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You asked: What is the difference between up-, cross- and down-selling?
The aim of X-selling is to change the intended purchase behavior of a customer. This can be done in three possible ways: up-selling, cross-selling or down-selling. The idea of up-selling is to sell more of a given product, usually at the time of purchase. An example of this is if you order a lager beer (e.g., Stella Artois) and the waiter recommends an upscale, more expensive beer instead (e.g., a specialty Trappist beer such as Westmalle). Cross-selling aims at selling an additional product or service. For example, the waiter might also recommend some abbey cheese as it pairs well with a Westmalle. Finally, down-selling means selling less of a product or service in order to maintain a sustainable, long-lasting customer relationship. For example, if you had too many beers and order yet another one, the waiter might discourage you from doing so and recommend water instead.
From an analytical perspective, X-selling applications are usually developed using descriptive analytics techniques. As an example, association rules can be used to detect frequently occurring patterns between purchased items and, as such, recommend products or services for cross-selling. The resulting associations can be used for product bundling, catalogue design, store layout and/or shelf organization. Association rules can also be used to develop recommender systems.