, …, BT, in such a way that Bk is optimum feasible for θk ≦ θ ≦ θk+1 for 1 ≦ k ≦ T − 1 and BT is either optimum feasible for all θT ≦ θ ≦ γ or unbounded or infeasible for 0 ≦ θ − θT ≦ ϵ, where ϵ is an arbitrarily small positive number. The essence of the algorithm consists of a series of simple transformations from one optimum feasible basis to another. The algorithm is illustrated with a numerical example.
Sequential Control of Homogeneous Activities—Linear Programming of Semi-Markovian Decisions
Authors: Hinomoto Hirohide
Published: November 2008

One simple method by which a manager can maintain a group of deteriorating activities at a high performance level is to inspect them in a fixed rotating sequence and immediately correct an activity performing at a low level. In this paper, this control method is applied to homogeneous independent activities under the assumption that the system of performance deterioration and improvement behaves as a semi-Markov chain. Two different plans to execute the control method are considered. Under one plan the rotating sequence stays fixed regardless of the conditions of activities, while under the other this sequence changes whenever an activity is in emergency and given immediate attention. Stationary solutions to optimal control strategies for these plans are obtained by the linear programming method for sequential decisions.
Group-Theoretic Results in Mixed Integer Programming
Authors: Wolsey Laurence A.
Published: November 2008

This paper shows how the asymptotic structure of the integer programming problem extends to the mixed integer problem. The group-theoretic ideas are then used to provide information about the solutions of the asymptotic mixed integer problem, and it is also shown how useful bounds can be obtained from the corresponding all-integer asymptotic problem. An example shows the application of some of the results.
An Approximate Measure of Value
Authors: Churchman C. West , Ackoff Russell L.
Published: November 2008

Selection of an optimum decision depends on two types of measures: (1) the efficiency of a course of action for an outcome; (2) the importance or weight of the outcomes. That course of action that maximizes the expected total weighted efficiency (effectiveness) is optimum. A method for estimating importance on a scale of value is provided. It is based on actual or verbal choices of decision-makers. The method can be applied to any number of objectives or outcomes, and to any number of decision-makers. Reliability of the results can be measured.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Organization and Information Handling in Task Groups
Authors: Christie Lee S.
Published: November 2008

Organizational factors in information handling in task-oriented groups have been studied recently at M.I.T. Laboratory groups were given very simple information-collection tasks under rigidly controlled conditions and the communication recorded completely. Decisions were restricted to choices of message destination and the influence of various imposed communication nets on the adequacy of group performance analysed. A technique of group-action quantization was used, which made possible a well-defined measure of group efficiency and an easily understood group goal. Experimental results show that an equiprobable random assumption is a poor model even for initial behavior. Centralized nets are shown to learn to do as well as the net permits fairly rapidly but to be characterized by high minimum-action. A net designed to give the lowest average action for task completion with random message-destination choices is shown to be essentially incapable of achieving its limiting minimum. Another similar net with a higher random average and a favorable minimum is shown to learn its minimum readily. Differences among the results for different nets are found to be explained in terms of a concept of “locally rational behavior” and the combinatorial characteristics of the nets.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Some Applications of the Theory of Dynamic Programming—A Review
Authors: Bellman Richard
Published: November 2008

The purpose of this paper is to provide an expository account of the theory of dynamic programming. To illustrate the general principles, two particular problems, one of deterministic type and one of stochastic type, are treated.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Parametric Objective Function (Part 1)
Authors: Saaty Thomas , Gass Saul
Published: November 2008

In the linear programming problem where there is a linear function to be optimized (called the objective function), it is desirable to study the behaviour of solutions when the (cost) coefficients in the objective function are parametrized. The problem is then to find the set of xj (j = 1, 2, …, n) which minimizes the linear form ∑(cj + λ cj′) xj and satisfy the constraints xj ≥ 0 and ∑aıjxj = aı0 (i = 1, 2, …, m) where cj, cj′, aıj, and aı0 are constants, with at least one cj ≠ 0, and λ a parameter. Using the simplex method, a computational procedure is described which enables one, given a feasible solution, to determine the values of the parameter (if any) for which the solution minimizes the objective function; and given a minimum feasible solution how one can generate by the simplex algorithm all minimum feasible solutions and the corresponding values of the parameter. To a minimum solution there corresponds one interval of values of λ (nondegeneracy assumed). The process indicates how to obtain a new solution and the corresponding interval of values of λ which is contiguous to the previous one both having only one point in common.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Erich Schneider's Inventory Control Analysis
Authors: Whitin T. M.
Published: November 2008

Much attention has been focussed on inventory control problems in this country in recent years by statisticians, economists, logisticians, and operations researchers. The author is aware of several instances where the discussion of these problems could have been substantially improved by knowledge of work completed by Professor Erich Schneider in 1938. The present article summarizes the principal results of this work, relates them to recent work accomplished in similar areas of operations research, and points out several similarities between Schneider's approach to the problem and the general philosophy of operations research.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Letter to the Editor—A Comment on Edie's “Traffic Delays at Toll Booths”
Authors: Dantzig George B.
Published: November 2008

E. W. Paxson of Rand has suggested that linear programming methods could be used as an alternative procedure in the scheduling section of Leslie C. Edie's interesting paper on “Traffic Delays at Toll Booths” (Leslie C. Edie. 1954. Traffic delays at toll booths. J. Opns. Res. Soc. Am. 2 107.). The purpose of this note is to elaborate on this suggestion.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Military Decision and Game Theory
Authors: Haywood O. G.
Published: November 2008

The United States military doctrine of decision prescribes that a commander select the course of action which offers the greatest promise of success in view of the enemy's capabilities of opposing him. This paper analyzes two battle decisions of World War II, and develops the analogy between existing military doctrine and the “theory of games” proposed by von Neumann. Current U.S. doctrine is conservative. The techniques of game theory permit analysis of the risk involved if the commander deviates from current doctrine to base his decision on his estimate of what his enemy intends to do rather than on what his enemy is capable of doing. The idea of “mixed strategies” presents more difficulties but may be useful, particularly for command decisions for small military organizations.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Solution of a Large-Scale Traveling-Salesman Problem
Authors: Dantzig G. , Fulkerson R. , Johnson S.
Published: November 2008

It is shown that a certain tour of 49 cities, one in each of the 48 states and Washington, D.C., has the shortest road distance.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Optimum Operation of a Complex Activity Under Conditions of Uncertainty
Authors: Solomon Morris J.
Published: November 2008

The model presented is suitable for determining the optimum manner of operation of a complex activity that depends on the maintenance of each of many subactivities, each subactivity being subject to uncertainty, measurable by a probability distribution. The activity discussed is the flying of planes at a base, the subactivities being the supply of spare parts. The first problem of the base is how many of each part to order. This has been satisfactorily solved by existing literature. The second problem is when to order, if the lack of any one of many different parts can ground an aircraft. It is this problem which the present paper solves. Consistent with stated assumptions, formulas are derived that yield minimum routine supply cost sets of reorder points (one reorder point for each part). Each set gives some specified protection against a plane being grounded because the base lacks one or more parts, at minimum cost, ignoring costs which arise from grounding of planes. Taking into account the costs that arise from the grounding of planes, such as the cost of rush requisitions and the need for additional aircraft and other considerations, a procedure is developed for choosing one set among all minimum cost sets which is optimum in an over-all sense. The solution is put in a form which can be used on a decentralized basis and under changing conditions. The use of the model under dynamic conditions is discussed. A variant of the main model is described which should be extremely useful for combat situations.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Numerical Solution of the Problem of Optimum Distribution of Effort
Authors: Miehle William
Published: November 2008

This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail. A similar method for multiplicative effects is sketched.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.
Extensions of the Evans-Gould Stability Theorems for Mathematical Programs
Authors: Greenberg Harvey J. , Pierskalla William P.
Published: November 2008

This paper extends the results of Evans and Gould for stability in mathematical programming. In particular, it shows that their conditions apply to functional perturbation, to equality constraints, and to policy stability under certain conditions. Further, it shows that strictly monotonic programs and positively homogeneous programs possess the closure property needed for stability. Finally, some necessary and sufficient conditions are presented for lower and upper semicontinuity of certain point-to-set mappings.
Primal Decomposition of Mathematical Programs by Resource Allocation: I—Basic Theory and a Direction-Finding Procedure
Authors: Silverman Gary J.
Published: November 2008

This paper presents a method for primal decomposition of large convex separable programs into a sequence of smaller subproblems. The main advantage of primal decomposition over Lagrange-multiplier or dual-decomposition methods is that a primal feasible solution is maintained during the course of the iterations. Feasibility is maintained by recasting the original convex separable program into a context of resource allocation. Then a direction-finding procedure for a method of feasible directions is developed for the derived resource-allocation problem. The direction-finding procedure utilizes the directional derivative to give a piecewise-linear approximation to the primal resource-allocation function. This approximation is more efficient than the usual linear gradient approximation used in methods of feasible direction, but it is still made with a linear program. The efficiency of the piecewise-linear approximation and the operation of the method of feasible directions are illustrated by a simple numerical example.