Conclusion
A novel continuous model for the LCAP with dense demand is proposed in this letter. Various demand densities are employed to adapt the population distribution in the market region, and a set of weighting coefficients are used to characterize the features of facilities, which represent the attracting process of facilities. Next, the power diagrams are applied to determine the allocation decisions of facilities, and a power diagram based iterative method is developed for solving the LCAP. Experimental results demonstrate the effectiveness of our proposed method.
References
Fan Q, Ansari N. On cost aware cloudlet placement for mobile edge computing. IEEE/CAA Journal of Automatica Sinica, 2019, 6(4): 926–937
Wu P, Yang C H, Chu F, Zhou M C, Sedraoui K, Al Sokhiry F S. Cost-profit trade-off for optimally locating automotive service firms under uncertainty. IEEE Transactions on Intelligent Transportation Systems, 2021, 22(2): 1014–1025
Iri M, Murota K, Ohya T. A fast voronoi-diagram algorithm with applications to geographical optimization problems. In: Proceedings of the 11th IFIP Conference Copenhagen. 1983, 273–288
Murat A, Verter V, Laporte G. A continuous analysis framework for the solution of location-allocation problems with dense demand. Computers & Operations Research, 2010, 37(1): 123–136
Bourne D P, Peletier M A, Roper S M. Hexagonal patterns in a simplified model for block copolymers. SIAM Journal on Applied Mathematics, 2014, 74(5): 1315–1337
Xin S Q, Lévy B, Chen Z G, Chu L, Yu Y H, Tu C H, Wang W P. Centroidal power diagrams with capacity constraints: computation, applications, and extension. ACM Transactions on Graphics, 2016, 35(6): 1–12
Acknowledgements
This study was partially supported by the National Natural Science Foundation of China (Grant No. 61972128).
Author information
Authors and Affiliations
Corresponding author
Additional information
Supporting information
The supporting information is available online at journal.hep.com.cn and link.springer.com.
Rights and permissions
About this article
Cite this article
Yao, Y., Wu, W., Zhang, G. et al. Power diagram based algorithm for the facility location and capacity acquisition problem with dense demand. Front. Comput. Sci. 16, 166709 (2022). https://doi.org/10.1007/s11704-022-0582-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11704-022-0582-2