Pamela H. Vance

Bio: Pamela H. Vance is an academic researcher from Auburn University. The author has contributed to research in topics: Column generation & Integer programming. The author has an hindex of 14, co-authored 17 publications receiving 4578 citations. Previous affiliations of Pamela H. Vance include Georgia Institute of Technology & Emory University.

Branch-And-Price: Column Generation for Solving Huge Integer Programs

Abstract: We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

Consumption Self-Control by Rationing Purchase Quantities of Virtue and Vice

Abstract: Consumers' attempts to control their unwanted consumption impulses influence many everyday purchases with broad implications for marketers' pricing policies. Addressing theoreticians and practitioners alike, this paper uses multiple empirical methods to show that consumers voluntarily and strategically ration their purchase quantities of goods that are likely to be consumed on impulse and that therefore may pose self-control problems. For example, many regular smokers buy their cigarettes by the pack, although they could easily afford to buy 10-pack cartons. These smokers knowingly forgo sizable per-unit savings from quantity discounts, which they could realize if they bought cartons; by rationing their purchase quantities, they also self-impose additional transactions costs on marginal consumption, which makes excessive smoking overly difficult and costly. Such strategic self-imposition of constraints is intuitively appealing yet theoretically problematic. The marketing literature lacks operationalizations and empirical tests of such consumption self-control strategies and of their managerial implications. This paper provides experimental evidence of the operation of consumer self-control and empirically illustrates its direct implications for the pricing of consumer goods. Moreover, the paper develops a conceptual framework for the design of empirical tests of such self-imposed constraints on consumption in consumer goods markets. Within matched pairs of products, we distinguish relative "virtue" and "vice" goods whose preference ordering changes with whet her consumers evaluate immediate or delayed consumption consequences. For example, ignoring long-term health effects, many smokers prefer regular (relative vice) to light (relative virtue) cigarettes, because they prefer the taste of the former. However, ignoring these short-term taste differences, the same smokers prefer light to regular cigarettes when they consider the long-term health effects of smoking. These preference orders can lead to dynamically inconsistent consumption choices by consumers whose tradeoffs between the immediate and delayed consequences of consumption depend on the time lag between purchase and consumption. This creates a potential self-control problem, because these consumers will be tempted to over consume the vices they have in stock at home. Purchase quantity rationing helps them solve the self-control problem by limiting their stock and hence their consumption opportunities. Such rationing implies that, per purchase occasion, vice consumers will be less likely than virtue consumers to buy larger quantities in response to unit price reductions such as quantity discounts. We first test this prediction in two laboratory experiments. We then examine the external validity of the results at the retail level with a field survey of quantity discounts and with a scanner data analysis of chain-wide store-level demand across a variety of different pairs of matched vice (regular) and virtue (reduced fat, calorie, or caffeine, etc.) product categories. The analyses of these experimental, field, and scanner data provide strong convergent evidence of a characteristic crossover in demand schedules for relative vices and virtues for categories as diverse as, among others, potato chips, chocolate chip cookies, cream cheese, beer, soft drinks, ice cream and frozen yogurt, chewing gum, coffee, and beef andturkey bologna. Vice consumers' demand increases less in response to price reductions than virtue consumers' demand, although their preferences are not generally weaker for vices than for virtues. Constraints on vice purchases are self-imposed and strategic rather than driven by simple preferences. We suggest that rationing their vice inventories at the point of purchase allows consumers to limit subsequent consumption. As a result of purchase quantity rationing, however, vice buyers forgo savings from price reductions through quantity discounts, effectively paying price premiums for the opportunity to engage in self-control. Thus, purchase quantity rationing vice consumers are relatively price in sensitive. From a managerial and public policy perspective, our findings should offer marketing practitioners in many consumer goods industries new opportunities to increase profits through segmentation and price discrimination based on consumer self-control. They can charge premium prices for small sizes of vices, relative to the corresponding quantity discounts for virtues. Virtue consumers, on the other hand, will buy larger amounts even when quantity discounts are relatively shallow. A key conceptual contribution of this paper lies in showing how marketing researchers can investigate a whole class of strategic self-constraining consumer behaviors empirically. Moreover, this research is the first to extend previous, theoretical work on impulse control by empirically demonstrating its broader implications for marketing decision making.

Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems

Abstract: We present a column-generation model and branch-and-price-and-cut algorithm for origin-destination integer multicommodity flow problems. The origin-destination integer multicommodity flow problem is a constrained version of the linear multicommodity flow problem in which flow of a commodity (defined in this case by an origin-destination pair) may use only one path from origin to destination. Branch-and-price-and-cut is a variant of branch-and-bound, with bounds provided by solving linear programs using column-and-cut generation at nodes of the branch-and-bound tree. Because our model contains one variable for each origin destination path, for every commodity, the linear programming relaxations at nodes of the branch-and-bound tree are solved using column generation, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality. We devise a new branching rule that allows columns to be generated efficiently at each node of the branch-and-bound tree. Then, we describe cuts (cover inequalities) that can be generated at each node of the branch-and-bound tree. These cuts help to strengthen the linear programming relaxation and to mitigate the effects of problem symmetry. We detail the implementation of our combined column and- cut generation method and present computational results for a set of test problems arising from telecommunications applications. We illustrate the value of our branching rule when used to find a heuristic solution and compare branch-and-price and branch-and-price-and-cut methods to find optimal solutions for highly capacitated problems.

Airline Crew Scheduling

Abstract: Airline crew scheduling is concerned with finding a minimum cost assignment of flight crews to a given flight schedule while satisfying restrictions dictated by collective bargaining agreements and...

Solving binary cutting stock problems by column generation and branch-and-bound

Abstract: We present an algorithm for the binary cutting stock problem that employs both column generation and branch-and-bound to obtain optimal integer solutions. We formulate a branching rule that can be incorporated into the subproblem to allow column generation at any node in the branch-and-bound tree. Implementation details and computational experience are discussed.

Branch-And-Price: Column Generation for Solving Huge Integer Programs

Abstract: We discuss formulations of integer programs with a huge number of variables and their solution by column generation methods, i.e., implicit pricing of nonbasic variables to generate new columns or to prove LP optimality at a node of the branch-and-bound tree. We present classes of models for which this approach decomposes the problem, provides tighter LP relaxations, and eliminates symmetry. We then discuss computational issues and implementation of column generation, branch-and-bound algorithms, including special branching rules and efficient ways to solve the LP relaxation. We also discuss the relationship with Lagrangian duality.

Heart and Mind in Conflict: The Interplay of Affect and Cognition in Consumer Decision Making

Abstract: This article examines how consumer decision making is influenced by automatically evoked task-induced affect and by cognitions that are generated in a more controlled manner on exposure to alternatives in a choice task. Across two experiments respondents chose between two alternatives: one (chocolate cake) associated with more intense positive affect but less favorable cognitions, compared to a second (fruit salad) associated with less favorable affect but more favorable cognitions. Findings from the two experiments suggest that if processing resources are limited, spontaneously evoked affective reactions rather than cognitions tend to have a greater impact on choice. As a result, the consumer is more likely to choose the alternative that is superior on the affective dimension but inferior on the cognitive dimension (e.g., chocolate cake). In contrast, when the availability of processing resources is high, cognitions related to the consequences of choosing the alternatives tend to have a bigger impact on choice compared to when the availability of these resources is low. As a result, the consumer is more likely to choose the alternative that is inferior on the affective dimension but superior on the cognitive dimension (e.g., fruit salad). The moderating roles of the mode of presentation of the alternatives and of a personality variable related to impulsivity are also reported.

Consumer choice between hedonic and utilitarian goods.

Abstract: In this article, the authors examine how consumer choice between hedonic and utilitarian goods is influenced by the nature of the decision task. Building on research on elaboration, the authors propose that the relative salience of hedonic dimensions is greater when consumers decide which of several items to give up (forfeiture choices) than when they decide which item to acquire (acquisition choices). The resulting hypothesis that a hedonic item is relatively preferred over the same utilitarian item in forfeiture choices than in acquisition choices was supported in two choice experiments. In a subsequent experiment, these findings were extended to hypothetical choices in which the acquisition and forfeiture conditions were created by manipulating initial attribute-level reference states instead of ownership. Finally, consistent with the experimental findings, a field survey showed that, relative to market prices, owners of relatively hedonic cars value their vehicles more than do owners of relat...