## 1 Introduction
In this case, the solution consists of a 2-period time horizon. In each period, there are 3 display tables with a capacity of 5 items each. Each display table and item is represented by its identifier (ID). Hence, for instance, in period \(h_{1}\), display table 2 will be composed of items 11, 29, 45, 18, and 5. When selecting a set of products to be displayed, one should always consider customer preferences and willingness to buy [15]. Current online display systems provide a list of products that are either based on the user's past behavior or on decisions made by similar users. This strategy has been widely applied in e-commerce, where it has generated raised sales as well as customer satisfaction [16]. Companies such as Amazon use a method called collaborative filtering. Here, ratings and purchases made by similar users are considered to suggest products to online customers [17]. This product selection problem is also relevant for brick-and-mortar stores, since they might benefit from an optimal selection of products to be displayed over a multi-period time horizon. The main contributions of this paper are described next: (i) a novel mathematical formulation for the multi-period  
Figure 1: A solution representation for a simple multi-period product display problem. product display problem with dynamic attractiveness levels is proposed in order to clearly define the problem under consideration--while analyzing a case study, the assumptions of this model were discussed with professionals of the retail sector, who were also students in an MBA offered at our business school--(ii) in order to solve this optimization problem in the context of a retail store with several display tables, biased-randomized (BR) versions of the greedy randomized adaptive search procedure (GRASP) and the iterated local search (ILS) are introduced; (iii) a set of novel benchmark instances, considering realistic constraints and different product characteristics, is proposed to test the quality of our approach when compared with non-linear solvers; and (iv) based on the outcomes of our experiments, a series of practical recommendations are provided. A complete introduction to biased-randomization techniques can be found in [PERSON] et al. (2018). A review of GRASP algorithms can be found in [PERSON] and [PERSON] (2019), while a description of the ILS metaheuristic framework can be found in [PERSON] et al. (2019). Finally, a recent study on the combination of biased-randomization techniques with GRASP is available in [PERSON] et al. (2019). Regarding the constraints considered in this work, they include diversity of fashion collections, selling-price categories, and marginal-profit categories. Likewise, dependencies across both periods and items are considered in our study. The rest of the paper is arranged as follows: Section 2 presents a literature review of related research; Section 3 describes the problem in more detail and provides a mathematical formulation for it; Section 4 introduces the proposed biased-randomized algorithms; Section 5 includes an explanation of the computational experiments carried out to test the quality of our approach, while Section 6 contains an analysis of the results; finally, Section 7 highlights the main conclusions of this work and proposes some lines for future research.