bluuebunny/crossref_metadata_2025 huggingface dataset:
Finding Equivalent Network Formulations for Constrained Network Problems
Authors: Klingman Darwin
Published: November 2008

This paper describes a procedure for determining if constrained network problems (i.e., network problems with additional linear constraints) can be transformed into equivalent pure network problems by a linear transformation involving the node constraints and the extra constraints. These results extend procedures for problems in which the extra constraints consist of bounding certain partial sums of variables. This has proved to be an effective managerial technique for a major automobile manufacturer and a major energy modeling company.
A Discrete Time, Single Server Queue from a Finite Population
Authors: Minh Do Le
Published: November 2008

One of the standard assumptions in queueing theory is that the system operates for an indefinite period of time. This assumption, however, is not valid for many practical situations where there is only a finite number of customers and each customer requires service only once. This paper studies such a finite queueing system in which all customers have the same time-dependent arrival probability function.

The method of solution allows one to “follow” each customer to record his arrival and departure times. While the study of the former is straightforward, the generating function of the departure time probabilities and the expected departure time of each customer are expressed in terms of the emptiness probabilities, which can be calculated from a recurrence relation. When the arrival probability function is independent of time, explicit results are obtained.
Mathematical Programming of Admissible Portfolios
Authors: Bawa Vijay S.
Published: November 2008

It is well known that when the distribution of portfolio returns is normal, the admissible set of portfolios for risk-averse investors with increasing and concave utility functions is the Markowtiz-Tobin mean-minimum variance admissible boundary: The admissible set is obtained by minimizing a convex quadratic function subject to linear constraints and can be obtained efficiently using Markowitz-Sharpe critical line algorithm. We show that the admissible set of portfolios for all investors (with increasing utility functions, including risk-averters, risk-seekers, risk-neutral and Friedman-Savage-type individuals) is the Markowitz-Tobin boundary plus a portion of the mean-maximum variance boundary. We propose a simple algorithm to obtain the mean-maximum variance boundary. Thus, our algorithm plus Markowitz-Sharpe algorithm obtains the admissible set of portfiolios for all investors.
Estimating the Relationship between Price and Time to Sale for Investment Property
Authors: Trippi Robert R.
Published: November 2008

This article develops an empirical model for estimating the relationship between selling price and length of time on market for a unique, large-ticket item. The model provides valuable information in the form of probability statements concerning the length of time to sale at any given price for a capital asset having a well-defined set of characteristics.
The Generalized Slack Variable Linear Program
Authors: Mattheiss T. H. , Widhelm William B.
Published: November 2008

The dilemma of when to cease analysis of a subproblem and go on to the next subproblem in convex programming is an especially difficult one. This paper views convex programming as an extension of linear programming and focuses attention on the analysis of a given subproblem. Specifically, if K = {x∣Ax ≤ b} is bounded with a nonempty interior and represents a residual unsearched region in some convex programming algorithm, what is (are) the “best” trial point(s) which can be selected? The generalized slack variable linear program (GSVLP) provides a mechanism for implementing trial point selection based on many strategies. Several implications of the L2 norm are revealed which are especially important in constraint deletion and rate of reduction of the hypervolume of the residual search region K.
Note—On the Use of Fictitious Bounds in Tree Search Algorithms
Authors: Bazaraa Mokhtar S. , Elshafei Alwalid N.
Published: November 2008

One of the strategies used by many tree search algorithms is to follow down one path in the tree until either a feasible solution is found or else fathoming occurs. For a minimization problem, the lower bounds calculated at various tree nodes tend to be well below the optimal value of the objective function, let alone the values of the successively improving upper bounds. As a result fathoming usually occurs only deep in the tree, and consequently, the search becomes rather lengthy. The purpose of this note is to describe a procedure for using and updating fictitious upper bounds in a systematic way so that optimal and suboptimal solutions can be obtained with a smaller computational effort. The procedure is illustrated by two examples: the traveling salesman problem and the quadratic assignment problem.
Note—On a Simultaneous Decision Model for Marketing, Production and Finance
Authors: Welam Ulf Peter
Published: November 2008

A previous study attempting to evaluate the benefits of coordination of marketing, production and finance decisions by Damon and Schramm is examined. It is noted that because of a flaw in the formulation of the marketing sector, the numerical results reported in this study are difficult to interpret. General issues in the design of experiments for evaluating functional coordination are also addressed.
Note—Nested Decomposition of a Dynamic Energy Model
Authors: Ho James K.
Published: November 2008

This paper reports computational experience in using a nested decomposition (staircase) algorithm to solve a version of Manne's linear programming model of U. S. energy options. Nested decomposition is found to be 28% to 52% faster than a direct simplex approach for our test problems. Effects of various computational strategies are also investigated. Our results indicate the applicability of nested decomposition to the important class of staircase linear programs arising from dynamic energy models.
Note—Effects of Substituting a Linear Goal for a Fractional Goal in the Goal Programming Problem
Authors: Hannan Edward L.
Published: November 2008

In a recent article in Management Science, Awerbuch et al. [Awerbuch, S., J. G. Ecker, W. A. Wallace. 1976. A note: hidden nonlinearities in the application of goal programming. Management Sci. 22 (8, April) 918–920] discuss the occurrence of nonlinearities in the application of goal programming and conclude that direct linearization may not be possible when goal constraints are of a fractional nature.
A Dynamic Programming Algorithm for Check Sorting
Authors: Murphy Frederic H. , Stohr Edward A.
Published: November 2008

The motivation for this paper is a problem faced by banks which process large volumes of deposited checks. The checks must be separated by bank number before shipment to the Federal Reserve or other banks. The sorting is usually accomplished using a reader-sorter which reads the magnetic ink characters on the checks and separates them into different “pockets.” This paper characterizes the optimal sorting strategy and describes an efficient procedure for finding the optimal solution for problems of the size generally found in practice. The algorithm is based on a two state dynamic programming recursion in which characterization theorems are used to drastically reduce the size of the state space and in which the storage requirements are minimal. The paper includes an analysis of computational experience and describes how the algorithm can be used in a real time environment with deadlines.
A Spike Collective Dynamic Factorization Algorithm for the Simplex Method
Authors: McBride Richard D.
Published: November 2008

A dynamic factorization algorithm is developed which uses a partition of the basis to permit the simplex method to be executed from a small working inverse and a small, sparse triangular submatrix of the basis. This partition is maintained dynamically using spike swapping in a way which seeks to keep the size of the working inverse as small as possible.

The algorithm is intended for use in solving general large scale linear programming problems. It is especially well suited for problems whose simplex basis has a small number of spikes after application of the Hellerman and Rarick P3 procedure.

Preliminary computation experience and direct comparison with Reid's sparsity-exploiting variant of the Bartels-Golub decomposition for LP bases indicate that a significant reduction is obtained with the dynamic factorization approach in the nonzero elements needed to represent the basis inverse. For all bases considered the number of nonzero elements needed to represent the inverse immediately prior to rein version is reduced by a factor of 1.7 to 20.
Note—On the Validity of the Analytic-Heuristic Instrument Utilized in “The Minnesota Experiments”
Authors: Zmud Robert W.
Published: November 2008

The results of this study indicate that the aspect of cognitive style addressed in “the Minnesota experiments” may pertain to a decision maker's choice of a planned or spontaneous solution strategy. Whether or not such a characterization is equivalent to an analytic-heuristic classification is beyond the scope of this note. It would appear that the analytic-heuristic cognitive dimension is a richer and more robust construct. Any MIS/cognitive style implications from “the Minnesota experiments” should therefore probably not be extended beyond the “planned vs. spontaneous” dichotomy that is apparently provided via the AHQ.
Note—On the Validity of the Analytic-Heuristic Instrument Utilized in “The Minnesota Experiments”: A Reply
Authors: Chervany Norman L. , Dickson Gary W.
Published: November 2008

Zmud [Zmud, R. W. On the validity of the analytic-heuristic instrument utilized in ‘The Minnesota Experiments’. Management Sci. (this issue).] has raised some important questions about the interpretation of the cognitive style results reported in “The Minnesota Experiments” [Dickson, G. W., J. A. Senn, N. L. Chervany. 1977. Research in management information systems: the Minnesota experiments. Management Sci. 23 (May) 913–923.]. His specific challenges are (1) the cognitive style instrument used in “The Minnesota Experiments” did not measure the “full breadth” of the analytic-heuristic dimension of cognitive style and (2) research studies must report instrument reliability and validity data to aid the reader in interpreting the results.
Communication: Box-Jenkins Rules, O.K.—Provided You Know It Makes Sense
Authors: Anderson Oliver D.
Published: November 2008

I have read the interesting contribution, “A Time Series Approach to Queueing Systems with Applications for Modeling Job-shop In-process Inventories,” by Harold J. Steudel and S. M. Wu, Management Sci., March 1977. But, as a defender of the faith, I feel it is incumbent on me to draw attention to the trace of Black-Box heresy, implicit in their analysis.
Communication: Dynamic Data System Modeling—Revisited
Authors: Steudel H. J. , Wu S. M.
Published: November 2008

In his comments on our paper, “A Time Series Approach to Queueing Systems with Applications for Modeling Job-Shop In-process Inventories,” Management Sci., March 1977, Oliver D. Anderson points out an inadequacy in the modeling results we presented on pp. 748–748. As a defender of the faith, he suggests that the culprit is our modeling strategy, a procedure he views as a Black-Box heresy. Since our modeling strategy is quite new and relatively unknown, especially compared to the Box-Jenkins (1) approach, Anderson's concluding remarks are not surprising.
Generalized Networks: A Fundamental Computer-Based Planning Tool
Authors: Glover F. , Hultz J. , Klingman D. , Stutz J.
Published: November 2008

This paper documents the recent emergence of generalized networks as a fundamental computer-based planning tool and demonstrates the power of the associated modeling and solution techniques when used together to solve real-world problems.

The first sections of the paper give a non-technical account, of how generalized networks are used to model a diversity of significant practical problems. To begin, we discuss the model structure of a generalized network (GN) and provide a brief survey of applications which have been modeled as GN problems. Next we explain a somewhat newer modeling technique in which generalized networks form a major, but not the only, component of the model.

The later sections give a technical exposition of the design and analysis of computer solution techniques for large-scale GN problems. They contain a study of GN solution strategies within the framework of specializations of the primal simplex method. We identify an efficient solution procedure derived from an integrated system of start, pivot, and degeneracy rules. The resulting computer code is shown, on large problems, to be at least 50 times more efficient than the LP system, APEX III.
Jointly Optimal Sales Commissions for Nonincome Maximizing Sales Forces
Authors: Weinberg Charles B.
Published: November 2008

In a multiproduct sales force, it has previously been shown that a commission structure based on equal fractions of each product's realized gross margin is jointly optimal if the sales force's goal is to maximize (expected) income and products are independent. Jointly optimal means that the sales force, which is presumed to be best able to estimate customer response to sales force activities, will simultaneously act to optimize its own objective and maximize corporate earnings. In this paper, it is shown that an equal gross margin commission system is also jointly optimal when products are interdependent and when the sales force does not have a goal of income maximization but has other objectives, such as minimizing time to reach a certain income goal or trading off time against money. Further, not all salespeople are required to have the same objective. For income maximizers an approach requiring less stringent assumptions than previously employed to show joint optimality is developed.
A Group Decision Process for Resource Allocation in the Health Setting
Authors: Nackel John G. , Goldman Jay , Fairman William L.
Published: November 2008

A group decision process is developed that allocates an available budget to health programs based on program effectiveness. The program effectiveness is measured by comparing alternative programs (at various funding levels) with respect to the weighted objectives of the health care organization. The organizational objectives are weighted by a constant-sum paired comparisons scaling technique. An integer programming formulation allows the decision makers to maximize program effectiveness within the given budgetary, resource, regulatory, and program structure constraints. The Effectiveness Evaluation-Resource Allocation Process (ERAP) is validated by actual decision making teams testing four processes for resource allocation. An example from the validation experiment is presented to demonstrate the process.
An Algorithm for Deploying a Crime Directed (Tactical) Patrol Force
Authors: Chelst Kenneth
Published: November 2008

This paper presents an algorithm for deploying a crime directed patrol force. The optimization problem is formulated as the allocation of N patrol among R high crime regions so as to maximize the weighted probability of a patrol intercept of a crime. The algorithm has full sensitivity analysis capabilities. This capability is critical because the model's input parameters include (1) crime weights, which in general will have a subjective component, (2) crime descriptive data, which are difficult to estimate, and (3) crime frequency data, which are likely to change with time. The paper presents an illustrative application of the algorithm. The resultant allocation is compared to a strategy which allocates patrol units in direct proportion to each region's total crime rate. The optimal allocation significantly increased the probability of an intercept.
Standard Setting in an Agency
Authors: Atkinson Anthony A.
Published: November 2008

The decision to hire an agent (manager) to transact business on the principal's (owner's) behalf reflects (and results) in the agent's use of specialized skills and information in managing the agency's (firm's) activities. This paper considers an agency relationship where the principal and the agent have differing beliefs regarding the uncertain economic returns to the agency and investigates the properties of standard setting and profit sharing as an incentive device. It is demonstrated that this incentive scheme causes the agent to use, without intervention by the principal, his presumably “superior” information in a manner which is mutually beneficial to the agent and the principal. It is also demonstrated that this incentive scheme is not inferior and is usually superior to a scheme in which the principal instructs the agent on which decision to implement.
A Framework for the Study of Work Settings
Authors: Dyer James S. , Millen Robert A. , Morse John J.
Published: November 2008

This paper describes the development of an operations management model and its implementation in a simulation mode in order to study the effects of alternative organizational designs and person/work assignment criteria on the utilization of the technological and human resources of a firm. The model treats personnel, technology, and organizational structure as simultaneous decision variables. This is in contrast to much of the current research and practice in organization design where one or two of these inputs are assumed fixed and the focus is on modifying the remaining inputs. The model explores the impact of the congruence or consistency among the three above variables on work system outcomes, thereby utilizing a contingency approach to the design and analysis of work settings. The model was implemented in a computer simulation mode in the context of a hypothetical firm to examine its utility as a resource planning tool. The results support the reasonableness of the framework and also provide insights into the behavior of productive systems that were not originally anticipated. In order to operationalize the model, it was necessary to define explicitly many relationships among the constructs that have been explored only tentatively before, if at all. By attempting to synthesize current organizational behavior and behavioral science literature into causal chains, necessary areas for future research became manifest that might not have been recognized otherwise. The paper concludes with a discussion of the value, limitations, and relevance of this approach to the study and design of work systems.
Analysis of the Time Indexed List Procedure for Synchronization of Discrete Event Simulations
Authors: Engelbrecht-Wiggans Richard , Maxwell William L.
Published: November 2008

Increasingly simulations have been required as supportive evidence to management of proposed system changes. It has long been recognized that the computer running costs of simulations are strongly influenced by the synchronization mechanism used.

Recently the time indexed list has been proposed as a superior alternative to existing event synchronization mechanisms for computer simulations. Intuition and empirical data indicate that such a mechanism should result in substantial savings of computer time; the mathematical results of this paper substantiate this.

This paper undertakes a rigorous mathematical and probabilistic analysis of the mechanism. Several different probabilistic event arrival models and arbitrary event schedule time distributions are considered. Results for several specific cases are calculated.

It is shown that the distribution is quite insensitive to the arrival process and is usually a simple integral of the interarrival time distribution. Next, the cost of scheduling new arrivals is calculated and shown to be approximately independent of the probabilistic details; the first order term depends only on the mean arrival rate. The robustness of these results, and the considerable savings in computer time realized, strongly recommend the time indexed list procedure.
Organizational Systematics: Taxonomic Lessons from Biology
Authors: McKelvey Bill
Published: November 2008

This paper argues that important lessons about the theory and method of organizational classification may be learned from biological systematics, defined as the “science of differences.” Three main components of systematics studies are discussed: (1) taxonomy, the development of a concept of organizational differences; (2) evolution, the tracing of the lineages of organizational form; and (3) classification, the development of procedures for identifying and placing organizational forms into classes. Furthermore, two kinds of classification are identified and several theories of classification are discussed. Systematics is seen as a necessary prerequisite to studies aiming to identify generalizable principles of organizational function and process. Finally, some implications for defining populations and drawing samples of organizations are noted, along with other implications for organization design and development and managerial practice.
A Direct Numerical Method for a Class of Queueing Problems
Authors: Wijngaard J.
Published: November 2008

In this paper an efficient numerical method is given for determining stationary probabilities and average cost in queueing systems where the customers arrive singly and the service mechanism is negative exponential. State dependent service and arrival rates and batch service are allowed. The method is based on the property that the matrix of the embedded Markov process which describes the number of customers at the moments of arrival is almost triangular.
An Analytical Investigation of Kotler's Competitive Simulation Model
Authors: Simon Hermann
Published: November 2008

Kotler's well-known dynamic competitive simulation model is investigated by means of analytical methods. Unlike the simulation studies run by Kotler the analytical investigation reveals (1) that the model produces changes in price elasticity over time, which do not appear economically plausible, and (2) that the representation of competitive relations is highly questionable. It is shown that these properties of the model lead to consequences for the optimal pricing and promotion strategy which can hardly be considered as reasonable: Both the optimal prices and the optimal promotion efforts increase continuously over time and—within a certain period of time—the optimal prices under competitive conditions are greater than the respective prices under monopolistic conditions.
The Nonstationary Infinite Horizon Inventory Problem
Authors: Morton Thomas E.
Published: November 2008

By allowing disposal in each period, a sequence of upper and lower bounds on the infinite horizon nonstationary periodic review inventory problem is obtained. The nth bounds depend only on knowledge of the demand distributions in the first n periods, giving planning horizon results. In general, calculation of any bound requires solution of an ordinary n period problem, although for the proportional cost case the solution for n = 1 and good approximations for n = 2 may easily be given. The upper and lower relative cost and policy bounds are monotonic in the horizon length and, under mild conditions, converge to a unique infinite horizon solution. An analytic expression is given for the asymptotic convergence rate, which is geometric even for the undiscounted case. The formulation given here is a concrete example of the general planning horizon formulation for infinite horizon dynamic programming models set forth in [Morton, T. 1975. Infinite horizon dynamic programming models—a planning horizon formulation. Carnegie-Mellon University Management Sciences Research Report No. 372, August (to appear in Operations Res.)].
An Evaluation of the Effectiveness of Dialectical Inquiry Systems
Authors: Cosier Richard A. , Ruble Thomas L. , Aplin John C.
Published: November 2008

Numerous quantitative planning models have been developed and successfully applied to facilitate the solutions of relatively well-structured problems. Unfortunately, qualitative models and techniques, particularly those applicable to ill-structured problems, are less well developed. One technique advocated by some researchers is the Dialectical Inquiry System (DIS), a planning process premised on Hegelian logic. Limited field studies have reported generally positive reactions toward DIS, but have not demonstrated that the DIS technique leads to improvement in objective performance or to more effective plans. This study reports the results of a controlled methodology that examines the effects of DIS on performance and participant attitudes. The results reveal that even though the conflict component of DIS was perceived as more useful in one instance, in general the DIS did not lead to significantly better objective performance when compared to alternative planning approaches. Given the risk and cost involved in organizational planning, further research should be conducted to evaluate the merit of the DIS.
Note—Sufficient Conditions for Maintaining a Balanced University Budget
Authors: Schinnar Arie P.
Published: November 2008

In a recent article, in Management Science, W. F. Massy [Massy, W. F. 1976. A dynamic equilibrium model for university budget planning. Management Sci. 23 (3, November) 248–256.] outlines an interesting difference equation model of the Stanford University budget system. He proceeds then to solve for first and second order (i.e., short-term) balanced budget conditions. However, Massy's assertion that the balanced budget requirement cannot be modeled “effectively” for an extended time horizon is inaccurate. This note shows that such long-range solutions are readily available from the eigenstructure of his model. We derive simple sufficient conditions for maintaining balanced university budgets. Related issues of balanced budget attainability, empirical correspondence, and policy feasibility are also discussed.
Note—A Goals/Values Solution to Mandatory Retirement Age for Tenured Faculty: An Application of Situational Normativism
Authors: Shakun Melvin F. , Sudit Ephraim F.
Published: November 2008

The controversial issue of mandatory retirement at age 70 for tenured faculty as considered by Congress is discussed using a goals/values analysis. A solution is proposed which permits such faculty to remain on active tenured status between ages 65 and 70 on a half-time basis only.
Note—An Interpretation of Fractional Objectives in Goal Programming as Related to Papers by Awerbuch, et al., and Hannan
Authors: Soyster A. L. , Lev B.
Published: November 2008

In this note we consider the validity of substituting a linear goal for a fractional goal in a mathematical program and provide a simple geometric interpretation that contrasts the essential differences between the two programs.
Forecasting Political Risk
Authors: Bunn D. W. , Mustafaoglu M. M.
Published: November 2008

An applied procedure is preserved in this paper which has been used to forecast some of the political risks ars oil company faces from investment in an overseas developing country, e.g., expropriation, taxation, price and production controls. The procedure makes use of a panel of experts, but requires, their estimates to be formulated in a way that takes explicit account of the precursive conditions for each of the adverse actions that the host country could take. A Bayesian method is used to derive the composite probabilities, for the political risk events under consideration and a Cross-Impact Analysis then provides s means of overall scenario generation.
Socially and Individually Optimal Control of Arrivals to a GI/M/1 Queue
Authors: Stidham Shaler
Published: November 2008

We study the problem of controlling the arrivals to a single-server queue with general interarrival-time distribution and exponential service-time distribution (a GI/M/1 system). Control is exercised by accepting or rejecting arriving customers or by charging entering customers a toll or entrance fee. An entering customer receives a reward, representing his utility of service. The rewards vary randomly from customer to customer. There is a holding cost, which is a convex function of the number of customers in the system. We compare socially and individually optimal entering policies when the decision horizon is finite, specifically, when the system must close after n future arrivals. There may be a terminal reward or cost, incurred as a function of the number of customers present at the end of the horizon, representing, for example, the holding cost incurred until all of them are served. We show that a socially optimal policy is less likely to accept a customer than an individually optimal policy, and both policies are less likely to accept as the number of customers already present increases, the horizon length increases, or the discount rate decreases. It is shown that, contrary to intuition, the optimal congestion toll cannot be monotonic in the number of customers present. These properties carry over to the infinite horizon, both with and without discounting, except that in the latter case, in which the criterion is long-run average net benefit, the toll can be monotonic. Implications for the study of rush-hour or peak-load phenomena in various congestion systems are briefly discussed.
Simulation of Decentralized Planning in Two Danish Organizations Using Linear Programming Decomposition
Authors: Christensen John , Obel Börge
Published: November 2008

This paper describes the results of two studies where decentralized planning has been simulated. The coordination mechanisms employed were based on the Dantzig-Wolfe decomposition algorithm, and the Ten Kate decomposition algorithm, which are price directive and budget directive planning procedures, respectively. The importance of the results is that the data and the structure of the two planning problems come from real organizations—a cooperative slaughterhouse and a forecast model for Danish agriculture. Thus conclusions based on using a price-directive and a budget-directive planning method to simulate decentralized planning in these organizations have relevance to the potential value of using such methods in real organizations. The main conclusions concern the importance of and the difficulties in finding good starting strategies for the two methods and the impact of the organizational structure on the rate of improvement for the methods.
Priority Ranking and Consensus Formation
Authors: Cook Wade D. , Seiford Lawrence M.
Published: November 2008

This paper investigates the problem of combining ordinal preferences, expressed as priority vectors, to form a consensus. An axiomatic structure relating to the concept of distance between rankings is developed, uniqueness of the distance measure is proven and its form derived. Adopting the median ranking as a form of consensus, it is shown that this ranking can be determined, in the case of complete rankings, by solving a certain assignment problem. The results are compared and contrasted to earlier work due to Arrow, Kendall, Kemeny and Snell, and Bogart.
Optimal Aggregation of Multi-Item Production Smoothing Models
Authors: Gaalman G. J.
Published: November 2008

This paper presents a method for aggregating multi-item versions of the HMMS model. Necessary conditions are used to reduce the multi-item model to a one-item model. The aggregation technique makes use of the structural properties of the inventory-production part of the model and can be performed regardless the structure of the work force-total production part. Disaggregation of the optimal decisions of the aggregated model gives the optimal decisions of the multi-item model.
Municipal Resource Allocation: Minimizing the Cost of Fire Protection
Authors: Seward Samuel M. , Plane Donald R. , Hendrick Thomas E.
Published: November 2008

Municipal decision-makers face the difficult task of determining the amount of funds to be allocated for fire department services. This decision affects both the insurance class of the city and the total cost of fire protection. Total fire protection cost is the sum of the tax dollars spent for fire department services (public expenditures) and fire insurance premiums paid by residents and businesses (private expenditures). This paper presents an integer programming model to minimize the sum of these two costs. Since insurance costs reflect only property losses the model does not explicitly include the consequences of loss of life or injury. Since the protection of persons is an important part of the fire protection mission it is important to realize that the model produces a lower bound for the value and level of fire department services. We go on to show how the results can be used to provide a method of inputing a life hazard benefit for decisions which produce more fire protection than suggested by the cost-minimizing model. The model was applied in Boulder, Colorado; the ways in which the results may be incorporated into the political decision process are also described.
Note—A New Approach to Urban Modelling
Authors: Brotchie John F.
Published: November 2008

This note describes a different approach to urban modelling, resulting in a new, more general form of model. The model can be used for prediction, prescription, explanation, or evaluation; or to distinguish between the objectives of individuals, the planning authority, and the community. It is utility maximizing, and also entropy maximizing, and includes diversity of activities in zones. It relates land use and transport decisions and allows dispersal of urban activities to be analysed.
Note—On “Further Results on Planning Horizons in the Production Smoothing Problem”
Authors: Johnson Robert E. , McClain John O.
Published: November 2008

Notes on paper [Lee, D. R., D. Orr. 1977. Further results on planning horizons in the production smoothing problem. Management Sci. 23 (5) 490–498.] pointing to some ambiguities and errors.
Cost-Volume-Profit Analysis Adjusted for Learning
Authors: McIntyre E. V.
Published: November 2008

A model is developed for cost-volume-profit analysis which incorporates a nonlinear cost function to express the effects of employee learning. Sensitivity analysis is applied to the model to assess the impact of estimation errors in the learning rate and steady-state production time on estimated profit and break-even quantities. The paper also examines the effects on the model of (1) alternative accounting treatments of production-related costs, and (2) continuous learning due to employee turnover.
Dynamic Programming Models of the Nonserial Critical Path-Cost Problem
Authors: Esogbue Augustine O. , Marks Barry R.
Published: November 2008

One of the major contributions to the planning and management of Research and Development organizations is the evolution of methods for dealing with PERT-Cost or CPM-Cost problems. Classically however, variations of the critical path-cost (CPM-Cost) problem, arising when different cost duration relationships are assumed, have been mostly studied via techniques other than dynamic programming. If the precedence relations possess a serial structure, one can develop two essentially equivalent dynamic programming formulations, of the resource allocation variety, by minimizing either the project cost or the completion time. When nonserial precedence relationships are involved, this problem cannot be solved by routine invocation of conventional dynamic programming formulations or algorithms. The intent of this paper is to show that efficient nonserial dynamic programming formulations can be developed for several complex nonserial CPM-Cost problem situations. In particular, the project time minimization procedure results in less complex dynamic programming models and is thus employed in this paper. Three recent computational reduction techniques based primarily on the introduction of the artifice of pseudo-tasks and pseudo-stages are invoked to treat different variations of this essentially nonserial critical path-cost problem. Considerable savings in computational requirements are achieved by consolidating all phases preceding a junction node prior to the invocation of the dynamic programming procedure. The advantages of these approaches over existing mathematical programming methods include their ability to handle nonlinear cost functions and constraints, as well as their highly efficient parametrization capabilities. Further, the complexity of the dynamic programming formulation does not, unlike other methods, increase with the number of phases (tasks) but only with the degree in which the additional tasks change the structure of the precedence relations.
Means and Variances of Stochastic Vector Products with Applications to Random Linear Models
Authors: Brown Gerald G. , Rutemiller Herbert C.
Published: November 2008

Applications in operations research often employ models which contain linear functions. These linear functions may have some components (coefficients and variables) which are random. (For instance, linear functions in mathematical programming often represent models of processes which exhibit randomness in resource availability, consumption rates, and activity levels.) Even when the linearity assumptions of these models is unquestioned, the effects of the randomness in the functions is of concern. Methods to accomodate, or at least estimate for a linear function the implications of randomness in its components typically make several simplifying assumptions. Unfortunately, when components are known to be random in a general, multivariate dependent fashion, concise specification of the randomness exhibited by the linear function is, at best, extremely complicated, usually requiring severe, unrealistic restrictions on the density functions of the random components. Frequent stipulations include assertion of normality of independence-yet, observed data, accepted collateral theory and common sense may dictate that a symmetric distribution with infinite domain limits is inappropriate, or that a dependent structure is definitely present. (For example, random resource levels may be highly correlated due to economic conditions, and non-negative for physical reasons.) Often, an investigation is performed by discretizing the random components at point quantile levels, or by replacing the random components by their means-methods which give a deterministic “equivalent” model with constant terms, but possibly very misleading results. Outright simulation can be used, but requires considerable time investment for setup and debugging (especially for generation of dependent sequences of pseudorandom variates) and gives results with high parametric specificity and computation cost. This paper shows how to use elementary methods to estimate the mean and variance of a linear function with arbitrary multivanate randomness in its components. Expressions are given for the mean and variance and are used to make Tchebycheff-type probability statements which can accomodate and exploit stochastic dependence. Simple estimation examples are given which lead to illustrative applications with (dependent-) stochastic programming models.
Maximum Throughput in Finite-Capacity Open Queueing Networks with Product-Form Solutions
Authors: Schweitzer Paul J.
Published: November 2008

A finite-capacity open queueing network with independent balance is considered. These are systems with customers undergoing stages of service, where the rate of flow into a state due to a customer entering a stage of service is equal to the flow out of that state due to a customer leaving that stage of service. Such systems have the convenient property that the steady-state probability of a given configuration of customers factors into a product of terms, each term involving the configuration at one service center. If service rates are constant for each customer class, and excess arrivals are discarded, then the following two results hold: (1) The maximum possible output rate for the finite-capacity case equals the value of the customer arrival rate which just saturates the slowest server in the infinite-capacity case. (2) An infinite-capacity network can have a strictly greater output rate than the corresponding finite-capacity network, no matter how large the capacity.
A Feedback Model for Automated Real Estate Assessment
Authors: Carbone Robert , Longini Richard L.
Published: November 2008

Pressing changes are needed in the administration of real estate taxation that will not only ensure that all properties be assessed accurately and equitably, but will enable taxpayers to perceive that they are being treated fairly. In this paper, we examine what properties an automated mass appraisal system should exhibit so as to meet efficacy, equity and public acceptability criteria. A new automated system designed on the basis of these properties which utilizes feedback control and pattern recognition concepts is presented. Results of an empirical study using Pittsburgh data supports the feasibility of the proposed system.
Classification for Market Segmentation: An Improved Linear Model for Solving Problems of Arbitrary Origin
Authors: Darden William R. , Perreault William D.
Published: November 2008

A current problem in marketing research involves the use of scale measures of consumer characteristics to develop homogeneous classifications of consumers. The quality of these classification efforts is influenced by the nature of the scales, which are frequently characterized by arbitrary origin and variance. This paper draws on recent developments in classification methodology to propose and illustrate an integrative classification methodology which overcomes some of the current problems of classification approaches.
Production Smoothing Under Piecewise Concave Costs, Capacity Constraints and Nondecreasing Requirements
Authors: Korgaonker M. G.
Published: November 2008

The production smoothing problem with known demands that are assumed to increase with time is treated. The production and inventory costs are concave. The cost of increasing production from one period to the next is a concave function of the increase; similarly, the cost of decreasing production is a concave function of the decrease. Backlogging is not permitted. In each period, a fixed production capacity that does not vary with time is available. The problem it similar to that discussed by Zangwill, except for the important difference of capacity constraint.

Feasible production plans are partitioned into sets on the basis of production differences from period to period—those with production increases in all N periods, those with a decrease only in the final period, etc. A minimum cost plan is an extreme point of one of these sets. We show that an extreme point plan is such that in between periods with zero inventory there is at most one sequence of periods when production is neither zero nor capacity and within these periods, production does not change.

An algorithm is proposed for generating extreme point production plans. It is shown that finding the minimum cost production plan is equivalent to finding the shortest route through an acyclic network of extreme point production plans. The approach put forth enables a complete solution to the problem discussed.
A Modified Benders' Partitioning Algorithm for Mixed Integer Programming
Authors: McDaniel Dale , Devine Mike
Published: November 2008

As applied to mixed-integer programming, Benders' original work made two primary contributions: (1) development of a “pure integer” problem (Problem P) that is equivalent to the original mixed-integer problem, and (2) a relaxation algorithm for solving Problem P that works iteratively on an LP problem and a “pure integer” problem. In this paper a modified algorithm for solving Problem P is proposed, in which the solution of a sequence of integer programs is replaced by the solution of a sequence of linear programs plus some (hopefully few) integer programs. The modified algorithm will still allow for taking advantage of any special structures (e.g., an LP subproblem that is a “network problem”) just as in Benders' original algorithm. The modified Benders' algorithm is explained and limited computational results are given.
Independence and Calibration in Decision Analysis
Authors: Harrison J. Michael
Published: November 2008

An individual is said to be potentially miscalibrated if he is not sure whether his future subjective probability assessments will agree with observed frequency. Alternately, the individual is said to be uncertain about his own calibration. It is argued that such a person will never perceive any two events as (probabilistically) independent, in the same sense that an ignorant person does not perceive events as certain. Uncertainty about one's own calibration does not prevent rational behavior in the decision theoretic sense, but it may make much more difficult the process of translating decision theoretic principles into practical procedures for analysis of real decision problems.
An Approximation to Queueing Systems with Interruptions
Authors: Fischer M. J.
Published: November 2008

Queueing systems with interruptions serve as models for a variety of situations occurring in every day life. Usually, for each type of interruption, a separate queueing analysis is required. In this paper we present a single queueing model which can be used to analyze many such systems. The model is in the form of an approximation that is based upon several parameters, which reflect the particular queueing system under consideration. Applications to queueing systems with priorities and breakdowns are given in the paper.
Modeling Facility Location Problems as Generalized Assignment Problems
Authors: Ross G. Terry , Soland Richard M.
Published: November 2008

A variety of well-known facility location and location-allocation models are shown to be equivalent to, and therefore solvable as, generalized assignment problems (GAP's). (The GAP is a 0-1 programming model in which it is desired to minimize the cost of assigning n tasks to a subset of m agents. Each task must be assigned to one agent, but each agent is limited only by the amount of a resource, e.g., time, available to him and the fact that the amount of resource required by a task depends on both the task and the agent performing it.) The facility location models considered are divided into public and private sector models. In the public sector, both p-median and capacity constrained p-median problems are treated (In the p-median problem exactly p of n sites must be selected to provide service to all n. Each site has an associated weight, e.g., its population, and it is desired to minimize the weighted average distance between the n sites and their respective service sites. The capacity constrained p-median problem differs only in that there is an upper limit on the sum of the weights of the sites served by each service site.) In the private sector we consider both capacitated and uncapacitated warehouse location problems in which each customer's demands must be satisfied by a single warehouse. In addition, we show how certain types of constraints limiting the site and capacity combinations allowed can be incorporated into these models through their treatment as GAP's. An existing algorithm for the GAP is modified to take advantage of the special structure of these facility location problems, and computational results are reported.
Note—A Graphical Aid for Determining Optimal Inventories in a Unit Replenishment Inventory System
Authors: Silver Edward A. , Smith Stephen A.
Published: November 2008

This note provides the methodology to construct a set of indifference curves that permit the exact determination of the optimal inventory level in a system where items are restocked one at a time and unsatisfied demand is lost. An illustrative set of curves is shown.