Dynamic Pricing

The pricing strategy can have two extreme settings. Maximum profit (or gross margin) is the strategy that prioritizes profit and sets prices with respect to maximum gross margin. On the other hand, maximum turnover is a strategy that maximizes turnover on the condition of at least zero profit. You can choose any strategy you wish between these two extremes, e.g. 30% profit and 70% turnover.

Products (items, types of goods) are grouped according to the purchasing behavior of the customer and according to the price level into homogeneous segments based on which the demand curve is modelled. For product segmentation we use hierarchical clustering that moves in the bottom-up method.  

Each product segment is subject to price elasticity analysis. We model what is referred to as the demand curve showing the interdependency of the price and the number of pieces sold. The demand model not only comprises the actual price of the item, but also the price charged by the competition, seasonality, the day of the week, the stage of the product’s life cycle etc. Demand is assessed in terms of the shape of the demand curve and model accuracy, based on which we decide whether the optimal price will be determined using optimization of the multi-armed bandit algorithm. Demand models are updated on a regular basis once every month together with product segmentation.

Optimization entails creating the optimal price. The task of optimization is formulated as a quadratic programming problem where the objective function is profit or the gross margin, the vector of unknowns is the optimal prices for individual items and the limitation is the conditions for a minimal total turnover, while in respect of individual items the limitation is a minimal price, maximal price, fixed price, minimal margin or the underestimating of competition. Optimization does not comprise all items but only those whose demand curves meet the set quality requirements. The resulting optimal prices are rounded up and saved in a database. Optimization is launched on a daily basis, with a summary report on changes in prices of margins likewise generated and issued on a daily basis.

In respect of a certain percentage of items, the demand model does not meet the minimal quality requirements (eg the resulting demand curve is rising, the item is new from yesterday and no demand curve exists for it as yet). In respect of items like these, optimization is not a suitable method. The solution is an algorithm referred to as the “multi-armed bandit”, using which Google successfully selects the best website design to achieve the maximal click rate. In essence, it entails the testing of several (say, three) pre-defined price levels and a smart rule which switches to the most profitable one as soon as possible. The advantage is that the bandit may be used wherever demand curves fail. Therefore, combined with optimization, the bandit provides a full solution to all items in the product catalogue