bluuebunny/crossref_metadata_2025 huggingface dataset:
The Formation of Key Marketing Variable Expectations and Their Impact on Firm Performance: Some Experimental Evidence
Authors: Glazer Rashi , Steckel Joel H. , Winer Russell S.
Published: October 2008

The expectation formation process has been extensively studied by economists, particularly for macroeconomic variables. However, no prior research has examined how expectations are formed and used in the context of marketing forecasting. In this paper, we use data from a simulated competitive environment (1) to examine the expectation formation process for important marketing variables such as market size, number of competing products, and average industry price, and (2) determine how inter-firm variation in the formation process affects performance. Using the Rational Expectations Hypothesis as a framework, we find that decision-makers' forecasts tend to be efficient, i.e., utilize all relevant available information, but are biased. Other key findings suggest that degree of firm rationality in the forecasting process as well as the level of forecasting accuracy are positively related to performance.
Note—The Factor Structure of Multidimensional Response to Marketing Stimuli: A Comparison of Two Approaches
Authors: Srinivasan V. , Abeele P. Vanden , Butaye I.
Published: October 2008

Factor Analysis is commonly used to reveal the structure underlying the multiple attributes that describe marketing stimuli. This paper provides a theoretical investigation and an empirical comparison of two approaches to Factor Analysis that are based on two different sources of variation in the input data. The “Among” Analysis is based on variation across marketing stimuli, while the “Within” Analysis is based on variation across individuals responding to the same marketing stimulus. We identify conditions under which one approach is superior to the other. If both approaches are applicable, we recommend the use of the “Total” analysis that pools the variation across stimuli and individuals. An empirical study, in the context of consumers' cognitive response to ads, shows that the Among Analysis results can be seriously distorted by differential familiarity with the ads so that it is important to partial out the spurious effects of familiarity.
Commentary
Authors: Hughes Donald A.
Published: October 2008

Commentary to Farris, P., J. Olver, C. De Kluyver. 1989. The relationship between distribution and market share. Marketing Sci. 8 107–128.
The Metric Quality of Ordered Categorical Data
Authors: Srinivasan V. , Basu Amiya K.
Published: October 2008

We quantify the information loss incurred by categorizing an unobserved continuous variable (X) into an ordered categorical scale (Z). The continuous variable is conceptualized as true score (τ) (which varies across individuals) plus random error (ϵ), with both components assumed to be normally distributed. The index of metric quality is operationalized as r2 (Z, τ)/r2(X, τ), where r2, the squared correlation coefficient, is a descriptive measure of the power of X or Z to predict τ. The index is useful in defining limits on explanatory power (population R2) in multiple regression models in which an ordered categorical variable is regressed against a set of predictors. The index can also be used to correct correlations for the effects of ordered categorical measurement.

The index of metric quality is extended to the case when several ordered categorical scales are averaged as in the multi-item measurement of a construct. We prove theoretically that as long as the error variance is “large,” the index of metric quality for the average Z̄ of ordered categorical scales goes to 1 as the number of scales becomes “large.” The index for averaged data is useful in answering questions such as whether the measurement of a construct by averaging three 5-point scales is better or worse than the measurement obtained by averaging five 3-point scales. The results indicate that the loss of information by marketing researchers' ad hoc use of Z as opposed to the more refined X is small (<10%) when the Z scale is well designed with at least five categories. The loss would be even smaller when a multi-item based Z̄ is employed.
Note—An Economic Rationale for Door Prizes
Authors: Young Allan Richard
Published: October 2008

If buyers face transaction costs, a workable pricing scheme might require door prizes in addition to a per-unit price. The door prize compensates customers for the transaction expense, and the seller earns positive profit because the price exceeds the cost of inframarginal units.
Perceptual Mapping Using Ordered Logit Analysis
Authors: Katahira Hotaka
Published: October 2008

This study is to present a new method for constructing a perceptual map based on logit analysis. This is an extension of the explosion logit model of an individual choice to a problem of perceptual mapping giving rise to advantages over existing methods in various aspects.

Firstly, input data format is flexible and user-friendly. Unlike traditional methods which typically requires a total dissimilarity ordering on all the pairs of the objects, it allows a partial ordering to any rank depth and a ‘pivot’ ordering which gives a dissimilarity ordering of objects with respect to a specific ‘pivot’ or ‘anchored’ object. Secondly, it introduces the concept of an evoked set into perceptual mapping and allows a respondent to make judgments only within his/her evoked set. This, together with the first point, contributes to the reduction of the respondents' burden and the data noise.

Thirdly, Monte Carlo experiments have revealed that our ML estimates give a considerably better fit to data than ALSCAL, one of the most widely used algorithms of MDS. Particularly worth noting is that our method using the data ranked only up to the top two thirds gives as good a fit as ALSCAL using totally ordered data. Although not exploited here, opening up a way for statistical inference in nonmetric MDS would be yet another advantage.

An empirical application is made to a Canadian car market for illustration.
New Models from Old: Forecasting Product Adoption by Hierarchical Bayes Procedures
Authors: Lenk Peter J. , Rao Ambar G.
Published: October 2008

A method for obtaining early forecasts for the sales of new durable products based on Hierarchical Bayes procedures is presented. The Bass model is implemented within this framework by using a nonlinear regression approach. The linear regression model has been shown to have numerous shortcomings. Two stages of prior distributions use sales data from a variety of dissimilar new products. The first prior distribution describes the variation among the parameters of the products, and the second prior distribution expresses the uncertainty about the hyperparameters of the first prior. Before observing sales data for a new product launch, the forecasts are the expectation of the first stage prior distribution. As sales data become available, the forecasts adapt to the unique features of the product. Early forecasting and the adaptive capability are the two major payoffs from using Hierarchical Bayes procedures. This contrasts with other estimation approaches which either use a linear model or provide reasonable forecasts only after the inflection point of the time series of the sales. The paper also indicates how the Hierarchical Bayes procedure can be extended to include exogenous variables.
Unobservable Effects and Business Performance
Authors: Jacobson Robert
Published: October 2008

While “unobservable” factors such as corporate culture, access to scarce resources, management skill, and luck can be postulated to be principal determinants of business success, their effects are all but ignored in studies of business performance. This study, making use of the PIMS data base, reports empirical evidence indicating that failure to control for unobservable factors influencing profitability both biases and exaggerates the effect of strategic factors. Indeed, the influence of unobservable factors is so pervasive as to invalidate many of the conclusions drawn from studies failing to control for their effects.
Can Bait and Switch Benefit Consumers?
Authors: Gerstner Eitan , Hess James D.
Published: October 2008

We present a model that leads to an equilibrium with characteristics similar to the following stylized facts observed in retail markets: (a) Retailers advertise only selected brands; (b) Often low priced advertised brands are understocked; (c) In-store promotions are biased towards more expensive substitute brands. Together these practices constitute illegal bait and switch. Is this phenomenon necessarily harmful to consumers and to the economy? We show that bait and switch can benefit consumers because utility is created through in-store promotions and price competition is enhanced. This suggests that the FTC investigate further its ban on bait and switch.
Demand Complementarities, Household Production, and Retail Assortments
Authors: Betancourt Roger , Gautschi David
Published: October 2008

This paper presents a formal model of retail demand, based upon a household production framework, that permits rigorous analysis of retail assortments. The model captures the essential shifting of distribution costs between retailers and consumers that manifests itself in retailers' provision of distribution services for consumers. We apply the model to define rigorously conventional retailing concepts, such as assortment breadth and depth, and to explain the appearance of certain well-known phenomena such as market-basket pricing, nonprice retail competition, and the incentives for retail agglomerations to form. Throughout, distribution services play a critical role in binding together the analytical model and the diverse reality giving rise to retail assortments.
Untangling the Effects of Purchase Reinforcement and Advertising Carryover
Authors: Givon Moshe , Horsky Dan
Published: October 2008

The dynamic evolvement of market share of a brand in a frequently purchased product category can be driven by two effects, purchase reinforcement, and advertising carryover. The first depends on the actual experience with the brand while the second on the retention of its producer's messages. We present a model to estimate simultaneously the relative magnitude of these two forces. The model also formally treats the issue of temporal aggregation. Our empirical results with several product categories indicate that for monthly and bi-monthly measurement periods, purchase reinforcement dominates carryover of advertising in affecting the evolution of market share.
A Knowledge-Based System for Advertising Design
Authors: Burke Raymond R. , Rangaswamy Arvind , Wind Jerry , Eliashberg Jehoshua
Published: October 2008

In recent years, artificial intelligence research has provided new tools and techniques for marketing model builders. These tools, when combined with problem-solving knowledge from a specific domain, can be used to create expert systems. This methodology is most applicable in semistructured problem domains where the key relationships are logical rather than numerical and problem-solving knowledge is incomplete. One such problem in marketing is advertising design.

In this paper, we describe the application of expert system techniques to the development of ADCAD, a system designed to assist advertisers of consumer products with the formulation of advertising objectives, copy strategy, and the selection of communication approaches. The paper highlights the assembly of ADCAD's knowledge base of ad design heuristics from multiple sources of published research and practitioner expertise and describes its structure and content. We discuss the procedures and obstacles associated with building, implementing, and validating such an expert system. Our experiences with ADCAD suggest that knowledge-based systems have significant potential for the consolidation and integration of marketing knowledge as interactive input for decision makers. We conclude by noting several avenues for the future development of advertising expert systems.
Improving Channel Coordination Through Franchising
Authors: Lal Rajiv
Published: October 2008

In this paper, we explore the role of franchising arrangements in improving coordination between channel members. In particular we focus on two elements of the franchising contract, namely, the royalty structure and the monitoring technology. We begin with a simple analysis where a manufacturer distributes its product through a retailer and the retail demand is affected by the retail price and the service provided by the retailer. In this context we show that neither royalty payments nor monitoring are needed for full coordination. We then extend the model to allow for free riding by franchisees and show that although monitoring helps affect the behavior of the franchisees, royalty payments are still unnecessary to coordinate the activities of the franchisor and the franchisees. Finally, we show that in environments where factors affecting retail sales are controlled by both the franchisor and the franchisee, royalty payments provide the necessary incentives for the franchisor while monitoring systems are used to ensure that franchisees also behave in the best interest of the channel. Our general results are found to be consistent with those in Brickley and Dark (1987) and Norton (1988), who conclude that franchising is affected by principal-agent problems. Our theory finds special support in the work of Lafontaine (1988) where it is concluded that the incidence of franchising is related to cost of monitoring and the importance of franchisor investments.
Minimum Graphs of Specified Diameter, Connectivity and Valence. I
Authors: Klee Victor , Quaife Howard
Published: October 2008

The minimum order (number of nodes) is determined for e-connected graphs of valence ≥c and diameter ≥d. The question arises naturally from reliability and defense considerations that may enter into the design of an armed communication network.
Theory of Maintained Systems: Distribution of Time to First System Failure
Authors: Barlow Richard E. , Proschan Frank
Published: October 2008

The distribution of time to first system failure is considered for systems whose repairable components are separately maintained. It is shown that if repairable components have exponential failure law, repair distributions have decreasing repair rate, and nonrepairable components have increasing failure rate, then the distribution of time to first system failure is new better than used. Improved bounds are given for the exponential repair case.
Bounding Global Minima
Authors: Mancini Louis J. , McCormick Garth P.
Published: October 2008

Conditions are given which are sufficient to prove the existence of a unique unconstrained minimizer in a convex compact set. An exact formula is given for the amount by which a value of the function exceeds its global minimum.
Long Monotone Paths in Abstract Polytopes
Authors: Adler I. , Saigal R.
Published: October 2008

As is now well known, the simplex method, under its various pivoting rules, is not a “good algorithm” in the sense of J. Edmonds, i.e., the number of pivots needed to solve a given linear programming problem by this method cannot be bounded by a polynomial function of the number of rows and columns defining it, Klee, Minty and Jerosolow have developed methods for constructing examples of such linear programs on polytopes. The aim of this paper is to extend these constructions to abstract polytopes.
On Random Walks and Stable GI/G/1 Queues
Authors: Lemoine Austin J.
Published: October 2008

Let X, X1, X2, … be independent and identically distributed random variables with E{X} < 0, let S0 ≡ 0, Sn = X1 + ⋯ + Xn for n ≥ 1, and M = sup(Sn, n ≥ 0). If r > 0 then a well-known result in random walk theory slates that M has a finite moment of order r if and only if the positive part of X has a finite moment of order r + 1. Utilizing the intimate relationship between random walks and single server queues, this paper presents a new and simple proof for this basic result. Identities involving the distribution functions and the integer moments of M and X are then derived by simple, probabilistic arguments. Bounds are then obtained for the expected values of some important variables associated with the random walk (Sn, n ≥ 1). All of these random-walk results are applied to the stable queue GI/G/1, and some standard queueing results are subsequently obtained in an effortless manner.
The Recruitment Trajectory Corresponding to Particular Stock Sequences in Markovian Person-Flow Models
Authors: Feichtinger Gustav , Mehlmann Alexander
Published: October 2008

Preston (Preston, S. H. 1970. The birth trajectory corresponding to particular population sequences. Theoret. Population Biol. 1 346–351.) treats the following problem: Given an exponential or linear sequence of population numbers, and assuming constant mortality and zero net migration, what birth sequence is required? In the following paper this question is investigated for more general person-flow models, namely for Markovian manpower models in the sense of Young & Almond (see Bartholomew [Bartholomew, D. J. 1973. Stochastic Models for Social Processes. Wiley, London.]). Considering the linear population-dynamic (Leslie) model as a special case, most of the results obtained by Preston may be derived. The general problem “what sequence of recruitment numbers is capable of generating a desired stock trajectory” is analyzed by means of inhomogeneous Markov chains. This technique yields also a new approach to the limiting behaviour of some manpower systems.
The General Solution of a Finite System of Linear Inequalities
Authors: Galperin A. M.
Published: October 2008

A simple procedure for the computation of a basis of the general solution of a finite system of linear inequalities is presented. It generalizes the well-known Burger's algorithm for homogeneous systems.
A Control Chart Model and a Generalised Stopping Problem for Brownian Motion
Authors: Bather J. A.
Published: October 2008

The ideas described in this paper arise from a particular investigation of the general question: when information relevant to a sequence of decisions is collected by statistical sampling, is it worth controlling the local rate of sampling to provide more accurate information at certain times? Here, the value of any sampling and decision procedure is measured by the long-term average of all information and decision costs. The model is concerned with the design of a control chart and it leads to a Markovian decision problem with three possible actions at each point of the state space. The determination of an optimal policy depends on the solution of a complicated free boundary problem. Although there is a well-established relation between the basic partial differential equation of this problem and Brownian motion, the investigation raises many questions, both analytical and probabilistic, which remain to be answered. However, some limited results are obtained by examining special formal solutions. In spite of serious gaps in the general theory, it is possible to establish useful bounds on the minimum average cost which can be attained.
Extension of the Generalized Complementarity Problem
Authors: Saigal Romesh
Published: October 2008

Given a closed convex cone K in the n-dimensional Euclidean space ℝn, its polar cone K+ and a point-to-set mapping f from K to subsets of ℝn, the extension of the generalized complementarity problem we consider is to find a vector x in K such that there is a y in f(x) ∩ K+ with xTy = 0. We prove, using directly a fixed point theorem, with an appropriate condition on f, that the above problem has a solution. We also show that this condition is satisfied by a certain class of mappings f which are encountered in various applications. We further establish “the basic theorem of complementarity” for this problem, which thus extends the previous existence results to the case where K is a pointed cone.
Delbert Ray Fulkerson (August 14, 1924–January 10, 1976)
Authors: Billera Louis J. , Lucas William F.
Published: October 2008

In memoriam of Delbert Ray Fulkerson.
On Existence of Overtaking Optimal Trajectories Over an Infinite Time Horizon
Authors: Brock W. A. , Haurie A.
Published: October 2008

The optimal control problem on an infinite horizon is considered in the case where there is no discounting. Under general convexity assumptions the existence of overtaking optimal and of weakly overtaking optimal trajectories is established. Convergence properties of optimal trajectories toward an optimal steady state are also proved.
On Paths Generated by Fixed Point Algorithms
Authors: Saigal R.
Published: October 2008

This paper considers algorithms that compute fixed points (or more generally solve equations) which are based on complementary pivoting. These algorithms, starting with a map f0 and its fixed point x0, deform ft to f∞ = f as t goes from 0 to ∞, and follow the path xt of fixed points of ft. In this paper we study these paths. In particular, we treat some special applications of these algorithms from a global point of view, and thus look at the behavior and properties of these paths sufficiently far from the solution. Our methods are motivated by methods of global analysis.

We show that in many implementations of these algorithms the path can be specified. These include the cases when the mapping is linear and when it is smooth and monotone. The results of the linear analysis are used to study the local behavior of these paths (i.e., properties and behavior sufficiently close to the solution) for smooth mappings.

An important implication of this study is that the paths can be modified and thus the work done by these algorithms can be controlled. We also show, for smooth mappings, how our results can be implemented to increase the efficiency of some standard algorithms.
On the Equilibrium Distribution of a Class of Finite-State Generalized Semi-Markov Processes
Authors: Schassberger R.
Published: October 2008

An algorithm is presented for computing the stationary distribution of a certain class of stochastic processes. The class comprises many known or potentially useful processes in the fields of operations research and applied probability.
Nonzero-Sum Two-Person Repeated Games with Incomplete Information
Authors: Hart Sergiu
Published: October 2008

Characterization of all equilibria of nonzero-sum two-person repeated games with incomplete information, in the standard one-sided information case. Informally, each such equilibrium is described by a sequence of communications between the players (consisting of information transmission and coordination), leading to some individually rational agreement. Formally, the concept of a bi-martingale is introduced.
The Mani-Walkup Spherical Counterexamples to the Wv-Path Conjecture are Not Polytopal
Authors: Altshuler Amos
Published: October 2008

Mani and Walkup (Mani, P., D. W. Walkup. 1980. A 3-sphere counterexample to the Wv-path conjecture. Math. Oper. Res. 5 595–598.) described two triangulated 3-spheres which give rise to “small” counterexamples to the Wv-path and Hirsch conjectures for spheres. We show that none of these spheres is combinatorially equivalent to any 4-polytope. Thus the Wv-path and Hirsch conjectures for polytopes are still open.
Markov Decision Drift Processes; Conditions for Optimality Obtained by Discretization
Authors: Hordijk Arie , van der Duyn Schouten Frank
Published: October 2008

In a recent paper (Hordijk, A., F. A. van der Duyn Schouten. 1983. Discretization and weak convergence in Markov decision drift processes. Math. Oper. Res. 8 112–141.) the authors gave sufficient conditions for the weak convergence of a sequence of discrete time Markov decision drift processes to a related continuous time Markov decision drift process. The goal of this analysis was to obtain for the continuous time model conditions for optimality of a limit point of a sequence of discounted discrete time optimal policies. However, the general conditions in (Hordijk, A., F. A. van der Duyn Schouten. 1983. Discretization and weak convergence in Markov decision drift processes. Math. Oper. Res. 8 112–141.) can only be applied to a very restrictive class of models. To obtain more widely applicable conditions we are concerned in this paper not with the weak convergence of the stochastic processes induced by policies, but rather with the convergence of the total expected discounted costs. Special attention is paid to the case of unbounded cost functions. Sufficient conditions on model parameters and policies are given to guarantee the convergence of the expected discounted costs of a sequence of discrete time models to those of a related continuous time model. These results are used to identify the optimal policy of a continuous time model by means of the optimal policies of a sequence of approximating discrete time models. An application to an M/M/1 queueing model is given.
A Random Family of Queueing Systems with a Dynamic Priority Discipline
Authors: Prabhu N. U. , Reeser Paul K.
Published: October 2008

We consider a family {∑u, 0 ≤ u ≤ ∞} of single server queueing systems whose customers belong to two priority classes. They arrive in two independent Poisson processes and their service times are independent with general distributions for each class. The system operates under a dynamic priority queue discipline in which the relative priority of a customer increases with his waiting time, and which can be characterized in terms of the urgency number u. The processes of interest are the waiting times of the two classes of customers. First we investigate the behavior of these processes as functions of the urgency number and establish stochastic orderings for them as u increases from 0 to ∞. Next we suppose that the urgency number is a random variable whose distribution has an exponential density for 0 < u < ∞ and atoms at u = 0 and u = ∞. We investigate the transient as well as the steady state behavior of the waiting time processes. Finally we derive limit theorems for these processes in the heavy traffic case.
An Algorithm for the Equipollent Resource Allocation Problem
Authors: Katoh N. , Ibaraki T. , Mine H.
Published: October 2008

The equipollent resource allocation problem asks to allocate a given amount of discrete resources to a given set of activities so that the maximum of the profit differences between activities is minimized. A typical example of this type of allocation problem may be found in the apportionment of a given number of seats to electoral districts. We present here an O(n log n + n log N/n) algorithm to find an optimal solution, where n is the number of activities and N is the amount of resources.
Average Optimal Singular Control and a Related Stopping Problem
Authors: Taksar M. I.
Published: October 2008

We observe a (μ, σ2) Brownian motion Xt. We can increase or decrease the value of the process paying r times the size of increase and l times the size of decrease. Holding costs are incurred continuously at a rate h(Zt) where Zt is the resulting process. We consider a convex holding cost function h which is either finite everywhere or finite inside a finite interval and equal to infinity outside this interval. The objective is to minimize average (per unit of time) expected cost.

It is shown that the optimal behavior is characterized by two constants a and b, a < b, such that the optimal policy is to keep the process inside the interval [a, b] with minimal efforts. It is shown that to find the optimal interval [a, b], one must solve a free boundary problem for the second order differential equation. We give a probabilistic solution of the free boundary problem in terms of the value of a special game. This game is a generalization of the optimal stopping problem. There are two players observing the (μ, σ2) Brownian motion, and two regions where respectively the first and the second players have the right to stop the process. The one who stops the process pays a constant fee. In addition the first player pays to the second a certain accumulated amount of money. The existence of optimal minmax strategies is shown and it is shown that the region where neither the first nor the second player should stop the process corresponds to the optimal interval [a, b] in the original control problem.
Nested Optimal Policies for Set Functions with Applications to Scheduling
Authors: Assad Arjang A.
Published: October 2008

Consider a set function v(·) defined on all subsets of a finite set N. This paper presents a class of set function maximization problems of the form Max{v(S)|S ⊆ N} that are solved optimally by the greedy algorithm. In particular, it is shown that there exists a nested sequence of subsets S*1 … S*m that increase to the optimal policy and S*k maximizes v(S) over all subsets of cardinality k. The class is characterized by conditions on the set function v(·) and related to the notion of submodularity. These results are then applied to two order-preserving machine scheduling problems. The greedy algorithm is shown to be optimal for these problems thereby providing a new algorithm different from previous approaches based on dynamic programming.
Testing the Odd Bicycle Wheel Inequalities for the Bipartite Subgraph Polytope
Authors: Gerards A. M. H.
Published: October 2008

In their paper on facets of the bipartite subgraph polytope Barahona, Grötschel and Mahjoub pose the question: Is there a polynomial time algorithm testing the odd bicycle wheel inequalities? This note describes such an algorithm.
Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions
Authors: Roth Alvin E.
Published: October 2008

The game-theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market (e.g., firms or workers) to be simultaneously maximized. This is shown to follow from the lattice structure of the set of stable outcomes. However it is shown that in a more general class of problems the optimality results persist, but the lattice structures do not. Thus this paper raises as many questions as it answers.
Semivalues of Political Economic Games
Authors: Neyman Abraham
Published: October 2008

The class of continuous semivalues is completely characterized for various spaces of nonatomic games.
Substitutes, Complements and Ripples in Network Flows
Authors: Granot Frieda , Veinott Arthur F.
Published: October 2008

We study the qualitative variation of minimum-cost network-flows and their associated costs with arc parameters. Demands are given at each node, flow is conserved, each arc's parameter lies in a lattice, and the flow cost is real or infinity-valued. Our main results are roughly as follows. If the flow cost is arc-additive, the problem can be decomposed into independent problems on each biconnected component of the graph. If also the flow cost is convex in the flow, the magnitude of the change in the optimal flow in arc a resulting from changing arc b's parameter diminishes the less biconnected a is to b. Arc a is less-biconnected-to b than is arc d if every simple cycle containing a and b also contains d. This relation is a quasi order with two distinct arcs being equivalent if and only if deleting them disconnects the graph. Hie Hasse diagram of the partial order of the induced equivalence classes is a tree with all arcs directed towards the class containing b. Two arcs are complements (resp., substitutes) if every simple cycle containing both orients them in the same (resp., opposite) way. For example, two arcs are conformal, i.e., complements or substitutes, if they are either incident, or lie on a common face of a planar graph, or (as Dirac [Dirac, G. A. 1952. A property of 4-chromatic graphs and some remarks on critical graphs. J. London Math. Soc. 27 85–92.] and Duffin [Duffin, R. J. 1965. Topology of series-parallel networks. J. Math. Anal. Appl. 10 303–318.] have shown) lie in a series-parallel graph. If also each arc cost is (lattice) subadditive, then the optimal flow in arc a is nondecreasing (resp., nonincreasing) in the parameter of each complement (resp., substitute) of a. If moreover each parameter lies in a chain, then the minimum cost is superadditive in the parameters of a set of substitutes. Suppose in addition that the arc parameters are real and the arc costs are doubly subadditive. Then the absolute difference of the optimal flows in an arc corresponding to two monotonically-step-connected parameter vectors does not exceed the sum of the absolute differences of their elements. If further the arc costs are affine between successive integers and the difference between the two parameter vectors is a unit vector, then the difference between corresponding integer optimal flows is a unit simple circulation. This fact leads to a parametric algorithm for finding optimal flows. Finally, suppose instead that the flow cost is a sum of a subadditive flow cost for arcs in a set S of complements and a flow cost for arcs not in S that is arc-additive and convex in the flows therein. Then the optimal flow in each arc in S is nondecreasing in the parameters of those arcs, and the minimum cost is subadditive therein. Moreover, the optimal flow in each arc a not in S is nondecreasing (resp., nonincreasing) in the parameters of arcs in S if a is a complement (resp., substitute) of every arc in S.
Extremal Splittings of Point Processes
Authors: Hajek Bruce
Published: October 2008

The sequence with nth term defined by [(n + 1)p] − [np] is an extremal zero-one valued sequence of asymptotic mean p in the following sense (for example): if a fraction p of customers from a point process with iid interarrival times is sent to an exponential server queue according to a prespecified splitting sequence, then the long-term average queue size is minimized when the above sequence is used.

The proof involves consideration of the lower convex envelope J (which is a function on Rm) of a function J on Zm. An explicit representation is given for J in terms of J, for J in a broad class of functions, which we call “multimodular.” The expected queue size just before an arrival, considered as a function of the zero-one splitting sequence, is shown to belong to this class.
Fixed Point Iterations and Global Stability in Economics
Authors: Thorlund-Petersen Lars
Published: October 2008

Stability is studied from the point of view of ordinary Picard iteration in a metric space. The Convergence Theorem proved here states that a sequence of Picard iterates converges if the mapping in question is a proper convex combination of a contraction (nonexpansive mapping) and the identity. It is shown by examples how this stability condition is related to other ones; in particular, the Convergence Theorem does not follow from any simple variant of the Shrinking Mapping Theorem.
Strongly Stable Equilibrium Points of N-Person Noncooperative Games
Authors: Kojima M. , Okada A. , Shindoh S.
Published: October 2008

We introduce a concept of a strongly stable (Nash) equilibrium point of an n-person noncooperative game in normal form. Roughly speaking, an equilibrium point is strongly stable if it changes continuously and uniquely against any small perturbation to payoffs of players. We establish a necessary and sufficient condition for an equilibrium point to be strongly stable. By the Karush-Kuhn-Tuckcr optimality condition for nonlinear programs, an equilibrium point is shown to correspond to a zero-point of a certain PC1-mapping. Then our condition is stated in terms of the local nonsingularity of the Jacobian matrix of this mapping. Our proof is based on the degree theory of mappings. Finally, we give an example of a 3-person game with two nonquasi-strong equilibrium points, only one of which is strongly stable.
Generalized Cheney-Loeb-Dinkelbach-Type Algorithms
Authors: Flachs Jacob
Published: October 2008

We present a class of generalized Cheney-Loeb-Dinkelbach-type (i.e. DC-type) algorithms, together with the problems they solve, and discuss convergence properties. Our algorithms, which are as simple as the DC one, are applicable to classes of programs larger than fractional. In two particular cases, the first being an essentially max-min problem and the second a Pareto extremum, we prove 1.61 and second order convergence respectively. Applications are given to extended fractional max-min and fractional Pareto extremum problems.
The Ellipsoid Method Generates Dual Variables
Authors: Burrell Bruce P. , Todd Michael J.
Published: October 2008

We show that the ellipsoid algorithm applied to a system of linear inequalities can be implemented in such a way that at each iteration there is a short proof of the containment of the feasible region in the current ellipsoid. Moreover, the data describing each ellipsoid also generate dual variables that provide bounds on the linear functions appearing in the inequalities.
Optimal Sequential Selection of Secretaries
Authors: Mallows C. L. , Nair V. N. , Shepp L. A. , Vardi Y.
Published: October 2008

The problem is to select as rapidly as possible a pre-specified number of secretaries (sequentially and without recall) from a proffered queue of applicants. Each candidate makes demands in each of several currencies, and we know the joint probability distribution of these demands. We also have a given total budget in each currency. We consider procedures that minimize the expected number of interviews and derive an asymptotically optimal procedure. Derivation of this procedure depends on the following result. Given a probability measure F on the positive orthant Q and a point ρ0 ∈ Q, consider a region A ⊂ Q whose center of gravity lies below ρ0 coordinatewise. Then F(A) is maximal when A is a simplicial section A = {ρ : ρ · θ ≤ r}, where r ≥ 0 and θ is a unit vector in Q.

The original motivation for this problem arose in connection with a scheme for selecting optical fibers.
Inefficiency of Nash Equilibria
Authors: Dubey Pradeep
Published: October 2008

It is shown that Nash Equilibria of smooth games generally tend to be inefficient in the Pareto sense.
The Orthogonal Decomposition of Games and an Averaging Formula for the Shapley Value
Authors: Kleinberg Norman L. , Weiss Jeffrey H.
Published: October 2008

In this paper we attempt to decompose a game v into two different components, one lying in the null space of the Shapley value and the other in its orthogonal complement. We observe that the Shapley value of the former must be 0, so that the Shapley value of the latter coincides with the value of the original game. In this way we arrive at a new explicit formula for the Shapley value which, unlike the typical one, involves averages of player worths across coalition sizes. Central to our ideas is the game-theoretic contrast between the spaces in which each component lies.
A Solvable One-Dimensional Model of a Diffusion Inventory System
Authors: Sulem Agnès
Published: October 2008

We analyse the optimal ordering policy for impulse control of a one-product inventory system subject to a demand modelised by a diffusion process. The purpose is to minimize the expected discounted cost that includes a fixed set-up cost and linear costs of purchase, storage and shortage. The optimal cost is explicitly obtained as the smoothest solution of a Quasi-Variational Inequality derived from the optimal principle of Dynamic Programming. The optimal (s, S) policy is determined as the unique solution of a system of algebraic equations.
On the Augmented Lagrangian
Authors: Han S.-P.
Published: October 2008

It is well known that, for a nonlinear program, any Karush–Kuhn–Tucker point that satisfies the second order sufficient condition is also a strict local minimum of the augmented Lagrangian with an underlying penalty parameter sufficiently large. A main theme of the paper is to strengthen the theorem and bring to light an interesting connection among general critical points of a nonlinear program and its augmented Lagrangian. When a penalty parameter is sufficiently large, it will be shown that a Karush–Kuhn–Tucker point of a nonlinear program is also a critical point of its augmented Lagrangian with the same index and the same nullity. The aforementioned theorem is just the special case when the index and the nullity are zeros. This result is established through an extension of a lemma due to Finsler and Debreu, which is interesting in its own right.

Consequently, under a constraint qualification, any Karush–Kuhn–Tucker point can also be shown to satisfy a second order necessary condition for a local maximum of the generalized Wolfe dual induced from the augmented Lagrangian. Interestingly, this relation holds without requiring the Karush–Kuhn–Tucker point itself to satisfy any second order optimality condition.
Combinatorial Theorems on the Simplotope that Generalize Results on the Simplex and Cube
Authors: Freund Robert M.
Published: October 2008

In the context of the theory and computation of fixed points of continuous mappings, researchers have developed combinatorial analogs of Brouwer's fixed-point theorem on the simplex and on the n-cube. Although the simplex and the cube have different combinatorial properties regarding their boundaries, they are both instances of a simplotope, which is the cross-product of simplices. This paper presents three combinatorial theorems on the simplotope, and shows how each translates into some known and new results on the simplex and cube, including various forms of Sperner's lemma. Each combinatorial theorem also implies set covering lemmas on the simplotope, the simplex, and the cube, including the Generalized Covering lemma, the Knaster–Kuratowski–Mazurkiewicz Lemma, and a lemma of Freidenfelds.
NBU Processes with General State Space
Authors: Marshall Albert W. , Shaked Moshe
Published: October 2008

Waiting times for many kinds of events can be represented as first passage times for appropriate stochastic processes. In some applications the most natural stochastic process is multidimensional. In other applications it may be more natural to consider a stochastic process which takes on values in a more general space. In this paper we consider new better than used (NBU) stochastic processes on partially ordered separable Banach spaces, that is processes which have NBU first passage times to closed upper sets. Various equivalent conditions for a process to be NBU are derived. Some of the results can be used also to characterize increasing hazard rate average (IHRA) processes. Examples of such processes include processes with shocks and recovery and processes with random repair times. Some applications in reliability theory and in other areas of probability are given.
Computational Complexity of Some Problems in Parametric Discrete Programming. I
Authors: Blair C. E. , Jeroslow R. G.
Published: October 2008

We explore the computational complexity of certain issues regarding parametric linear and integer linear programming.

For example, we demonstrate that: (1) The equality of optimal value of two integer programs for all right-hand sides (r.h.s) is NP-complete either when the problem is stated in matrix or in functional form; (2) The equality of optimal value of two linear programs for all r.h.s. in matrix form is polynomial, but it becomes NP-complete when one desires equality for all r.h.s. in a polyhedral cone described by generators; (3) The equality of a general polyhedral function (allowing nested “maxes”) to the value of a linear program in matrix form, or to another polyhedral function, is NP-complete; (4) The shortest expression, for the optimum to the subadditive dual of an integer program in matrix form, can require exponential space.
Forward Recursion for Markov Decision Processes with Skip-Free-to-the-Right Transitions, Part I: Theory and Algorithm
Authors: Wijngaard Jacob , Stidham Shaler
Published: October 2008

We consider a Markovian decision process with countable state space (states 0, 1, 2, …) which is skip-free to the right (a transition from i to j is impossible if j > i + 1). In this type of system it is easy to calculate by forward recursion the maximal total expected reward going from state 0 to state i; the same can be done, of course, for the case where a constant g is subtracted from the one-period reward function (g-revised reward). Let −wg(i) be the maximal total expected g-revised reward going from state 0 to state i. We show that wg(·) satisfies the average-reward optimality equation. If wg(·) satisfies a growth condition, then g = g*, the maximal average reward. For all other g, the function wg increases or decreases so fast that this cannot be the case. Thus, in principle the solution wg can be used to check if g < g* or g > g*, which suggests a method for approximating g* and an associated average-return optimal policy. We develop an efficient algorithm based on this idea. In a companion paper we shall show how the algorithm, or modifications of it, can be applied to some special cases, such as control of arrivals to a queue, control of the service rate, and controlled random walks.
Double-Exponential Utility Functions
Authors: Bell David E.
Published: October 2008

Ordinal additivity between two attributes X and Y is a property that permits the utility function u(x, y) to be represented as ϕ(v(x) + w(y)) for some functions ϕ, v and w where ϕ may be thought of as a single attribute utility function over v + w. In applications ϕ is usually taken to be either linear (the additive decomposition) or exponential (the multiplicative decomposition). The utility function can be shown to be exactly one of these forms whenever the two attributes are mutually utility independent. In this paper we introduce a relaxation of utility independence and show that it too implies ordinal additivity. We identify the class of utility functions ϕ that are consistent with the relaxed assumptions.

One member of this class, ϕ(z) = −exp(b exp(−cz)), which we call double-exponential, seems particularly appealing, for when b and c are positive it is increasing, risk averse and decreasingly risk averse for all z. The multiattribute decomposition corresponding to it −exp(b exp(−c(v + w))) may be represented as u(x, y) = c exp(cv(x)w(y)) which we call the exponential product.
Layered Augmenting Path Algorithms
Authors: Tardos Éva , Tovey Craig A. , Trick Michael A.
Published: October 2008

Augmenting path algorithms, first introduced by Ford and Fulkerson (Ford, L. R., D. R. Fulkerson. 1962. Flows in Networks. Princeton University Press, Princeton, N.J.), are widely used in optimization. Examples include Schönsleben's polymatroid intersection algorithm (Schönsleben, P. 1980. Ganzzahlige polymatroid-intersection-algorithmen. Ph.D. thesis, Eidgenössischen Technischen Hochschule, Zürich.), the maximum polymatroidal network flow algorithm of Lawler and Martel (Lawler, E. L., C. U. Martel. 1982. Computing maximal polymatroidal network flows. Math. Oper. Res. 7 334–347.), Frank's algorithm for the Edmonds–Giles polyhedron (Frank, A. 1984. Finding feasible vectors of Edmonds-Giles polyhedra. J. Combin. Theory Ser. B 36 221-239.) and Cunningham's algorithm for testing membership in matroid polyhedra (Cunningham, H. W. 1984. Testing membership in matroid polyhedra. J. Combin. Theory Ser. B 36 161–188.).

Here we give an order of magnitude improvement for the above algorithms by using an approach analogous to that of Dinits’ maximum flow algorithm (Dinits, E. A. 1970. Algorithm for solution of a problem of maximum flow in a network with power estimation. Soviet Math. Dokl. 11 1277–1280.).
Network Reliability and Inner-Four-Cycle-Free Graphs
Authors: Politof Themistocles , Satyanarayana A.
Published: October 2008

A planar graph G = (V, E) is an Inner-Four-Cycle-Free graph (IFCF-graph) if, after all series and parallel replacements, it has a planar embedding G′ with a face f such that every cycle of G′ having four or more edges contains a vertex of f. It is shown that an IFCF-graph can be reduced to an edge by a recursive application of series, parallel and Δ − Y replacements. This property forms the basis of an O(|V|2) algorithm to compute the probability that a probabilistic IFCF-graph is connected. This result is extended to graphs whose triconnected components are IFCF (such graphs are not necessarily IFCF). The class of IFCF-graphs includes the series-parallel graphs, wheel-graphs, ladder networks and graphs in normal form, for which polynomial network reliability algorithms are already known.