## Basic Variable Neighborhood Search for the Multi-Row facility layout problem considering facilities of equal length

**Nicolás Rodríguez**, Alberto Herrán, J. Manuel Colmenar, Abraham Duarte

The Multiple-Row Equal Facility Layout Problem (MREFLP) is particular case of MRFLP, where the facilities have the same width, which belongs to the family of Facility Layout Problems (FLP). This family is well-known in the industry sector, where this kind of problems has several real-life applications. Many papers can be found related to FLP, being one of the most referenced problems the Single Row Layout Problem (SFRFLP), which is a particular case of MRFLP where the number of rows is one. In the MREFLP the objective is to minimize a function that is calculated taking account the distance between facilities and the pairwise weights between the facilities. In the state of the art, we can find exact approaches to the MREFLP problem, but, to the best of our knowledge, this problem has not been approached from the heuristic side. Therefore, we propose the application of a Basic Variable Neighborhood Search algorithm to this problem. To increase the efficiency of the search, we have developed an efficient local search that is able to traverse the neighborhoods obtaining the cost of every solution by means of incremental steps. The experimental results show that this approach is able to find very good solutions spending very short computation times.

## BVNS approach for the Order Processing in Parallel Picking Workstations

**Abdessamad Ouzidan**, Eduardo G. Pardo, Marc Sevaux, Alexandru-Liviu Olteanu, Abraham Duarte

The Order Processing in Parallel Picking Workstations is an optimization problem that can be found in the industry and is related to the order picking process in a warehouse. The objective of this problem is to minimize the number of movements of goods within a warehouse in order to fulfill the demand made by the customers. The goods are originally stored in containers in a storage location and need to be moved to a processing area. The processing area is composed of several identical workstations. We are particularly interested in minimizing the time needed to fulfill all demands, which corresponds to the highest number of container movements to any given workstation. This problem is NP-Hard since it is a generalization of the well-known Order Processing in Picking Workstations which is also known to be NP-Hard. In this paper, we provide a mathematical formulation for the problem and additionally, due to its hardness, we have also developed several heuristic procedures based on Variable Neighborhood Search, to tackle the problem. The proposed methods have been evaluated over different sets of instances.

## Determining the time window for the Online Order Batching Problem and its combination with Variable Neighborhood Search

**Sergio Gil Borrás**, Eduardo G. Pardo, Antonio Alonso Ayuso, Abraham Duarte

The Online Order Batching Problem (OOBP) is an optimization problem consisting of determining an efficient picking operation in a warehouse, when the picking policy follows the order batching strategy. A subtask defined in the context of OOBP is to set the time window that a picker waits before starting the retrieval of the next available batch. A naïve approach consists of simply starting a new picking route as soon as possible (“No-Waiting”). However, there are two benefits related to the application of a waiting strategy: there might be more customer orders available in the system to conform the batches, and there are longer times to compute a solution. It is known that determining the right time- window strategy highly affects the quality of the final solutions for the OOBP. In this work, we compare the “No-Waiting” strategy with several Fixed Time Window and Variable Time Window proposals. We select the best strategy and we combine it with a General Variable Neighborhood Search (GVNS) procedure to tackle the OOBP. The use of a GVNS increases the profitable effect of applying time-window algorithms to obtain better overall solutions for the OOBP. Furthermore, in this study we compare the impact of these strategies over two different objective functions for the OOBP: the picking time and the completion time.
**Acknowledgement:** This research was partially funded by the projects: RTI2018-094269-B-I00 and PGC2018-095322-B-C22 from Ministerio de Ciencia, Innovación y Universidades (Spain); by Comunidad de Madrid and European Regional Development Fund, grant ref. P2018/TCS-4566; and by Programa Propio de I+D+i de la Universidad Politécnica de Madrid (Programa 466A).