Using Biased-Randomized Algorithms for the Multi-Period Product Display Problem with Dynamic Attractiveness

From brick-and-mortar stores to omnichannel retail, the efficient selection of products to be displayed on store tables, advertising brochures, or online front pages has become a critical issue. One possible goal is to maximize the overall ‘attractiveness’ level of the displayed items, i.e., to enhance the shopping experience of our potential customers as a way to increase sales and revenue. With the goal of maximizing the total attractiveness value for the visiting customers over a multi-period time horizon, this paper studies how to configure an assortment of products to be included in limited display spaces, either physical or online. In order to define a realistic scenario, several constraints are considered for each period and display table: (i) the inclusion of both expensive and non-expensive products on the display tables; (ii) the diversification of product collections; and (iii) the achievement of a minimum profit margin. Moreover, the attractiveness level of each product is assumed to be dynamic, i.e., it is reduced if the product has been displayed in a previous period (loss of novelty) and vice versa. This generates dependencies across periods. Likewise, correlations across items are also considered to account for complementary or substitute products. In the case of brick-and-mortar stores, for instance, solving this rich multi-period product display problem enables them to provide an exciting experience to their customers. As a consequence, an increase in sales revenue should be expected. In order to deal with the underlying optimization problem, which contains a quadratic objective function in its simplest version and a non-smooth one in its complete version, two biased-randomized metaheuristic algorithms are proposed. A set of new instances has been generated to test our approach and compare its performance with that of non-linear solvers.