Main Article Content
In this study, two novel stochastic models are introduced to solve the dynamic sectorization problem, in which sectors are created by assigning points to service centres. The objective function of the first model is defined based on the equilibration of the distance in the sectors, while in the second one, it is based on the equilibration of the demands of the sectors. Both models impose constraints on assignments and compactness of sectors. In the problem, the coordinates of the points and their demand change over time, hence it is called a dynamic problem. A new solution method is used to solve the models, in which expected values of the coordinates of the points and their demand are assessed by using the Monte Carlo simulation. Thus, the problem is converted into a deterministic one. The linear and deterministic type of the model, which is originally non-linear is implemented in Python's Pulp library and in this way the generated benchmarks are solved. Information about how benchmarks are derived and the obtained solutions are presented.
Sectorization , Dynamic problems, Stochastic modelling, Monte Carlo simulation, Shape optimization
 A. Teymourifar, A.M. Rodrigues, J.S. Ferreira. A comparison between simultaneous and hierarchical approaches to solve a multi-objective location-routing problem. Graphs and Combinatorial Optimization: from Theory to Applications. Springer2021. pp. 251-63.
 V. Romanciuc, C. Lopes, A. Teymourifar, A.M. Rodrigues, J.S. Ferreira, C. Oliveira, et al. An Integer Programming Approach to Sectorization with Compactness and Equilibrium Constraints. International Conference Innovation in Engineering. Springer2021. pp. 185-96.
 A. Teymourifar, A.M. Rodrigues, J.S. Ferreira, C. Lopes, C. Oliveira, V. Romanciuc. A Two-Stage Method to Solve Location-Routing Problems Based on Sectorization. International Conference Innovation in Engineering. Springer2021. pp. 148-59.
 A. Teymourifar, A.M. Rodrigues, J.S. Ferreira. A New Model for Location-Allocation Problem Based on Sectorization.
 S. Barreto, C. Ferreira, J. Paixao, B.S. Santos. Using clustering analysis in a capacitated location-routing problem. European Journal of Operational Research. 179 (2007) 968-77.
 M. Camacho-Collados, F. Liberatore, J.M. Angulo. A multi-criteria police districting problem for the efficient and effective design of patrol sector. European journal of operational research. 246 (2015) 674-84.
 O. Degtyarev, V. Minaenko, M. Orekhov. Solution of sectorization problems for an air traffic control area. I. Basic principles and questions of airspace sectorization and its formalization as an optimization problem. Journal of Computer and Systems Sciences International. 48 (2009) 384-400.
 I. Litvinchev, G. Cedillo, M. Velarde. Integrating territory design and routing problems. Journal of Computer & Systems Sciences International. 56 (2017) 969-74.
 A. Martinho, E. Alves, A.M. Rodrigues, J.S. Ferreira. Multicriteria location-routing problems with sectorization. Congress of APDIO, the Portuguese Operational Research Society. Springer2017. pp. 215-34.
 A.M. Rodrigues, J.S. Ferreira. Measures in sectorization problems. Operations research and big data. Springer2015. pp. 203-11.
 A.M. Rodrigues, J.S. Ferreira. Sectors and routes in solid waste collection. Operational Research. Springer2015. pp. 353-75.
 A.M. Rodrigues, J. Soeiro Ferreira. Waste collection routing—limited multiple landfills and heterogeneous fleet. Networks. 65 (2015) 155-65.
 K. Zhang, H. Yan, H. Zeng, K. Xin, T. Tao. A practical multi-objective optimization sectorization method for water distribution network. Science of The Total Environment. 656 (2019) 1401-12.
 A. Shapiro. Monte Carlo simulation approach to stochastic programming. proceeding of the 2001 winter simulation conference (cat no 01CH37304). IEEE2001. pp. 428-31.
 A. Teymourifar, G. Ozturk, O. Bahadir. A comparison between two modified NSGA-II algorithms for solving the multi-objective flexible job shop scheduling problem. Univ J Appl Math. 6 (2018) 79-93.
 H. Lei, R. Wang, G. Laporte. Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm. Computers & Operations Research. 67 (2016) 12-24.
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The copyright in the text of individual articles (including research articles, opinion articles, book reviews, conference proceedings and abstracts) is the property of their respective authors, subject to a general license granted to Mapta Publishing Group and a Creative Commons CC-BY licence granted to all others, as specified below. The compilation of all content on this site, as well as the design and look and feel of this website are the exclusive property of Mapta Publishing Group.
All contributions to Mapta Publishig Group may be copied and re-posted or re-published in accordance with the Creative Commons licence referred to below.
Articles and other user-contributed materials may be downloaded and reproduced subject to any copyright or other notices.
As an author or contributor you grant permission to others to reproduce your articles, including any graphics and third-party materials supplied by you, in accordance with the Mapta Publishing GroupTerms and Conditions and subject to any copyright notices which you include in connection with such materials. The licence granted to third parties is a Creative Common Attribution ("CC BY") licence. The current version is CC-BY, version 4.0 (http://creativecommons.org/licenses/by/4.0/), and the licence will automatically be updated as and when updated by the Creative Commons organisation.