Abstract
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.
Highlights
As discussed in Verhoef et al [1], customers today are changing the way they decide where, how, and even when to buy
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; Section 7 highlights the main conclusions of this work and proposes some lines for future research
Newly generated solutions are compared with the base solution, and the former is updated in two cases: (i) when the new solution is better than the base solution; or (ii) when the new solution is worse than the base solution, but the difference in value is lower than the improvement obtained in the last update of the base solution
Summary
As discussed in Verhoef et al [1], customers today are changing the way they decide where, how, and even when to buy. The main contributions of this paper are described : (i) a novel mathematical formulation for the multi-period 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 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. 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; Section 7 highlights the main conclusions of this work and proposes some lines for future research
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