bluuebunny/crossref_metadata_2025 huggingface dataset:
The Role of Operations Research in Regional Health Planning
Authors: Shuman Larry J. , Wolfe Harvey , Dixon Speas R.
Published: November 2008

Operations-research workers have not met with much success in being accepted as integral members of regional-health-planning teams, owing in part to a lack of understanding by health planners of the skills the operations researcher has to offer and in part the analyst's inability to demonstrate that he can close the gap between theoretical modeling and the implementation of his results. This paper explores the growth of regional health planning in the United States and highlights its important problem areas. The literature of operations-research applications to health planning is reviewed critically with respect to the feasibility of models and the appropriateness of assumptions. Specific problems with the types of studies currently in the literature are identified and recommendations are made for improved coordination between operations-research workers and health planners.
An Algorithm for the Dynamic Relocation of Fire Companies
Authors: Kolesar Peter , Walker Warren E.
Published: November 2008

When all the fire companies in a region are engaged in fighting fires, protection against a future fire is considerably reduced. It is standard practice in many urban fire departments to protect the exposed region by relocating outside fire companies temporarily to some of the vacant houses. In New York City, situations requiring such relocations arise ten times a day on the average. The Fire Department of the City of New York (FDNY) currently makes its relocations according to a system of preplanned moves. This system was designed at a time when alarm rates were low and is based on the assumption that only one fire is in progress at a time. Because of the high alarm rates currently being experienced in parts of New York City, this assumption is no longer valid, and the preplanned relocation system breaks down at the times when it is needed most.

This paper describes a computer-based method for determining relocations that overcomes the deficiencies of the existing method by utilizing the computer’s ability to (1) store up-to-date information about the status of all fires in progress and the location and activity of all fire companies, (2) generate and compare many alternative relocation plans quickly. The method, which will become part of the FDNY’s real-time Management Information and Control System (MICS), is designed to be fast and to require little computer memory.

After giving some background of the problem and the objectives of relocation, we give the problem a mathematical programming formulation and then describe the heuristic algorithm to be used for generating relocations in the MICS. The remainder of the paper is devoted to a discussion of an example illustrating how the algorithm works, a rigorous test of the algorithm using a computer simulation model of Fire-Department operations, and a description of the current use of the computer algorithm by dispatchers in an interactive time-shared environment. The results of the testing indicate that the proposed algorithm is a significant improvement over existing methods, particularly in crisis situations. Although designed to solve a problem for the New York City Fire Department, the algorithm should be applicable to other cities.
Some Differential Games of Tactical Interest
Authors: Taylor James G.
Published: November 2008

This paper applies the recent theory of differential games to the supporting-weapon-system game of H. K. Weiss, which was originally solved by heuristic means. The solution procedure is applicable to any terminal-control attrition differential game that has a pure-strategy solution. Conditions that guarantee the existence of saddle points in such games are discussed. This development motivates a new solution concept and encounters solution behavior not previously noted for differential games. Finally, the paper discusses the structure of optimal allocation policies.
A Heuristic Algorithm for the Vehicle-Dispatch Problem
Authors: Gillett Billy E. , Miller Leland R.
Published: November 2008

This paper introduces and illustrates an efficient algorithm, called the sweep algorithm, for solving medium- as well as large-scale vehicle-dispatch problems with load and distance constraints for each vehicle. The locations that are used to make up each route are determined according to the polar-coordinate angle for each location. An iterative procedure is then used to improve the total distance traveled over all routes. The algorithm has the feature that the amount of computation required increases linearly with the number of locations if the average number of locations for each route remains relatively constant. For example, if the average number of locations per route is 7.5, the algorithm takes approximately 75 seconds to solve a 75-location problem on an IBM 360/67 and approximately 115 seconds to solve a 100-location problem. In contrast, the time to solve a problem with a fixed number of locations increases quadratically with the average number of locations per route. The sweep algorithm generally produces results that are significantly better than those produced by Gaskell's savings approach and are generally slightly better than Christofides and Eilon's results; however, the sweep algorithm is not as computationally efficient as Gaskell's and is slightly less so than Christofides and Eilon's.
Chance-Constrained Programming with Joint Constraints
Authors: Jagannathan R.
Published: November 2008

Miller and Wagner have shown that a deterministic equivalent of a joint chance-constrained programming model with independent random right-hand-side elements is a concave programming problem. This paper obtains similar equivalents for chance-constrained programming models with coefficient matrices whose elements are normally distributed and with dependent random right-hand-side elements.
Technical Note—Clustering a Data Array and the Traveling-Salesman Problem
Authors: Lenstra J. K.
Published: November 2008

A clustering of a nonnegative M×N array is obtained by permuting its rows and columns. W. T. McCormick et al. [Opns. Res. 20, 993–1009 (1972)] measure the effectiveness of a clustering by the sum of all products of nearest-neighbor elements in the permuted array. This note points out that this clustering problem can be stated as two traveling-salesman problems.
Technical Note—A Note on the Application of Nonlinear Programming to Chemical-Process Optimization
Authors: Jaakola T. H. I. , Luus Rein
Published: November 2008

Proper rearrangement of equality constraint equations can simplify considerably an otherwise complex optimization problem. This note shows that, with proper rearrangement, the equations describing a moderately complex chemical process can be solved seriatim. With such a system structure, the optimization procedure presented by Luus and Jaakola [A. I. Ch. E. J. 19, 760 (1973)] can be applied readily.
The Optimal Location of Nuclear-Power Facilities in the Pacific Northwest
Authors: Dutton Ron , Hinman George , Millham C. B.
Published: November 2008

This paper treats the optimal location of nuclear-power plants in the Pacific Northwest with respect to capital-construction, operating, and transmission costs. It presents a mathematical formulation of this two-product (peak and energy power) plant-location problem, using the simplex method in conjunction with a branch-and-bound process, and indicates a check procedure using Vogel’s approximation method in conjunction with an algorithm for solving the transportation problem and a branch-and-bound process. The paper gives results for demand-growth rates of 4, 5, 6 and 7 percent and alternative designs and their costs. It also discusses the stability of the optimal solution.
Reachable Sets for Tracking
Authors: Wong Peter J. , Korsak Andrew J.
Published: November 2008

In many aircraft-tracking systems the following problem is of importance in correlating radar returns with tracks: Given the aircraft position and velocity at time t − Δt and the limits on the ability of the aircraft to maneuver and/or change speed, what is the set of all possible aircraft positions at time t? We call this set the reachable set (or set of attainability) at time t. This paper uses the Pontryagin maximum principle to derive a set of equations for describing the reachable set.
Optimal Dynamic Pricing Policies for an M/M/s Queue
Authors: Low David W.
Published: November 2008

We consider the problem of maximizing the long-run average expected reward per unit time in a queuing-reward system, which we formulate as a semi-Markov decision process. Control of the system is effected by increasing or decreasing the price charged for the facility's service in order to discourage or encourage the arrival of customers. We assume that the arrival process is Poisson with arrival rate a strictly decreasing function of the currently advertized price, and that the service times are independent exponentially distributed random variables. The reward structure consists of customer payments and holding costs (possibly nonlinear). At each transition (customer arrival or service completion), the manager of the facility must choose one of a finite number of prices to advertize until the next transition. We show that there exist optimal stationary policies and that each possesses the monotonicity property: the optimal price to advertize is a nondecreasing function of the number of customers in the system. An efficient computational algorithm is developed that, in a finite number of steps, produces a stationary policy that is optimal.
The M/M/1 Queue in a Markovian Environment
Authors: Purdue Peter
Published: November 2008

This paper discusses the M/M/1 queue embedded in a Markovian environment (or, subject to extraneous phase changes). It studies the busy period, equilibrium conditions, and emptiness probabilities by using analytic matric functions, and makes comparisons with the work of Neuts and of Naor and Yechiali.
An Efficient Equipment-Layout Algorithm
Authors: Neghabat Farrokh
Published: November 2008

This paper treats the problem of locating a given number of interrelated physical facilities in a single- or multi-story building as an optimization model such that the weighted sum of the distances along orthogonal directions is minimized, and describes a constructive heuristic algorithm for the one-dimensional model. This linear placement algorithm is then extended to higher dimensions for placing uniform-size equipment modules at homogeneous fixed locations. The algorithm accommodates lower-bound constraints for the linear case efficiently and produces near-optimal solutions. Its significance, as demonstrated by comparison with some existing heuristic procedures, is that it has the capability of handling efficiently problems with large numbers of equal-size facilities whose solutions are computationally intractable using the present optimum-producing methods.
An Analysis of Baseball Batting Order by Monte Carlo Simulation
Authors: Freeze R. Allan
Published: November 2008

A Monte Carlo simulation of over 200,000 baseball games, using a programmed embodiment of the main features of the Sports Illustrated baseball game, shows that batting order exerts only a small influence on the outcomes of baseball games. The effect of using the best batting order rather than the worst is less than three extra wins per 162-game season. The traditional lineup, wherein a team's strongest batters hit in the third through fifth positions, is superior to a lineup in which batters are arranged in decreasing order of productivity.
Solving Lanchester-Type Equations for “Modern Warfare” with Variable Coefficients
Authors: Taylor James G.
Published: November 2008

This paper develops solutions to extensions of F. W. Lanchester's classical equations of “modern warfare” (frequently referred to as aimed-fire equations) for combat between two homogeneous forces. In these extensions the lethality of the fire (as expressed by the Lanchester attrition-rate coefficient) depends on time. When the dependence is arbitrary, the solution is an infinite series of recursively related integrals; in special cases, more convenient representations (including representation in terms of tabulated functions) are available. Solutions are obtained in the following cases: (1) the lethality of each side's fire proportional to a power of time and both lethalities initially zero, and (2) the lethality of each side's fire linear with time, but only one side's lethality initially zero. The latter case models the constant-speed approach between forces whose weapons have different maximum effective ranges.
Simultaneous Price-Production Decisions
Authors: Pekelman Dov
Published: November 2008

This paper deals with the problem of determining the price and production schedule of a firm over a known horizon simultaneously when the demand parameters are time-dependent. It characterizes the optimal solution and shows the similarity of our problem to the well known problem of Modigliani and Hohn [Econometrica 23, 46–66 (1955)]. It also demonstrates the possible existence of a planning horizon. These results are obtained by using control theory, in particular, by using the necessary and sufficient conditions for a state constraint in the form of a nonnegative constraint on the inventory level.
Technical Note—A Duality Theory for Convex Programming with Set-Inclusive Constraints
Authors: Soyster A. L.
Published: November 2008

This paper extends the notion of convex programming with set-inclusive constraints as set forth by Soyster [Opns. Res. 21, 1154–1157 (1973)] by replacing the objective vector c with a convex set C and formulating a dual problem. The primal problem to be considered is [Formula: see text] where the sets {Kj} are convex activity sets, K(b) is a polyhedral resource set, C is a convex set of objective vectors, and the binary operation + refers to addition of sets. Any feasible solution to the dual problem provides an upper bound to (I) and, at optimality conditions, the value of (I) is equal to the value of the dual. Furthermore, the optimal solution of the dual problem can be used to reduce (I) to an ordinary linear programming problem.
Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal
Authors: Ignall Edward , Kolesar Peter
Published: November 2008

We study the optimal control of a shuttle system consisting of a single infinite-capacity carrier transporting passengers between two terminals. Passengers arrive according to independent Poisson processes, and at only one of the terminals can the dispatcher hold the carrier for more passengers. Our objective: to determine dispatching rules that minimize the long-run average of a linear passenger-waiting-time cost and a charge per trip made by the carrier. When complete information about the system state is available, and travel times are not random, we prove that it is best to dispatch the carrier if, and only if, the total number of passengers waiting at both terminals is greater than a cutoff value. To compute this cutoff value, we propose an iterative method and find that we can approximate it quite well by a simple function of system costs and parameters similar to the economic-lot-size formula. We propose a dispatching rule (which may not be optimal) for the case when only the number of passengers waiting at one terminal is known, and we compare its efficiency to that of the optimal rule that uses complete information. We outline extensions to other optimality criteria and to the case of stochastic travel times.
Technical Note—The Equivalence of Two Mathematical Programs with Optimization Problems in the Constraints
Authors: Bracken Jerome , Falk James E. , McGill James T.
Published: November 2008

Bracken and McGill have recently studied two classes of mathematical programs with optimization problems in the constraints [Opns. Res. 21, 37–44 (1973)], the first class involving mathematical programs in the constraints and the second max-min problems there. They have also developed a computational technique and shown that it is effective in solving problems of the first class [Opns. Res. 22, 1097–1101 (1974)]. This note shows that the computational technique can be applied to problems of the apparently wider second class.
Technical Note—Some Explanatory Remarks on the Optimal Control of the Vidale-Wolfe Advertising Model
Authors: Sethi Suresh P.
Published: November 2008

This note adds three remarks to an earlier paper on the optimal control of the Vidale-Wolfe advertising model [Opns. Res. 21, 998–1013 (1973).
Actuarial Techniques and Their Relations to Noninsurance Models
Authors: Halmstad David G.
Published: November 2008

Actuarial science is one of the oldest applications of mathematical principles to a branch of commerce, namely, insurance. This paper summarizes classic and modern areas of actuarial theory and relates them to traditional non-insurance techniques.
Optimal Claim Decisions by Policyholders in Automobile Insurance with Merit-Rating Structures
Authors: Haehling von Lanzenauer Christoph
Published: November 2008

Merit-rating structures in automobile-insurance systems require the insured to decide whether to file a claim for an accident when he is at fault. This decision can only be analyzed in the light of future developments and future decisions, and thus must be formulated as a sequential decision process that can be solved by dynamic programming. If future developments are estimated in light of new experience, the decision problem can be analyzed by adaptive programming. The approach is illustrated by sample calculations providing a number of observations that are of interest from the insurance industry's point of view.
An Optimal-Control-Theory Approach to the Education-Investment Decision
Authors: Southwick Lawrence , Zionts Stanley
Published: November 2008

This paper presents an optimal-control-theory model that maximizes the present value of future earnings for an individual—particularly a poor one. Income is assumed to be a function of age and education level, and the rate of schooling is the control variable. A linear tax function is assumed that admits a negative income tax. In spite of numerous difficulties in measuring certain parameters, regression analysis is used to fit income data to age and education level. Then some specific functions for the optimal education plan are derived for different parameter values. The sensitivity of the model to changes in certain controllable and noncontrollable parameters is analyzed, and some implications for government policy are found.
A Stochastic Analysis of Programs for the Mentally Retarded
Authors: Trinkl Frank H.
Published: November 2008

This paper presents a constrained value-weighted Markovian approach to evaluating public-policy alternatives. It incorporates value judgments and constraints into a Markov chain so that relative comparisons of value-cost time profiles associated with alternative programs can he made. Although the model was developed to analyze programs for the mentally retarded, other applications appear promising.
Technical Note—Counterexamples for the Location of Emergency Service Facilities
Authors: Rao Ashok
Published: November 2008

This note gives two counterexamples to the single-cut procedure of Tokegas, Swain, Revelle, and Bergman [Opns. Res. 19, 1363–1373 (1971)] for solving the simple set-covering problem: the first shows that a single cut may not always be sufficient, the second that the cut may not always result in an integer optimal solution.
Optimal Priority Assignment with Heterogeneous Waiting Costs
Authors: Beja Avraham , Sid Esther
Published: November 2008

For an M/G/1 queuing system, this paper assumes (l) that the discipline is administratively constrained to a “head-of-the-line” rule with n classes, and (2) that priorities are centrally assigned to customers according to their individual cost per unit time spent in the system, or their individual service-time requirements, or both (as the available information may be), but independently of the state of the queue. Then optimal priority-assignment rules for the various information structures are characterized. When n = 2, the higher priority may always be optimally assigned to all customers who are “no worse than average” and with sufficiently high load to “practically all” customers.
A Branch-and-Bound Algorithm for Two-Stage Production-Sequencing Problems
Authors: Uskup Ergin , Smith Spencer B.
Published: November 2008

This paper presents an algorithm for determining an optimum solution to a two-stage production sequencing problem with these characteristics: There are n jobs to be sequenced in a two-stage production environment; each production stage is equipped with a single facility; jobs to be sequenced are subject to due-date constraints; facilities in both stages require setup prior to processing each job; setup times in both stages are sequence dependent, and setup cost is assumed to be directly proportional to setup time; and the optimal solution is one that minimizes the total setup cost (of stages I and II) without violating job-due dates. The algorithm employs controlled enumeration through branch-and-bound procedures, together with feasibility tests.
Technical Note—An Elimination Method for the Flow-Shop Problem
Authors: Baker Kenneth R.
Published: November 2008

Elimination methods for the flow-shop problem have been investigated by-several authors using special elimination conditions to construct a set of dominant schedules and then enumerate them in order to find an optimum. The few papers reporting computational experience with elimination algorithms indicate that the approach may be an efficient method for obtaining optimal schedules. This note builds a simple model in order to help provide some perspective on these computational results and to describe how elimination algorithms may behave in moderate-sized problems.
Technical Note—Assembly-Line Balancing: Zero-One Programming with Fibonacci Search
Authors: Patterson James H. , Albracht Joseph J.
Published: November 2008

This paper presents a zero-one integer-programming formulation of the assembly line balancing (ALB) problem. Results indicate that this formulation requires as few as 50 to 60 percent of the number of variables required by other zero-one formulations of the ALB problem now in existence. Once formulated, problems are solved by examining a sequence of 0-1 programming problems for feasible solutions. Full advantage is taken of the structure of the 0-1 programs in determining feasibility. Computational results demonstrate the efficacy of the approach.
Optimal Diagnostic Questionnaires
Authors: Duncan George T.
Published: November 2008

This paper develops dynamic-programming and other shortest-route algorithms for optimizing sequentially patterned questioning procedures, called diagnostic questionnaires. It uses graph-theoretic methods and solves certain combinatorial problems associated with the Catalan numbers. The paper obtains general properties of optimal questionnaires, including an ordering relation, a convexity result, and the determination of essentially complete classes of questionnaires. It explores a logarithmic charging scheme in detail and obtains a minimal result. Finally, the paper examines the relation with Huffman coding of information theory, and a simple method of Shannon efficiency.
Optimal Ordering Policy for a Perishable Commodity with Fixed Lifetime
Authors: Fries Brant E.
Published: November 2008

This paper extends the classical single-item, multiperiod inventory model of Arrow, Karlin, and Scarf to the case where a good in storage perishes exactly l periods after its receipt on order. Units are followed from the time they are purchased and enter the inventory until they are either issued or perish. For general l the paper obtains the optimal policy recursively and derives several properties of the solution.
An Interactive Procedure for the School Boundary Problem with Declining Enrollment
Authors: Holloway Charles A. , Wehrung Donald A. , Zeitlin Michael P. , Nelson Rosser T.
Published: November 2008

School districts in some urban areas are facing reduced enrollments. Educational and economic considerations dictate closing schools. Parents, on the other hand, often resist closing neighborhood elementary schools and object to having children periodically reassigned. This paper presents an interactive procedure for establishing, under conditions of declining enrollment, boundaries that reflect educational, economic, and parental concerns. The procedure can incorporate a variety of administrative policies and requires inputs from administrators regarding characteristics of the district. The multi-period planning horizon is decomposed by year with coordination taking place through the use of restriction in a linear programming problem that forms the basis for reassignment of districts. The emphasis is not on optimization but rather on the achievement of a solution which satisfies the objectives of each group. Feasibility checks are designed to reduce the number of alternatives that must be considered in detail, and feasible solutions can be compared on the basis of summary statistics.
Dynamic Scheduling of a Multiclass Queue: Discount Optimality
Authors: Harrison J. Michael
Published: November 2008

We consider a single-server queuing system with several classes of customers who arrive according to independent Poisson processes. The service time distributions are arbitrary, and we assume a linear cost structure. The problem is to decide, at the completion of each service and given the state of the system, which class (if any) to admit next into service. The objective is to maximize the expected net present value of service rewards received minus holding costs incurred over an infinite planning horizon, the interest rate being positive. One very special type of scheduling rule, called a modified static policy, simply enforces a (nonpreemptive) priority ranking except that certain classes are never served. It is shown that there is a modified static policy that is optimal, and a simple algorithm for its computation is presented.
Decomposition Algorithms for Single-Machine Sequencing with Precedence Relations and Deferral Costs
Authors: Sidney Jeffrey B.
Published: November 2008

A one-machine deterministic job-shop sequencing problem is considered. Associated with each job is its processing time and linear deferral cost. In addition, the jobs are related by a general precedence relation. The objective is to order the jobs so as to minimize the sum of the deferral costs, subject to the constraint that the ordering must be consistent with the precedence relation. A decomposition algorithm is presented, and it is proved that a permutation is optimal if and only if it can be generated by this algorithm. Four special network structures are then considered, and specializations of the general algorithm are presented.
Technical Note—Comments on the Distribution of Inventory Position in a Continuous-Review (s, S) Inventory System
Authors: Richards F. R.
Published: November 2008

This paper comments on the limiting distribution of the inventory position in a continuous-review (s, S) inventory system with arbitrary customer interarrival-time distribution. The limiting distribution is derived for the general case in which the demand quantity is random. We show that the limiting distribution is uniform on (s + 1, …, S) if and only if units are demanded one at a time. However, with a slight modification of the procurement policy, the uniform distribution is recaptured even with random demand quantities.
Probabilistic Analysis of a System with Two Dissimilar Units Subject to Preventive Maintenance and a Single Service Facility
Authors: Gopalan M. N. , D'Souza C. A.
Published: November 2008

This paper deals with the availability and the reliability analysis of a system consisting of two dissimilar units having a single service facility and subject to preventive maintenance. The times to failure, the repair times, and the preventive maintenance times of the units are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. By identifying suitable regenerative stochastic processes, we derive integral equations for these probabilities corresponding to different initial conditions, and we use Laplace transform technique to solve the equations. Explicit expressions for the mean down-time of the system during the period (0, t) and for the mean-time-to-system-failure are obtained. The case when the system is not subject to preventive maintenance is considered as a particular case.
Technical Note—Vertex Generation and Cardinality Constrained Linear Programs
Authors: Rubin David S.
Published: November 2008

Tanahashi and Luenberger have recently discussed a class of problems that they call “cardinality constrained linear programs (CCLP's).” These are linear programs with an additional constraint limiting the number of variables that may take on strictly positive values. Tanahashi and Luenberger presented cutting plane methods to solve the CCLP. We show how to solve the CCLP by modifying a procedure for generating all the vertices of the feasible region of the associated linear program. We also illustrate the relations between the CCLP and some other problems discussed in the literature.
Determining the Relation between Fire Engine Travel Times and Travel Distances in New York City
Authors: Kolesar Peter , Walker Warren , Hausner Jack
Published: November 2008

A simple physical model of the way fire engines travel leads to the hypothesis that T, the average fire engine travel time, depends on D, the distance travelled according to T(D) = 2(D/a)1/2 if D ≦ d and T(D) = vc/a + D/vc if D > d. The parameter a can be interpreted as an acceleration and vc as a cruising velocity. A field experiment was run, and the above model validated and the parameters estimated, for New York City. It was also found that regional traffic conditions and hour of day appear to have only minor effects on average response velocities.
BRANDAID: A Marketing-Mix Model, Part 1: Structure
Authors: Little John D. C.
Published: November 2008

Marketing managers make decisions about price, advertising, promotion, and other marketing variables on the basis of factual data, judgments, and assumptions about how the market works. BRANDAID is a flexible, on-line model for assembling these elements to describe the market and evaluate strategies. This paper motivates the model and presents its mathematics. The structure is modular so that individual decision areas can be added or deleted at will. The model is of the aggregate response type, in which decision variables relate closely to specific sales performance measures. The major submodels are advertising, promotion, price, salesmen, and retail distribution. The advertising submodel employs a long-run sales response to advertising function and a linear lag process. Promotional effects are built up from a characteristic time pattern for the type of promotion and a response curve. Salesman affect sales through a response process structurally similar to that for advertising. Retail distribution variables are intermediaries that the company affects and that in turn affect customer response. Submodel outputs combine multiplicatively. Competition enters in a modular, symmetric way through a matrix of competitive coefficients that determine the source of sales for each brand as it seeks to increase its market position.
BRANDAID: A Marketing-Mix Model, Part 2: Implementation, Calibration, and Case Study
Authors: Little John D. C.
Published: November 2008

Model implementation starts with introductory steps that include orienting management, forming a team, selecting and formulating a problem, calibrating the model, and initial use. Then on-going steps take over with firefighting, tracking and diagnosis, updating and evolution, and re-use. Calibration of the model is approached eclectically in stages that include judgment, analysis of historical data, tracking, field measurement, and adaptive control. A three-year case study shows that unexpected events intersperse a planned implementation. The model emerges with multiple roles in the marketing management process. The model serves not only as a means of evaluating strategies in annual planning and day-to-day operations but also as part of a monitoring system that compares model predictions with actual sales to uncover marketing problems and focus managerial attention upon them.
Waiting Time in an (S − 1, S) Inventory System
Authors: Higa Isamu , Feyerherm Arlin M. , Machado Arlette L.
Published: November 2008

Steady-state distribution functions are derived for waiting time in an (S − 1, S) inventory system in which arrivals are governed by members of the geometric Poisson family, resupply times are independently and identically distributed negative exponential variates, and service is on a first-come-first-served basis. For small values of S, probabilities can be computed readily from the final forms of the distribution functions using gamma and exponential function tables.
Optimal Ordering Policies for Perishable Inventory—II
Authors: Nahmias Steven
Published: November 2008

This paper deals with the problem of computing optimal ordering policies for a single product with a lifetime of exactly m periods. Costs are charged against ordering, holding, shortages, and out-dating. To take explicit account of the perishability, we substitute a cost to be incurred at the time of outdating. The functional equation approach of dynamic programming is used to extend this model to the multiperiod case, and the structure of optimal ordering policies is analyzed.
Technical Note—A Recursion Algorithm for Finding Pure Admissible Decision Functions in Statistical Decisions
Authors: Moskowitz Herbert
Published: November 2008

This note develops a recursion algorithm for finding the set of ordinally admissible decision functions in statistical decision problems when such functions have a Cartesian product structure. An example is used to demonstrate the computations. The generality of the algorithm is discussed briefly, and some computational experience is presented.
Approximating the Performance of Urban Emergency Service Systems
Authors: Larson Richard C.
Published: November 2008

This paper presents an approximate procedure for computing selected performance characteristics of an urban emergency service system. Based on a recently developed hypercube queuing model, the procedure requires for N servers solution of only N simultaneous equations, rather than 2N as in the exact model. The procedure relies on the theory of M/M/N queues in which servers are selected randomly and without replacement until the first available (free) server is found. The underlying model is intended for analyzing problems of vehicle location and response district design in urban emergency services, includes interdistrict as well as intradistrict responses, and allows computation of several point-specific as well as area-specific performance measures.
A Fractional Hypercube Decomposition Theorem for Multiattribute Utility Functions
Authors: Farquhar Peter H.
Published: November 2008

This paper establishes a fundamental decomposition theorem in multiattribute utility theory. The methodology uses fractional hypercubes to generate a variety of attribute independence conditions that are necessary and sufficient for various decompositions: the additive, Keeney's quasi-additive, Fishburrt's diagonal, and others. These other nonaddirive utility decompositions contain some nonseparable interaction terms and are therefore applicable to decision problems not covered by earlier models. The paper defines a fractional hypercube and introduces the corresponding multiple element conditional preference order. The main theorem is produced from the solution of equations that are derived from transformations of linear functions that preserve these conditional preference orders. The computations and scaling required in implementing the main result are demonstrated by obtaining four utility decompositions on three attributes: apex, diagonal, quasi-pyramid, and semicube. We illustrate the methodology with geometric structures that correspond to the fractional hypercubes.
Optimal Starting Height for Pole-Vaulting
Authors: Ladany Shaul P.
Published: November 2008

We have constructed a model for computing the expected height a pole-vaulter will clear when he starts his vaulting at a predetermined height, provided that the bar is raised in constant steps. The model uses conditional joint probabilities that the pole-vaulter will clear certain heights in one of the three possible trial vaults at each height, provided that he has already vaulted a certain number of times. These probabilities decrease as the number of vaults increases. The optimal starting height for pole-vaulting is determined by searching for the starting height that will maximize the expected height cleared. An approach is outlined for deriving the required probabilities from easily obtainable data. The model and its assumptions are validated with a numerical example, and a comparison is shown between pre- and post-optimal results.
Two Models for Optimal Allocation of Aircraft Sorties
Authors: Bracken Jerome , Falk James E. , Karr Alan F.
Published: November 2008

This paper presents two models for allocating general-purpose aircraft to missions in a multiperiod war. The models are two-person, zero-sum, sequential games with simultaneous moves each period. Ground forces as well as air forces are included. Three measures of effectiveness are available. The paper treats both a game allowing nonadaptive strategies and a game allowing behavioral strategies. It is shown that the latter game is equivalent to a game allowing the larger class of adaptive strategies.
On Competitive Bidding
Authors: Oren M. E. , Williams A. C.
Published: November 2008

This paper develops a model for describing some aspects of competitive bidding. The motivating purpose of the model was that of formally examining the hypothesis put forward by Capen, Clapp and Campbell: In a competitive oil and gas lease sale, or indeed in any bidding situation in which the ultimate value of the object to be won is subject to uncertainty, the highest bidder tends to be one who has overvalued the prize. As a result, any company tends to win tracts (or prizes) which it has overvalued and tends to lose those which it has undervalued. Therefore, even if the pre-sale value estimates, on the average, turn out to be correct for each of the tracts bid on, the estimates for those that are actually won will tend to prove to have been too high.

The model developed not only supports the hypothesis as set forth, but also establishes its validity much more generally.
Optimization Problems Subject to a Budget Constraint with Economies of Scale
Authors: Hillestad R. J.
Published: November 2008

This paper describes a finite procedure for locating a global minimum of a problem with linear objective constraints except for one nonlinear constraint, which is of the “reverse convex” variety; that is, the direction of the inequality is the opposite of that requited for a convex constraint. Budget constraints in which the cost functions are subject to economies of scale are typically of this form. An illustrative example of the procedure is provided.
Merging and Sorting Applied to the Zero-One Knapsack Problem
Authors: Ahrens J. H. , Finke G.
Published: November 2008

Branch-and-bound algorithms are adequate for the solution of a wide range of 0-1 knapsack problems. It is shown that the simplest method of branching is as good as any. However, problems with highly correlated large weights and values quickly become unsolvable in a reasonable time. This paper develops algorithms that are aimed specifically at the hardest possible examples. The new methods use merging and sorting ideas and require a moderate amount of additional memory space. They are, however, faster by factors far in excess of 1,000 in many cases, thereby extending considerably the range of practically solvable 0-1 knapsack problems.
An Algorithm for the Solution of 0-1 Loading Problems
Authors: Ingargiola Giorgio , Korsh James F.
Published: November 2008

An enumerative algorithm is presented for the solution of 0-1 many-knapsack or loading problems. It is based on the principle that before a search is attempted as many decisions as possible should be made about inclusion or exclusion of objects from the knapsacks. This is accomplished by the introduction of a new ordering relation among the objects. This ordering relation, coupled with other relations we define, allows a drastic reduction in the extent of the search required to determine a solution.
Approximate Solutions for Some Two-Stage Tandem Queues, Part 1: Individual Arrivals at the Second Stage
Authors: Rosenshine Matthew , Chandra M. Jeya
Published: November 2008

The analysis of tandem queues in which the output of each stage immediately becomes the input to the next is, in general, quite difficult. Although the analytic solution for the steady-state departure distribution from an M/M/N queue is well-known and that of an M/G/1 queue can be obtained if the analyst is willing to view it through a “Laplacian curtain,” the list of existing analytic solutions is not long. Some analytic “tricks” exist, but their utility is usually limited to the single-server queue. The treatment of tandem queues not fitting into these categories has been largely left to simulation. Yet this approach has its drawbacks. It is expensive and involves difficulties in designing and analyzing the simulation experiment. Approximation techniques are beginning to emerge as a wiser, faster, cheaper, and less troublesome alternative to simulation. In this paper we develop approximate solutions for average steady-state queue length in four different but related tandem queues that arise in connection with the service sys-of an air terminal complex. The approximate expressions obtained are validated by simulation.
Technical Note—A Note on the Busy Period of an M/G/1 Finite Queue
Authors: Miller Louis W.
Published: November 2008

Recursive formulas for computing the Laplace-Stieltjes transform and the mean of the distribution of the lengths of busy periods for the M/G/1 finite queue are derived by a simple method that avoids simultaneous equations.
An Analysis of General Exponential Smoothing
Authors: McKenzie Ed.
Published: November 2008

General exponential smoothing and adaptive smoothing are terms used to describe the application of discounted least squares to the fitting of certain mathematical functions to time series data. The technique yields forecasts satisfying simple recursive equations that generally contain fairly complex terms. We obtain the transfer function of such forecasting systems and derive from it an equivalent but simpler and more economic forecasting system. Other advantages of using the transfer function form for these complicated forecasting systems are discussed from both theoretical and computational viewpoints.
A Solution Procedure for Geometric Programming
Authors: McNamara John R.
Published: November 2008

The theory of geometric programming is concerned with the solution of certain nonlinear programming problems in which the objective function and the constraints are polynomial expressions with positive coefficients. The solution of the primal geometric programming problem can be obtained by solving the dual problem. In certain cases the solution to the dual problem, and hence the solution to the primal problem, is obtained immediately by solving the dual constraint system for the optimal dual vector. Such problems are said to possess “degree of difficulty zero.” This paper describes a solution procedure for geometric programming. The procedure involves the formation of an augmented problem possessing degree of difficulty zero. The solution to the original problem requires the estimation of certain parameters in the augmented problem. An iterative procedure for estimating these parameters is described.
Bayes Analysis of Reliability for Complex Systems
Authors: Chang Eugene Y. , Thompson William E.
Published: November 2008

We present a method for computing Bayes confidence limits for the reliability of an arbitrary series-parallel system consisting of failure independent modules. Each module has an internal structure of one or more failure independent devices in series, and each device consists of one operating component with identical nonoperating standby components. Each component is assumed to have exponential distribution of life with unknown failure rates that must be estimated from test data. We outline a systematic procedure to compute the posterior distribution of system reliability, from which exact confidence limits can be obtained. The posterior distribution function is developed in terms of an expansion in shifted Chebyshev polynomials of the second kind whose convergence properties and numerical evaluation are well suited for practical applications.
Reliability of a Repairable System with Standby Failure
Authors: Subramanian R. , Venkatakrishnan K. S. , Kistner K. P.
Published: November 2008

This paper deals with a system in which one unit is operating online and is backed my m spares as warm standbys. There are r repair facilities. The on-line unit has an arbitrary lifetime distribution, while the spares have exponential failure time distributions. The repair time distribution is also exponential. This problem, viewed as a queuing problem, cannot be solved; but by locating a set of renewal points, we write the equations governing the states of the system and calculate the reliability and availability. Explicit results are obtained in the case of five redundant units and three repair facilities.
Technical Note—Expected Completion Time in Pert Networks
Authors: Robillard Pierre , Trahan Michel
Published: November 2008

This note introduces a general approach to obtain lower bounds for the expected completion time in PERT networks where activity durations are random (discrete or continuous) variables. We show that some well-known bounds can be derived as particular cases of this general approach based on Jensen's inequality. We assume that the durations of the activities terminating at a node are independent of the durations of the activities terminating at another node and that all the activity durations have a finite positive range.
Technical Note—Optimality of a Heuristic Solution for a Class of Knapsack Problems
Authors: Hu T. C. , Lenard M. L.
Published: November 2008

This paper presents a simpler proof for a result of Magazine, Nemhauser, and Trotter, which states recursive necessary and sufficient conditions for the optimality of a heuristic solution for a class of knapsack problems.
Canonical Methods in the Solution of Variable-Coefficient Lanchester-Type Equations of Modern Warfare
Authors: Taylor James G. , Brown Gerald G.
Published: November 2008

This paper develops a mathematical theory for solving deterministic, Lanchester-type, “square-law” attrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It gives a general form for expressing the solution of such variable-coefficient combat attrition equations in terms of Lanchester functions, which are introduced here and can be readily tabulated. Different Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. We give results for two such forms: (1) effectiveness of each side's fire proportional to a power of time, and (2) effectiveness of each side's fire linear with time but with a nonconstant ratio of attrition-rate coefficients. Previous results in the literature for a nonconstant ratio of these attrition-rate coefficients only took a convenient form under rather restrictive conditions.