# Optimization of Warehouse Operations with Genetic Algorithms
## 1 Introduction  
A large share of operating costs related to product storage is connected to order picking. Based on many studies, it has been established that about 60% of warehouse operation costs are the costs of picking up goods when completing orders [1]. As the speed of this operation is a decisive factor in the response time to customers' orders and is one of the factors contributing to their decision about choosing or not the same company at the next purchase, it seems that the role of the speed of order completion is even greater. Thus, shortening the time of order picking is the most important and most beneficial factor in reducing the costs of operating the warehouse. It can be achieved without significant costs by optimizing the locations for particular products in a warehouse and then determining the fastest order completion routes in the optimized product placement. Some aspects of the optimization seems obvious, for example that items that are often ordered together should be placed close to each other, and frequently purchased items should be located close to the delivery point. However, for the case of discrete variables, considered in this paper, where the location sizes are fixed (some goods, e.g., storage of the sand, gravel, and so forth, can be expressed by continuous variables, but this problem is not considered here), with \(N\) items in the warehouse,the number of all possible their placements is \(N!\). For \(N=100\) it gives \(N!=9.33\times 10^{157}\), and even if the computer could analyze 1 billion permutations per second, it would \(9.33\times 10^{157}\) years to find the best product placement. So in practice, designing manually an optimal product placement is impossible, as the number of possible arrangements significantly exceeds the possibilities of analyzing all solutions by humans, or even by a computer program, which tries all possible configurations. In this paper, we present a complete, fully automated system based on artificial intelligence, particularly on genetic algorithms, which can overcome the limitations of the search space by an intelligent search. The system usually analyzes only several thousands to several tens of thousands possible product placements to find the optimal solution or at least a solution so close to the optimal one, that in practice it will not make any difference. Moreover, the system returns also the quickest order picking routes. The advantage of applying such a solution is speeding up the operations and thus reduction of warehouse operating costs (where typically 60% are the costs of order picking [1]) and the possibility to serve more customers by the same employees in the same time and thus to further increase the sales and profits. Although this issue has been analyzed for a long time, and especially in recent years its intensive development has been taking place [2; 3; 4], we were not able to find in the literature a complete, accurate, fully automatic solution, which would consider the real distribution of orders in the optimization of product placements. All the papers we were able to find presented only some partial approaches, with big simplifications, for example that the route length is determined only by one product with the longest distance from the entrance [2], or that the user is responsible for re-allocating the products by placing the more frequently used closer to the entrance [5]. Moreover, frequently the list of products within a single order is quite long, especially in the warehouses which sell goods mostly to retailers, what makes the optimization even more important. The purpose of this paper is to fill the gap by presenting our solution and by discussing its particular aspects and their influence on the accuracy and speed of the warehouse optimization process.