Probabilistic Traveling Salesman Problem and Harmony Search Algorithms in Pharmacy Supply Optimization

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DOI:

https://doi.org/10.18778/0208-6018.345.06

Keywords:

Probabilistic Traveling Salesman Problem, Harmony Search, Pharmacy Supply Reliability

Abstract

This paper demonstrates the utilitarian significance of the Probabilistic Traveling Salesman Problem (PTSP) in planning travel routes by companies which provide distribution services for pharmacies, with a particular consideration of variable customer demand. The optimization problem was solved using the Harmony Search (HS) algorithm, thus verifying its utility based on one real instance of PTSP (representing the problem of pharmacy supply reliability) and three tasks from the public TSPLIB library (adjusted to PTSP). As a result of the conducted research, significant utility of the hybrid approach was identified, assuming the combination of HS with popular 2‑opt method, which enabled achievement of good results within acceptable period (in practical applications).

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References

Bianchi L., Gambardella L. M., Dorigo M. (2002), Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic, [in:] M. Dorigo, G. Di Caro, M. Sampels (eds.), Ant Algorithms. ANTS. Lecture Notes in Computer Science, vol. 2463, Springer, Berlin–Heidelberg, pp. 176–187, https://doi.org/10.1007/3-540-45724-0_15
Google Scholar

Boryczka U., Szwarc K. (2018), The Adaptation of the Harmony Search Algorithm to the ATSP, [in:] N. Nguyen, D. Hoang, T. P. Hong, H. Pham, B. Trawiński (eds.), Intelligent Information and Database Systems. ACIIDS 2018. Lecture Notes in Computer Science, vol. 10751, Springer, Cham, pp. 341–351, https://doi.org/10.1007/978-3-319-75417-8_32
Google Scholar

Boryczka U., Szwarc K. (2019), The Adaptation of the Harmony Search Algorithm to the ATSP with the evaluation of the influence of the pitch adjustment place on the quality of results, “Journal of Information and Telecommunication”, vol. 3(1), pp. 2–18, https://doi.org/10.1080/24751839.2018.1503149
Google Scholar

Bowler N. E., Fink T. M.A., Ball R. C. (2003), Characterization of the probabilistic traveling salesman problem, “Physical Review E”, vol. 68(3), https://doi.org/10.1103/PhysRevE.68.036703
Google Scholar

Geem Z. W. (2000), Optimal design of water distribution networks using harmony search, PhD thesis, Korea University.
Google Scholar

GUS (2017), Apteki i punkty apteczne w Polsce, https://stat.gov.pl/files/gfx/portalinformacyjny/pl/defaultaktualnosci/5513/15/2/1/apteki_i_punkty_apteczne_w_2017.pdf (accessed: 3.08.2018).
Google Scholar

Hetmaniok E., Jama D., Słota D., Zielonka A. (2011), Application of the Harmony Search algorithm in solving the inverse heat conduction problem, “Zeszyty Naukowe. Matematyka Stosowana/Politechnika Śląska”, no. 1, pp. 99–108.
Google Scholar

IQVIA (2017), Rynek farmaceutyczny w 2017 roku, https://www.nia.org.pl/wp-content/uploads/2018/01/IQVIA_Rynek_farmaceutyczny_2017_RAPORT.pdf (accessed: 3.08.2018).
Google Scholar

Jaillet P. (1985), Probabilistic Traveling Salesman Problems, PhD thesis, MIT, Cambridge.
Google Scholar

Jaillet P. (1988), A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers are Visited, “Operations Research”, vol. 36(6), pp. 929–936, https://doi.org/10.1287/opre.36.6.929
Google Scholar

Kiełkowicz K., Kokosiński Z. (2012), Algorytm hybrydowy dla probabilistycznego problemu komiwojażera, “Czasopismo Techniczne. Automatyka”, no. 109 (1 AC), pp. 115–126.
Google Scholar

Liu Y. H. (2007), A hybrid scatter search for the probabilistic traveling salesman problem, “Computers & Operations Research”, vol. 34(10), pp. 2949–2963, https://doi.org/10.1016/j.cor.2005.11.008
Google Scholar

Rynek aptek (2018), Trend spadkowy jest trwały – liczba aptek spada, http://www.rynekaptek.pl/marketing‑i‑zarzadzanie/trend‑spadkowy‑jest‑trwaly‑liczba‑aptek‑spada,27271.html (accessed: 3.08.2018).
Google Scholar

Szołtysek J. (2016), Logistyka w sferze dystrybucji, [in:] S. Kuf, E. Płaczek, A. Sadowski, J. Szołtysek, S. Twaróg, Vademecum logistyki, Difin, Warszawa, pp. 116–136.
Google Scholar

Weiler C., Biesinger B., Hu B., Raidl G. R. (2015), Heuristic Approaches for the Probabilistic Traveling Salesman Problem, [in:] R. Moreno Díaz, F. Pichler, A. Quesada Arencibia (eds.), Computer Aided Systems Theory – EUROCAST 2015. EUROCAST 2015. Lecture Notes in Computer Science, vol. 9520, Springer, Cham, pp. 342–349, https://doi.org/10.1007/978-3-319-27340-2_43
Google Scholar

Yang X. S. (2009), Harmony Search as a Metaheuristic Algorithm, [in:] Z. W. Geem (eds.), Music Inspired Harmony Search Algorithm. Studies in Computational Intelligence, vol. 191, Springer, Berlin–Heidelberg, pp. 1–14, https://doi.org/10.1007/978-3-642-00185-7_1
Google Scholar

Zott C., Amit R., Massa L. (2011), The cusiness model: Recent developments and future research, “Journal of Management”, vol. 37(4), pp. 1019–1049, https://doi.org/10.1177/0149206311406265
Google Scholar

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Published

2019-12-30

How to Cite

Twaróg, S., Szołtysek, J., Szwarc, K., & Boryczka, U. (2019). Probabilistic Traveling Salesman Problem and Harmony Search Algorithms in Pharmacy Supply Optimization. Acta Universitatis Lodziensis. Folia Oeconomica, 6(345), 111-125. https://doi.org/10.18778/0208-6018.345.06

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