bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Model of Brand Choice and Purchase Quantity Price Sensitivities
Authors: Krishnamurthi Lakshman , Raj S. P. 
Published: October 2008

Many consumer decisions involve a discrete choice and a continuous outcome. Examples of such decisions are whether to own a home or rent one and how much to spend, which brand of orange juice to buy and how many ounces to buy. In cases like these, the choice decision is typically modeled separately, say, using a logit model and the continuous outcomes modeled separately using regression analysis. However, the continuous outcomes may not be independent of the discrete choice and vice versa, and modeling the two decisions independently can lead to inefficient choice parameter estimates and biased and inconsistent regression parameter estimates. In this paper, we present a methodology from the limited-dependent variable literature to model the dependence between the choice and quantity decisions. Our substantive interest is in the role of price in the choice and quantity decisions. When choosing among alternatives, we argue that consumers consider prices of all the competitive brands. In the quantity decision on the other hand, only the price of the chosen alternative is expected to impact how much of the alternative is purchased. The analysis of three brands, using disaggregate level panel data, strongly supports our hypothesis about the role of competitive prices in the choice and quantity decisions.
Note—Consumer Store Choice and Choice Set Definition
Authors: Fotheringham A. Stewart 
Published: October 2008

Consumer store choice results from a process whereby information on various alternatives is evaluated by the consumer prior to the selection of one of these alternatives. In the application of store choice models it is often assumed that the information-processing strategy underlying store choice is a simultaneous one in which all possible alternatives are evaluated by an individual. A competing assumption, increasingly recognized in aspatial choice, is that individuals initially evaluate clusters of alternatives and then only evaluate alternatives within a chosen cluster. The nested logit model is a well-known formulation for capturing this type of choice process. This paper adds to the above understanding of consumer spatial choice in the following ways: (i) It describes an alternative to the nested logit model, known as a competing destinations model, which can be used to model hierarchical spatial choice processes. While this model has been described previously in the geography and planning literature, this paper contains a novel derivation of it from within the random utility maximization framework. (ii) A general choice formulation is derived from which the logit, nested logit, and competing destinations models can be obtained. This allows the behavioral assumptions embedded in each model to be seen clearly and it allows a comparison of the nested logit and competing destinations formulations. The latter is shown to be preferable in most spatial choice situations. In particular, the latter can be used when restricted choice sets are fuzzy. (iii) The errors that arise when spatial choice results from a hierarchical process and when a simultaneous choice structure is assumed are demonstrated and are related to the presence of consumer competition/agglomeration effects between stores which are thought to be important in store choice.
Optimal Pricing Strategies for New Products in Dynamic Oligopolies
Authors: Dockner Engelbert , Jørgensen Steffen 
Published: October 2008

This paper deals with the determination of optimal pricing policies for firms in oligopolistic markets. The problem is studied as a differential game and optimal pricing policies are established as Nash open-loop controls. Cost learning effects are assumed such that unit costs are decreasing with cumulative output. Discounting of future profits is also taken into consideration. Initially, the problem is addressed in a general framework, and we proceed to study some specific cases that are related to models presented in recent literature. Three basic classes of sales dynamics are analyzed: competition with price effects only, competition with price as well as adoption effects, and competition with adoption effects only. In some cases it turns out that results which hold for the monopoly case, carry over to the multi-firm case, in the sense that the qualitative structure of optimal pricing strategies is the same in the monopoly and the oligopoly cases. However, due to competitive interdependencies, differences certainly exist in the levels as well as the rates of change of optimal prices.
Designing Products and Services for Consumer Welfare: Theoretical and Empirical Issues
Authors: Gupta Sunil , Kohli Rajeev 
Published: October 2008

In this paper we examine the theoretical and empirical issues that arise for a public-sector decision maker who wishes to use the target population's preferences as an input for designing new products and services. The marketing literature suggests using essentially the same approach as that for the private-sector problem, with one exception. Instead of maximizing profits, share or volume, the sum-of-benefits to society is maximized. However, the social welfare literature has suggested several other measures of welfare and shows that no single welfare function dominates all others. Therefore, to choose an appropriate welfare function to maximize the decision maker must first examine the theoretical and empirical similarities between the alternatives. For six prominent welfare functions, we examine the theoretical differences in terms of the notion of fairness promoted and the kind of preference data required. Empirically, we examine the similarities in social rankings and first choices induced by these welfare functions under various preference configurations. We also examine their sensitivity to measurement error and preference normalization.
An Integrated Model-Based Approach for Sales Force Structuring
Authors: Rangaswamy Arvind , Sinha Prabhakant , Zoltners Andris 
Published: October 2008

This paper analyzes the problem of designing the structure of multiproduct sales forces selling in an environment where purchase decisions are made on a straight rebuy or modified rebuy basis. It addresses two key issues pertaining to structure: How many sales forces should the firm have and which products should be assigned to each sales force? First, the key determinants of sales force structure are identified and described. Next, a mathematical programming model is formulated that can aid firms in designing the structure of their multiproduct sales force. An application is then described in detail including sales response specification, parameter estimation, solution procedure, and model implementation. Insights from several of the numerous implementations of the model in the pharmaceutical industry are also summarized.
Series Solutions to Static Team Control Problems
Authors: Rudge J. F. 
Published: October 2008

The concept of infinite second guessing is known to play a role in the consideration of multi-person control problems. By considering the problem in its appropriate Hilbert space context we formalize this concept and show that it does in fact play a vital part in the structure of those solutions that are available. We give an explicit series solution to the constant coefficient quadratic cost team problem. This solution is valid for any distribution of noise, which is square integrable. The well-known linearity of optimal control in the Gaussian case is immediately apparent. An important special case is given further consideration and other applications are indicated. Finally a theorem characterising the limit behaviour of the series in terms of the information common to all players is presented.
Computational Efficiency of Approximate Branch-and-Bound Algorithms
Authors: Ibaraki Toshihide 
Published: October 2008

To improve the computational efficiency of a branch-and-bound algorithm at the sacrifice of obtaining an optimal solution, the lower bound test is sometimes strengthened beyond its limit, i.e., a partial problem Pi is terminated if g(Pi) ≥ z − ϵ(z) (instead of g(Pi) ≥ z), where g(Pi) is a lower bound of Pi, z is the current incumbent value and ϵ(z) (≥0) specifies the allowance within which the value of an obtained solution can deviate from the optimal. This paper first shows that the efficiency (as measured by the number of decomposed partial problems) does not generally improve by introducing ϵ or by increasing ϵ, and then isolates subclasses of branch-and-bound algorithms for which a monotone increase in efficiency with respect to ϵ is guaranteed.
Sequencing Problems in Two-Server Systems
Authors: Calderbank A. R. , Coffman E. G. , Flatto L. 
Published: October 2008

We analyze a service system in which two identical servers move one at a time along a linear array of N positions. Requests for service, each designating one of the N positions, join a first-in-first-out queue, where processing of the nth request does not begin until processing of the (n − 1)th requested is completed. Processing the nth request entails determining which server to move, moving this server to the requested position, and then performing the service. Several potential applications of the model are mentioned, the most notable being the design of computer storage systems with multiple access devices. Within a simple probability model we compare server-selection policies in terms of the equilibrium expected distance a server is moved in processing a request. Distance is measured under two regimes, both assigning a unit distance between adjacent positions. In the first, the positions are thought of as equally spaced along a line (interval), and in the second, equally spaced along a circle (positions 1 and N are adjacent). For the interval problem the server-selection policies examined include the partition rule, whereby die interval is bisected and a server restricted to the requests in each half-interval, and the nearer-server rule whereby service is always provided by the server closer to the requested position, with ties broken in favor of the right-hand server. Under the assumption that requested positions are distributed uniformly over the set of N, our results show that expected server motion under the nearer-server rule is approximately 0.1625 N for moderately large N, which is to be compared with the known result of N/6 = 0.1666 … N for the partition rule. We also derive an optimization rule for which numerical calculations indicate that 0.1598 N is the approximate performance for large N. A number of other results plus two conjectures are presented which characterize optimization rules on the interval. Finally, extensive numerical calculations are displayed which describe the joint distributions of server positions under the nearer-server and a related rule. For the more tractable circle problem we prove that die nearer-server rule is optimal, and we derive an explicit form for the stationary density of the distance between servers. It is noted that the nearer-server rule is also optimal when the circle is generalized to 2-point homogeneous spaces (e.g., a Euclidean sphere) in more than one dimension.
Von Neumann-Morgenstern Utilities and Cardinal Preferences
Authors: Chichilnisky Graciela 
Published: October 2008

We study the aggregation of preferences when intensities are taken into account: the aggregation of cardinal preferences, and also of von Neumann-Morgenstern utilities for choices under uncertainty. We show that with a finite number of choices there exist no continuous anonymous aggregation rules that respect unanimity, for such preferences or utilities. With infinitely many (discrete sets of) choices, such rules do exist and they are constructed here. However, their existence is not robust: each is a limit of rules that do not respect unanimity. Both results are for a finite number of individuals. The results are obtained by studying the global topological structure of spaces of cardinal preferences and of von Neumann-Morgenstern utilities. With a finite number of choices, these spaces are proven to be noncontractible. With infinitely many choices, on the other hand, they are proven to be contractible.
Continuity of Generalized Gradients and Multipliers Under Perturbations
Authors: Zolezzi Tullio 
Published: October 2008

We prove that the multiplier rule, given by Clarke for mathematical programming problems with locally Lipschitz data, is stable under epi-convergent data perturbations in the finite-dimensional case for global solutions. This stability result is derived from a continuity theorem for generalized gradients extending the classical formula lim ∇fn = ∇(lim fn). Continuous dependence theorems for multipliers in the Fritz-John form proved in this paper extend stability results of Gauvin, Robinson and others for nonlinear programming problems with smooth data.
Transversality Conditions for Some Infinite Horizon Discrete Time Optimization Problems
Authors: Ekeland Ivar , Scheinkman José Alexandre 
Published: October 2008

This paper considers a class of discrete-time, infinite-horizon optimization problems arising in economics. Necessary optimality conditions for such problems consist of an Euler equation and a transversality condition at infinity. Our concern here is with the latter condition. Previous results for this type of problem have required such restrictions as concavity and boundedness of the utility functions whose sum is being maximized. Here we derive a transversality condition that remains valid under considerably more general hypotheses. In doing so, we introduce methods that may also be applicable to other situations, such as optimization in continuous time.
Generalized S-Shapedness of Reliability Functions
Authors: Pilpel Shaiy 
Published: October 2008

Reliability functions have the property that if they intersect the diagonal y = x it is done in an S-shaped form (Moore and Shannon). In this paper a wider class of polynomials is presented, the members of which form a dense grid on the unit square. The S-shapedness intersection property holds whenever a reliability function intersects a polynomial in this set. The members of this set are all reliability polynomials. The diagonal y = x is also a member of this set, thus a generalization of Moore-Shannon result is achieved.
A 98%-Effective Lot-Sizing Rule for a Multi-Product, Multi-Stage Production / Inventory System
Authors: Roundy Robin 
Published: October 2008

We study a multi-product, multi-stage production inventory system in continuous time. In-process and finished goods are referred to as products and inventories of a single item held at different locations are treated as different products. External demand can occur for any or all of the products at a constant, product-dependent rate. When an order is placed for a product it is instantly delivered. The set-up cost is a function of the set of products being ordered at that point in time. The goal is to schedule orders for each of the products over an infinite horizon so as to minimize the long-run average cost. We define a new class of policies in which each product uses a stationary interval of time between successive orders, and the ratio of the order intervals of any two products is an integer power of two. We show that there is always a policy in this class that is within 2% of optimal. This extends a similar result for the one-warehouse, multi-retailer system. For assembly systems we show how to compute such a policy in 0(N log N) time. For general systems a sequence of max-flow, min-cut computations is required. The algorithm is efficient for very large systems.
The Multi-Armed Bandit Problem: Decomposition and Computation
Authors: Katehakis Michael N. , Veinott Arthur F. 
Published: October 2008

This paper is dedicated to our friend and mentor, Cyrus Derman, on the occasion of his 60th birthday. The multi-armed bandit problem arises in sequentially allocating effort to one of N projects and sequentially assigning patients to one of N treatments in clinical trials. Gittins and Jones (Gittins, J. C., Jones, D. M. 1974. A dynamic allocation index for the sequential design of experiments. J. Gani, K. Sarkadi, L. Vince, eds. Progress in Statistics. European Meeting of Statisticians, 1972, 1, North Holland, Amsterdam, 241–266.) have shown that one optimal policy for the N-project problem, an N-dimensional discounted Markov decision chain, is determined by the following largest-index rule. There is an index for each state of each given project that depends only on the data of that project. In each period one allocates effort to a project with largest current index. The purpose of this paper is to give a short proof of this result and a new characterization of the index of a project in state i, viz., as the maximum expected present value in state i for the restart-in-i problem in which, in each state and period, one either continues allocating effort to the project or immediately restarts the project in state i. Moreover, it is shown that an approximate largest-index rule yields an approximately optimal policy. These results lead to more efficient methods of computing the indices on-line and/or for sparse transition matrices in large state spaces than have been suggested heretofore. By using a suitable implementation of successive approximations, a policy whose expected present value is within 100ϵ% of the maximum possible range of values of the indices can be found on-line with at most (N + T − 1)TM operations where M is the number of operations required to calculate one approximation, T is the least integer majorizing the ratio ln ϵ/ln a and 0 < a < 1 is the discount factor.
Communication Equilibria in Repeated Games with Incomplete Information
Authors: Forges Françoise 
Published: October 2008

Correlated equilibria (in the sense of Aumann, i.e., normal form correlated equilibria) are studied in two-person infinitely repeated games with lack of information on one side. Extensions of the solution concept are introduced, several of which are shown to be payoff equivalent in the model under consideration. A normal form correlated equilibrium is a Nash equilibrium of the game where each player gets a private output from a correlation device before the beginning of the original game. An r-device (r = 0, 1, …, ∞) is a communication device, receiving an input from each player before every stage t = 1, …, r and selecting a pair of outputs, one for each player, at every stage t = 1, 2, …, according to a memory dependent transition probability. An r-communication equilibrium is a Nash equilibrium of the game extended by means of an r-device. Let C (resp. Dr, r = 0, 1, …, ∞) be the set of normal form correlated (resp. r-communication) equilibrium payoffs. D0 is the set of “extensive form correlated equilibrium payoffs,” achieved by means of an “autonomous device,” acting only by sending a stream of outputs to each player. And D∞ is the set of all communication equilibrium payoffs, corresponding to communication devices which can receive inputs at every stage (even arbitrarily large). The paper characterizes the different sets and investigate whether they coincide.
A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees
Authors: Taksar Michael , Klass Michael J. , Assaf David 
Published: October 2008

We consider a financial market model with two assets. One has deterministic rate of growth, while the rate of growth of the second asset is governed by a Brownian motion with drift. We can shift money from one asset to another; however, there are losses of money (brokerage fees) involved in shifting money from the risky to the nonrisky asset. We want to maximize the expected rate of growth of funds. It is proved that an optimal policy keeps the ratio of funds in risky and nonrisky assets within a certain interval with minimal effort.
Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives
Authors: Rockafellar R. Tyrrell 
Published: October 2008

Dedicated to the memory of Robin W. Chaney Second-order optimality conditions for finite-dimensional smooth and nonsmooth nonlinear programming are obtained by a new method that emphasizes a close connection with geometrical approximation of the essential objective function. The approximation is secured by the use of certain epi-derivatives defined by epiconvergence. The optimality conditions are expressed in a form that covers general interval constraints and their possible representation through penalties or an augmented Lagrangian. An abstract constraint involving restriction to a convex polyhedron is incorporated.
Finding Minimum-Cost Circulations by Successive Approximation
Authors: Goldberg Andrew V. , Tarjan Robert E. 
Published: October 2008

We develop a new approach to solving minimum-cost circulation problems. Our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling. We measure the accuracy of a solution by the amount that the complementary slackness conditions are violated. We propose a simple minimum-cost circulation algorithm, one version of which runs in O(n3log(nC)) time on an n-vertex network with integer arc costs of absolute value at most C. By incorporating sophisticated data structures into the algorithm, we obtain a time bound of O(nm log(n2/m)log(nC)) on a network with m arcs. A slightly different use of our approach shows that a minimum-cost circulation can be computed by solving a sequence of O(n log(nC)) blocking flow problems. A corollary of this result is an O(n2(log n)log(nC))-time, m-processor parallel minimum-cost circulation algorithm. Our approach also yields strongly polynomial minimum-cost circulation algorithms. Our results provide evidence that the minimum-cost circulation problem is not much harder than the maximum flow problem. We believe that a suitable implementation of our method will perform extremely well in practice.
Efficiency of the Primal Network Simplex Algorithm for the Minimum-Cost Circulation Problem
Authors: Tarjan Robert E. 
Published: October 2008

We study the number of pivots required by the primal network simplex algorithm to solve the minimum-cost circulation problem. We propose a pivot selection rule with a bound of n(logn)/2+O(1) on the number of pivots, for an n-vertex network. This is the first known subexponential bound. The network simplex algorithm with this rule can be implemented to run in n(logn)/2+O(1) time. In the special case of planar graphs, we obtain a polynomial bound on the number of pivots and the running time. We also consider the relaxation of the network simplex algorithm in which cost-increasing pivots are allowed as well as cost-decreasing ones. For this algorithm we propose a pivot selection rule with a bound of O(nm · min{log(nC), m log n}) on the number of pivots, for a network with n vertices, m arcs, and integer arc costs bounded in magnitude by C. The total running time is O(nm log n · min{(log nC), m log n}). This bound is within a logarithmic factor of those of the best previously known algorithms for the minimum-cost circulation problem.
Integer Solution to Synthesis of Communication Networks
Authors: Sridhar S. , Chandrasekaran R. 
Published: October 2008

This paper describes a polynomial-time algorithm for the following problem: Let ri,j be the given requirements for all i, j ∈ {1, …, n}, with ri,j = rj,i for i, j. Find integer capacities ci,j for all i, j ∈ {1, …, n} such that (considering 1, …, n as the vertices of an undirected network N, with capacities ci,j): (i) for for all i ≠ j there exists a flow in N from i to j of value, at least ri,j; (ii) ∑i<j ci,j is minimized. This is the integer version of Gomory and Hu's problem to synthesize an undirected network. It is shown that rounding holds when there is no node with unit potential.