Skip to main content

Advertisement

Springer Nature Link
Log in

A discrete bilevel brain storm algorithm for solving a sales territory design problem: a case study

  • Regular Research Paper
  • Published:
Memetic Computing Aims and scope Submit manuscript

Abstract

A sales territory design problem faced by a manufacturing company that supplies products to a group of customers located in a service region is addressed in this paper. The planning process of designing the territories has the objective to minimizing the total dispersion of the customers without exceeding a limited budget assigned to each territory. Once territories have been determined, a salesperson has to define the day-by-day routes to satisfy the demand of customers. Currently, the company has established a service level policy that aims to minimize total waiting times during the distribution process. Also, each territory is served by a single salesperson. A novel discrete bilevel optimization model for the sales territory design problem is proposed. This problem can be seen as a bilevel problem with a single leader and multiple independent followers, in which the leader’s problem corresponds to the design of territories (manager of the company), and the routing decision for each territory corresponds to each follower. The hierarchical nature of the current company’s decision-making process triggers some particular characteristics of the bilevel model. A brain storm algorithm that exploits these characteristics is proposed to solve the discrete bilevel problem. The main features of the proposed algorithm are that the workload is used to verify the feasibility and to cluster the leader’s solutions. In addition, four discrete mechanisms are used to generate new solutions, and an elite set of solutions is considered to reduce computational cost. This algorithm is used to solve a real case study, and the results are compared against the current solution given by the company. Results show a reduction of more than 20% in the current costs with the solution obtained by the proposed algorithm. Furthermore, a sensitivity analysis is performed, providing interesting managerial insights to improve the current operations of the company.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Altman M (1997) Is automation the answer: the computational complexity of automated redistricting. Rutgers Comput Technol Law J 23(1):81–142

    Google Scholar 

  2. Angel-Bello F, Martínez-Salazar I, Alvarez A (2013) Minimizing waiting times in a route design problem with multiple use of a single vehicle. Electron. Notes Discrete Math 41:269–276

    Article  Google Scholar 

  3. Bacao F, Lobo V, Painho M (2005) Applying genetic algorithms to zone design. Soft Comput 9:341–348

    Article  Google Scholar 

  4. Bard JF (1991) Some properties of the bilevel programming problem. J Optim Theory Appl 68(2):371–378

    Article  MathSciNet  Google Scholar 

  5. Caramia M, Mari R (2016) A decomposition approach to solve a bilevel capacitated facility location problem with equity constraints. Optim Lett 10(5):997–1019

    Article  MathSciNet  Google Scholar 

  6. Cheng S, Qin Q, Chen J, Shi Y (2016) Brain storm optimization algorithm: a review. Artif Intell Rev 46:445–458

    Article  Google Scholar 

  7. Chou C, Kimbrough SO, Sullivan-Fedock J, Woodard CJ, Murphy FH (2012) Using interactive evolutionary computation (IEC) with validated surrogate fitness functions for redistricting. In: Genetic and evolutionary computation conference. ACM Digital Library, pp 1071–1078

  8. Chou CI (2011) A knowledge-based evolution algorithm approach to political districting problem. Comput Phys Commun 182:209–212

    Article  MathSciNet  Google Scholar 

  9. El-Abd M (2017) Global-best brain storm optimization algorithm. Swarm Evol Comput 37:27–44

    Article  Google Scholar 

  10. Hansen P, Jaumard B, Savard G (1992) New branch-and-bound rules for linear bilevel programming. SIAM J Sci Stat Comput 13(5):1194–1217

    Article  MathSciNet  Google Scholar 

  11. Hu F, Yang S, Xu W (2014) A non-dominated sorting genetic algorithm for the location and districting planning of earthquake shelters. Int J Geogr Inf Sci 28(7):1482–1501

    Article  Google Scholar 

  12. Iannoni AP, Morabito R, Saydam C (2009) An optimization approach for ambulance location and the districting of the response segments on highways. Eur J Oper Res 195:528–542

    Article  Google Scholar 

  13. Kalcsics J, Nickel S, Schröder M (2005) Towards a unified territorial design approach: applications, algorithms and GIS integration. Top 13(1):1–56

    Article  MathSciNet  Google Scholar 

  14. Karahan I, Köksalan M (2010) A territory defining multiobjective evolutionary algorithms and preference incorporation. Trans Evol Comput 14(4):636–664

    Article  Google Scholar 

  15. Lei H, Laporte G, Guo B (2012) Districting for routing with stochastic customers. EURO J Transp Logist 1(1–2):67–85

    Article  Google Scholar 

  16. Lei H, Wang R, Laporte G (2016) Solving a multi-objective dynamic stochastic districting and routing problem with a co-evolutionary algorithm. Comput Oper Res 67:12–24

    Article  MathSciNet  Google Scholar 

  17. Nucamendi-Guillén S, Martínez-Salazar I, Angel-Bello F, Moreno-Vega JM (2016) A mixed integer formulation and an efficient metaheuristic procedure for the k-travelling repairmen problem. J Oper Res Soc 67(8):1121–1134

    Article  Google Scholar 

  18. Ribeiro GM, Laporte G (2012) An adaptive large neighborhood search heuristic for the cumulative capacitated vehicle routing problem. Comput Oper Res 39(3):728–735

    Article  MathSciNet  Google Scholar 

  19. Rincón-García EA, Gutiérrez-Andrade MA, de-los Cobos-Silva SG, Lara-Velázquez P, Mora-Gutiérrez RA, Ponsich A (2012) A discrete particle swarm optimization algorithm for designing electoral zones. In: Methods for decision making in an uncertain environment, pp 174–197

  20. Rivera JC, Afsar HM, Prins C (2015) A multistart iterated local search for the multitrip cumulative capacitated vehicle routing problem. Comput Optim Appl 61(1):159–187

    Article  MathSciNet  Google Scholar 

  21. Salazar-Aguilar MA, Ríos-Mercado RZ, González-Velarde JL, Molina J (2012) Multiobjective scatter search for a commercial territory design problem. Ann Oper Res 199(1):343–360

    Article  MathSciNet  Google Scholar 

  22. Saucedo-Martínez JA, Pérez-Lara M, Marmolejo-Saucedo JA, Salais-Fierro TE, Vasant P (2017) Industry 4.0 framework for management and operations: a review. J Ambient Intell Humaniz Comput 9:1–13

    Google Scholar 

  23. Shen L (2014) Research and application of v-SVR based on brain storm optimization algorithm. Master’s thesis, Lanzhou University

  24. Shi Y (2011) Brain storm optimization algorithm. Springer, Berlin, pp 303–309. https://doi.org/10.1007/978-3-642-21515-5_36

    Google Scholar 

  25. Sun Y (2014) A hybrid approach by integrating brain storm optimization algorithm with grey neural network for stock index forecasting. Abstr. Appl. Anal. 2014:1–10

    Google Scholar 

  26. Talbi EG (2013) Metaheuristics for bi-level optimization, vol 482. Springer, Berlin

    MATH  Google Scholar 

  27. Tavares-Pereira F, Rui Figueira J, Mousseau V, Roy B (2007) Multiple criteria districting problems. The public transportation network pricing system of the paris region. Ann Oper Res 154:69–92

    Article  MathSciNet  Google Scholar 

  28. Vanneschi L, Henriques R, Castelli M (2017) Multi-objective genetic algorithm with variable neighbourhood search for the electoral redistricting problem. Swarm Evol Comput 36:37–51

    Article  Google Scholar 

  29. Xiao N (2008) A unified conceptual framework for geographical optimization using evolutionary algorithms. Ann Assoc Am Geogr 98(4):795–817

    Article  Google Scholar 

  30. Zoltners AA, Sinha P (1983) Sales territory alignment: a review and model. Manag Sci 29(11):1237–1256

    Article  Google Scholar 

Download references

Acknowledgements

The research of the third author has been partially supported by the Mexican National Council for Science and Technology (CONACYT) through Grant SEP-CONACYT CB-2014-01-240814 and by the program of professional development of professors with the Grant PRODEP/511-6/17/7425 for research stays during his sabbatical year. The research of the first author has been funded by Universidad Panamericana through the grant “Fomento a la Investigación UP 2017”, under Project Code UP-CI-2017-ING-GDL-07.

Author information

Authors and Affiliations

  1. Campus Guadalajara, Facultad de Ingeniera, Universidad Panamericana, 45010, Zapopan, Jalisco, Mexico

    Samuel Nucamendi-Guillén

  2. Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León, Ave. Universidad s/n, San Nicolás de los Garza, CP 66450, Nuevo León, Mexico

    Dámaris Dávila & José-Fernando Camacho-Vallejo

  3. Facultad de Ingeniería y Ciencias Aplicadas, Universidad De Los Andes, Mons.Álvaro del Portillo, 12455, Las Condes, Santiago, Chile

    Rosa G. González-Ramírez

Authors
  1. Samuel Nucamendi-Guillén
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dámaris Dávila
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. José-Fernando Camacho-Vallejo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rosa G. González-Ramírez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to José-Fernando Camacho-Vallejo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nucamendi-Guillén, S., Dávila, D., Camacho-Vallejo, JF. et al. A discrete bilevel brain storm algorithm for solving a sales territory design problem: a case study. Memetic Comp. 10, 441–458 (2018). https://doi.org/10.1007/s12293-018-0266-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12293-018-0266-5

Keywords

Search

Navigation

pFad - Phonifier reborn

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.


Alternative Proxies:

Alternative Proxy

pFad Proxy

pFad v3 Proxy

pFad v4 Proxy