The multiple-choice knapsack problem is defined as a binary knapsack problem with the addition of disjoint multiple-choice constraints. The strength of the branch-and-bound algorithm we present for this problem resides with the quick solution of the linear programming relaxation and its efficient, subsequent reoptimization as a result of branching. An implemented version of this algorithm has performed well on a large set of test problems. We cite computational results as well as a comparison with a previously reported algorithm. Several useful applications of the multiple-choice knapsack problem are also suggested.

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The sales territory alignment problem may be viewed as the problem of grouping small geographic sales coverage units into larger geographic clusters called sales territories in a way that the sales territories are acceptable according to managerially relevant alignment criteria. This paper first reviews sales territory alignment models which have appeared in the marketing literature. A framework for sales territory alignment and several properties of a good sales territory alignment are developed in the course of the review. A general sales territory alignment model which accommodates these properties is developed. A solution procedure for the general model is presented. Finally, an actual implementation of the general model is described. The implementation provides a comparison of the general model with a similar model which has been frequently cited in the marketing literature.marketing models, sales force planning, mathematical programming application

A four segment trial-repeat model is developed to model sales of a frequently purchased product in the early stage of the product's life cycle. The model can be calibrated using aggregate data alone. Two versions of the model, one emphasizing the competitive aspect of marketing communications and another emphasizing the informative aspect, are estimated from data on 21 newly launched pharmaceutical products. The model provides valuable diagnostics such as an early estimate of the long-run market share of the new product, a decomposition of total sales (into trial sales due to marketing activities, trial sales due to word-of-mouth, and repeat sales), the changing composition of the trial market and repeat market over time, and the time when the trial market is expected to be saturated. In addition, the effectiveness of the entrant's marketing efforts, word-of-mouth communication, and buyers' trial experience are analyzed with the model. A cross-sectional analysis based on the empirical estimation results of our model reveals interesting insights into product introduction strategies. We find that: 1) the effectiveness of the firms' communication activities on trial is related mainly to product quality attributes and market growth whereas that of word-of-mouth is associated with product class characteristics and market competitiveness, and 2) the effect of product trial on repeat purchases is related mainly to product quality attributes and various market characteristics such as size, growth, competitiveness, and familiarity.diffusion, new product research

S ales territory alignment is the assignment of accounts and their associated selling activities to salespeople and teams. Models, systems, processes, and wisdom have evolved over 1,500 project implementations for 500 companies with 500,000 sales territories.Optimization models have evolved over time to explicitly consider travel time along road networks and customer disruption. Personal computers with continually increasing speeds and storage capabilities, the Internet, and mapping databases have enabled the development of systems that communicate alignments visually to sales managers. Because of their combinatorial complexity, multiple conflicting objectives, and personnel aspects that touch everyone in the salesforce, the alignment models were unable to completely solve the sales territory alignment issues faced by companies. Consequently, processes that add local managerial knowledge were used to communicate and enhance model-derived solutions, while achieving very high implementation rates.The territory alignment team gains knowledge with every sales territory alignment. Alignment insights get codified. Alignment experts improve every model-derived solution. This wisdom becomes part of subsequent alignments and triggers further innovation. Over time, the role of processes and wisdom becomes larger than the role of the models and systems.