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.
Bibliographical noteFunding Information:
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.
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- Bilevel optimization
- Brain storm algorithm
- Sales territory design