# Genetic Algorithm for the Retailers' Shelf Space Allocation Profit Maximization Problem
## 7 Discussion  
Shelf space is one of the most essential and difficult resources to manage in detail. In this paper, the practical model of shelf space allocation restricted by four constraint subsets, and based on the retailer's visual merchandising rules, is formulated with the aim of maximizing profit through a planogram. Efficient shelf space allocation increases the visibility of the products, customer satisfaction, and sales generation, which is the key point for the retailer. Merchandising is the key driver of the visual representation of planogram in a retail store. In the retail industry, merchandising is the activity of promoting products in order to increase sales. Merchandising includes the way of displaying products in stores as well as free samples, distributing marketing materials, on-the-spot demonstration, and special offers or pricing. The aim of the merchandiser is to determine which types of fixtures, on which shelf types, and in which positions the product will be displayed. This is a very important task because incorrect product allocation negatively affects sales [35]. This research investigates an important merchandising rule of dividing shelves into segments and using horizontal and vertical ties between products and their location on the shelves, which varies between segments. Moreover, the segments are of flexible sizes. [PERSON] et al. [7, 8] developed an automatic planogram replication tool with regard to product families. [PERSON] and [PERSON] [44] model the problem by specifying the position of products on the shelves and block the product families into rectangular shapes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Products**} & \multirow{2}{*}{**Shelf Width**} & \multicolumn{2}{c}{**Two Rankings**} & **Roulette Wheel** & \multicolumn{1}{c}{**Tournament**} \\  & & **GA\({}^{+}\) Is Better** & \multicolumn{1}{c}{**GA\({}^{+}\) Is Better**} & \multicolumn{1}{c}{**GA\({}^{+}\) Is Better**} \\ \hline \multirow{4}{*}{10} & 100 & 83.51\% & 77.32\% & 79.13\% \\  & 200 & 76.07\% & 78.67\% & 66.38\% \\  & 250 & 51.65\% & 40.43\% & 32.24\% \\  & 375 & 90.35\% & 92.41\% & 90.86\% \\  & 500 & 82.95\% & 69.87\% & 31.94\% \\ \hline \multirow{4}{*}{15} & 100 & 96.66\% & 97.38\% & 95.46\% \\  & 200 & 35.77\% & 29.52\% & 64.99\% \\  & 250 & 41.15\% & 37.29\% & 56.93\% \\  & 375 & 74.83\% & 72.77\% & 71.72\% \\  & 500 & 45.02\% & 70.40\% & 74.47\% \\ \hline \multirow{4}{*}{20} & 100 & 95.34\% & 95.38\% & 94.92\% \\  & 200 & 30.68\% & 22.69\% & 47.48\% \\  & 250 & 31.21\% & 34.47\% & 49.96\% \\  & 375 & 30.17\% & 35.68\% & 44.13\% \\  & 500 & 66.62\% & 57.75\% & 52.37\% \\ \hline \multirow{4}{*}{25} & 200 & 77.55\% & 69.84\% & 83.64\% \\  & 250 & 91.93\% & 81.14\% & 67.66\% \\  & 375 & 46.49\% & 36.63\% & 63.16\% \\  & 500 & 64.31\% & 26.65\% & 59.91\% \\ \hline \multirow{4}{*}{50} & 250 & 65.00\% & 45.39\% & 62.66\% \\  & 375 & 54.31\% & 68.38\% & 69.06\% \\  & 500 & 91.62\% & 92.03\% & 71.55\% \\ \hline \multirow{4}{*}{25} & Min & 30.17\% & 22.69\% & 31.94\% \\  & Avg & 64.69\% & 60.55\% & 65.03\% \\ \cline{1-1}  & Max & 96.66\% & 97.38\% & 95.46\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard deviation of GA- solutions compared to standard deviation of GA+ solutions. Our approach is related to this stream and defines different types of shelf location (we name them virtual segments because the shelf is not divided physically into the segments, there are no borders between the segments, but space planners need an idea of creating such segments visually and this approach is very convenient). We also provide a method of defining such virtual segments with the centre coordinate specified and with flexible borders that could be reduced or extended. As a solution to the introduced SSAP, a genetic algorithm has been proposed, the efficiency of which has been evaluated using the CPLEX solver.