Rajeev Kohli

Internet Recommendation Systems

Several online firms, including Yahoo!, Amazon.com, and Movie Critic, recommend documents and products to consumers. Typically, the recommendations are based on content and/or collaborative filtering methods. The authors examine the merits of these methods, suggest that preference models used in marketing offer good alternatives, and describe a Bayesian preference model that allows statistical integration of five types of information useful for making recommendations: a persons expressed preferences, preferences of other consumers, expert evaluations, item characteristics, and individual characteristics. The proposed method accounts for not only preference heterogeneity across users but also unobserved product heterogeneity by introducing the interaction of unobserved product attributes with customer characteristics. The authors describe estimation by means of Markov chain Monte Carlo methods and use the model with a large data set to recommend movies either when collaborative filtering methods are viable alternatives or when no recommendations can be made by these methods.

The Minimum Satisfiability Problem

This paper shows that a minimization version of satisfiability is strongly NP-hard, even if each clause contains no more than two literals and/or each clause contains at most one unnegated variable. The worst-case and average-case performances of greedy and probabilistic greedy heuristics for the problem are examined, and tight upper bounds on the performance ratio in each case are developed.

Optimal product design using conjoint analysis: Computational complexity and algorithms *

Abstract The problem of maximizing the share of a new product introduced in a competitive market is shown to be NP-hard. A directed graph representation of the problem is used to construct shortest-path and dynamic-programming heuristics. Both heuristics are shown to have arbitrarily-bad worst-case bounds. Computational experience with real-sized problems is reported. Both heuristics identify near-optimal solutions for the simulated problems, the dynamic-programming heuristic performing better than the shortest-path heuristic.

EXTENT AND IMPACT OF INCUBATION TIME IN NEW PRODUCT DIFFUSION

This article examines the time between product development and market launch, and its relation to the subsequent diffusion of consumer durables. We find that this “incubation time” is long. Further, it is a useful predictor of the shape of the subsequent sales diffusion curve. Using the Bass model as a base, we find that the longer the incubation time, the lower the coefficient of innovation (p) and the longer the time to peak sales. Further, using the incubation time in a Bayesian forecasting model significantly improves forecasts early in the life cycle.

Probabilistic Subset-Conjunctive Models for Heterogeneous Consumers

The authors propose two generalizations of conjunctive and disjunctive screening rules. First, they relax the requirement that an acceptable alternative must be satisfactory on one criterion (disjunctive) or on all criteria (conjunctive). Second, they relax the assumption that consumers make deterministic judgments when evaluating alternatives. They combine the two generalizations into a probabilistic subset-conjunctive rule, which allows consumers to use any number or subset of decision criteria when screening alternatives and permits them to be uncertain about the acceptability of attribute levels. These two features allow for a screening process that is uncertain and more flexible than the deterministic conjunctive and disjunctive rules currently described in the literature. The authors describe a latent-class method for the estimation of the subset-conjunctive rules and the attribute-level consideration probabilities using either consideration or choice data. Applications using both types of data suggest that the proposed models predict as well as linear models do; can make different predictions of consideration, choice, and market shares; and provide insights into consumer decision processes that are different from those obtained with linear models.

Package Size Decisions

We describe a model examining how a firm might choose the package size and price for a product that deteriorates over time. Our model considers four factors: (1) the usable life of the product, (2) the rates at which consumers use the product, (3) the relation between package size and the variable cost of the product, and (4) the minimum quantities consumers seek to consume for each dollar they spend (we call these reservation quantities). We allow heterogeneity in the usage rates and reservation quantities for the consumers. We show that when the cost increases as a linear or convex function of the package size, the firm should make packages of the smallest possible size. Smaller packages reduce waste and allow consumers to more closely match their purchases with desired consumption. This in turn allows the firm to charge a higher unit price and also sell more unit volume. The results imply that in a market with multiple package sizes (produced by the same or competing firms), at least one of the packages must have the smallest possible size, provided the fixed cost of making the product is sufficiently low. For concave cost functions, the firm may find it optimal to make larger than smallest-size packages.

The capacitated max k -cut problem

We consider a capacitated max k-cut problem in which a set of vertices is partitioned into k subsets. Each edge has a non-negative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that maximizes the sum of edge weights across all pairs of vertices that lie in different subsets. We describe a local-search algorithm that obtains a solution with value no smaller than 1 − 1/k of the optimal solution value. This improves a previous bound of 1/2 for the max k-cut problem with fixed, though possibly different, sizes of subsets.

Some Empirical Regularities in Market Shares

We present some empirical regularities in the market shares of brands. Our cross-sectional data on market shares consists of 1,171 brands in 91 product categories of foods and sporting goods sold in the United States. One of our results is that the pattern of market shares for each of the categories (many of which are fundamentally dissimilar, such as breakfast cereals and rifles) is represented well by the power law. The power law also does better than an alternative model---namely, the exponential form---which has previously been studied in the literature but without having been compared to any alternative. These two models have sharply different implications; for example, the power law predicts that the ratio of market shares for two successively ranked brands becomes smaller as one progresses from higher-ranked to lower-ranked brands, whereas the exponential form predicts that this ratio is a constant. Our findings have several managerial and research implications, which we summarize.

Average performance of greedy heuristics for the integer knapsack problem

Abstract This paper derives a lower bound on the average performance of a total-value greedy heuristic for the integer knapsack problem. This heuristic selects items in order of their maximum possible contribution to the solution value at each stage. We show that, as for the worst-case bound, the average performance bound for the total-value heuristic dominates the corresponding bound for the density-ordered greedy heuristic.

Conflict Resolution in the Scheduling of Television Commercials

We extend a previous model for scheduling commercial advertisements during breaks in television programming. The proposed extension allows differential weighting of conflicts between pairs of commercials. We formulate the problem as a capacitated generalization of the max k-cut problem in which the vertices of a graph correspond to commercial insertions and the edge weights to the conflicts between pairs of insertions. The objective is to partition the vertices into k capacitated sets to maximize the sum of conflict weights across partitions. We note that the problem is NP-hard. We extend a previous local-search procedure to allow for the differential weighting of edge weights. We show that for problems with equal insertion lengths and break durations, the worst-case bound on the performance of the proposed algorithm increases with the number of program breaks and the number of insertions per break, and that it is independent of the number of conflicts between pairs of insertions. Simulation results suggest that the algorithm performs well even if the problem size is small.