Shelf Space Considerations
The retail industry is extremely competitive and every advantage even if small can make a difference for retailers. One of the most important problems in a retail store is shelf space management. The reason for this lies in the fact that shelf space has a limited capacity and, therefore, product allocation has to be carefully managed. Experimental studies show that there are factors that can influence sales, particularly in circumstances of impulse purchases. Among these factors is the number of facings, the location of products on shelves (vertical or horizontal) and product adjacencies. According to studies, products placed at eye-level and at the horizontal center of shelves are thought to have privileged locations which may increase their sales. Retailers also believe that products and their families (brand, size, among others), should form either uniform columns or uniform rows on shelves, for aesthetic purposes. Models reviewed, generally, do not include all constraints preferred by retailers and, therefore, still require improvements until they are adequate for real life application. The software applications available for shelf space management still require significant human interaction.Algorithms proposed
Two original Biased Random-key Genetic Algorithms have been developed and tested with real case study instances. Biased Random-key Genetic Algorithms have previously been successfully used to solve problems (Cutting and Packing Problems) that share similarities with the problem studied. In spite of this, BRKGAs had not yet been used to tackle the Shelf Space Allocation Problem. Algorithms developed take into considerations preferences from a real case study, namely: - The number of facings of a product should minimize its rotation days (number of days until the product becomes out-of-stock); - Facings of the same product should be preferably placed horizontally on shelves; - Families should form vertical or horizontal rectangular shapes on shelves; - The minimum number of facings should be respected; - The impact in sales of vertical and horizontal positioning is included. The first original algorithm developed was based on the algorithm developed by Gonçalves and Resende, for the Constrained Two-Dimensional Non-Guillotine Orthogonal Cutting Problem. The steps for this algorithm are the following: - Determine the number of facings: An input target number of facings suffers variations based on chromosome keys, to establish the number of facings of each product; - Calculate areas: Based on the number of facings, the area that each family will occupy on a shelf is calculated; - Sequence and allocate blocks: blocks are placed on shelves according to the order established by the chromosome. For the placement of blocks, methods used include: Bottom-Left, Left-Bottom and the Difference Process by Lai and Chan; - Evaluation of the solution: the solution obtained is evaluated according to a fitness function. The second algorithm developed is similar to the previous one, but with changes made concerning the allocation of product families on shelves. In this case, to place families vertically it is considered that they will occupy the entirety of the height of their containing family. the other hand to place product families horizontally, it is considered that they will occupy the entirety of the width of their containing family, in case they need more than one shelf. An exception happens if a family only needs one shelf and the same happens to the next family to be placed. In this case, more than one family will be placed on the same shelf. Both algorithms were tested with real case study instances. The results obtained by changing BRKGA parameters lead to the conclusion that, for the values tested, parameters do not significantly influence the final result, although a slightly higher percentage of instances was solved with a lower deviation from the best fitness for lower rhoe values. This means that the probability that offspring will result from the the elite parent should not be too high. Concerning the influence of the complexity of the planogram on time needed to solve the problem, results show that, among the parameters tested, the number of products to be placed on shelves is the one that has the most influence. Analyzing the results for the decoders, it can be concluded that decoder 1 solves a higher percentage of instances for lower values of the deviation from the best fitness function, compared to decoder 2. A reason for this lies in the fact that decoder 2 has additional constraints and, therefore, is more complex.Future Work
In spite of the algorithms developed there is still margin for improvement in the future. One possible improvement would be to consider products heights, although it is usually not necessary, since shelves are generally adjustable. The depth of facings is also not included in the algorithms due to the fact that it is not directly seen. By including it in the algorithms, the problem would become three-dimensional. There is also the possibility of incorporating cross-space elasticities in the algorithm, although these parameters are difficult to estimate. The algorithms receive a target number of facings as input, which is calculated, based on the rotations days of products. The fitness function aims to minimize the deviation from this target. In order for the algorithms to be more generic, the target number of facings could be calculated within the algorithms, eventually incorporating space and cross-space elasticities. To improve the algorithm's applicability in reality, changes can be made to the algorithm that would allow retailers to choose whether they prefer product families to be placed vertically or horizontally. Other retailer preferences can also be included. The algorithms developed were only tested for food retail instances placed in regular shelves. The algorithm could potentially be improved in order to be able to allocate other types of products and to place products on different types of shelves Finally, in the algorithm developed it is considered that the choice of products to be displayed (assortment problem) has already been made. It would be interesting to incorporate the assortment problem in the algorithm as this problem is interrelated with shelf space planning.