Towards Unifying Scheduling and Location Problems: A Non-Stationary Hypercube Model (This article was invited to be published in Gepros)
DOI:
https://doi.org/10.15675/gepros.v16i4.2865Palavras-chave:
Emergency Service Systems, Queueing Theory, Time-dependent, Discrete Event Simulation, Performance Measurement.Resumo
Purpose – this paper aims to develop a non-stationary hypercube model capable of uniting the properties that models for both problems seek (location and shift-scheduling problems).Theoretical framework – We present the proposed model using a mixed discrete-continuous time Markov chain and compares it to a discrete-event simulation through an illustrative example.
Design/methodology/approach – The method used in this paper is quantitative with a comparison between an approach of simulation and an exact model.
Findings – The results show a high similarity between both models. However, the proposed model does not present noise in performance measures such as waiting times and travel times. Nevertheless, the study of their residuals revealed that the proposed model has a lower sensitivity to events, such as shift endings and imperfections in dispatch preferences. Further studies may reduce such a variation by improvements in the calculations of performance measurements.
Research, Practical & Social implications – The mentioned results suggest that the proposed model may become an option for applications uniting location and shift-scheduling problems.
Originality/value – When developing location problems, we seek models that are capable of representing the pertinent geographic characteristics to the problem. On the other hand, when developing shift-scheduling problems, we seek models capable of capturing transient fluctuations in the components (such as demand, service times, available workforce, among others) of such a system. Therefore, in the search to improve the daily operations of systems, such as emergency service systems (ambulances, police, firefighters) using either of the two problems individually, it may lead to flawed conclusions.
Keywords - Emergency Service Systems; Queueing Theory; Hypercube non-stationary; Discrete Event Simulation; Performance Measurement.
Referências
Ansari, S., McLay, L. A., & Mayorga, M. E. (2017). A Maximum Expected Covering Problem for District Design. Transportation Science, 51(1), pp. 376-390. DOI: https://doi.org/10.1287/trsc.2015.0610
Atkinson, J. B., Kovalenko, I. N., Kuznetsov, N., & Mykhalevych, K. V. (2008). A hypercube queueing loss model with customer-dependent service rates. European Journal of Operational Research, 191, pp. 223-239. DOI: https://doi.org/10.1016/j.ejor.2007.08.014
Boyaci, B., & Geroliminis, N. (2015). Approximation methods for large-scale spatial queueing systems. Transportation Research Part B, 74, pp. 151-181. DOI: https://doi.org/10.1016/j.trb.2014.12.011
Brown, L., Gans, N., Mandelbaum, A., Sakov, A., Shen, H., Zeltyn, S., & Zhao, L. (2005). Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective. Journal of the American Statistical Association, 100(469), pp. 36-50. DOI: https://doi.org/10.1198/016214504000001808
Burwell, T. H., Jarvis, J. P., & McKnew, M. A. (1993). Modeling co-located servers and dispatch ties in the hypercube model. Computers & Operations Research, 20(2), pp. 113-119. DOI: https://doi.org/10.1016/0305-0548(93)90067-S
Defraeye, M., & Van Nieuwenhuyse, I. (2016). Staffing and Scheduling under nonstationary demand for service: A literature review. Omega, 58, pp. 4-25. DOI: https://doi.org/10.1016/j.omega.2015.04.002
Galvão, R. D., & Reinaldo, M. (2008). Emergency service systems: The use of hypercube queueing model in the solution of probabilistic location problems. International Transactions in Operational Research, 15, pp. 522-549. DOI: https://doi.org/10.1111/j.1475-3995.2008.00654.x
Gans, N., Koole, G., & Mandelbaum, A. (2003). Telephone Call Centers: Tutorial, Review, and Research Propects. Manufacturing & Service Operations Management, 5(2), pp. 79-141. DOI: https://doi.org/10.1287/msom.5.2.79.16071
Geroliminis, N., Kepaptsoglou, K., & Karlaftis, M. G. (2011). A hybrid hypercube - Genetic algorithm approach for deploying many emergency response mobile units in an urban network. European Journal of Operational Research, 210, pp. 287-300. DOI: https://doi.org/10.1016/j.ejor.2010.08.031
Gillard, J., & Knight, V. (2014). Using Singular Spectrum Analysis to obtain staffing level requirements in emergency units. Journal of the Operational Research Society, 65, pp. 735-746. DOI: https://doi.org/10.1057/jors.2013.41
Green, L. V., & Kolesar, P. J. (1995). On the Accuracy of the Simple Peak Hour Approximation for Markovian Queues. Management Science, 41(8), pp. 1353-1370. DOI: https://doi.org/10.1287/mnsc.41.8.1353
Green, L. V., & Soares, J. (2007). Note-Computing Time-Dependent Waiting Time Probabilities in M(t)/M/s(t) Queuing Systems. Manufacturing & Service Operations Management, 9(1), pp. 54-61. DOI: https://doi.org/10.1287/msom.1060.0127
Green, L. V., Kolesar, P. J., & Soares, J. (2001). Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands. Operations Research, 49(4), pp. 549-564. DOI: https://doi.org/10.1287/opre.49.4.549.11228
Iannoni, A. P., Chiyoshi, F., & Morabito, R. (2015). A spatially distributed queuing model considering dispatching policies with server reservation. Transportation Research Part E, 75, pp. 49-66. DOI: https://doi.org/10.1016/j.tre.2014.12.012
Ingolfsson, A. (2005). Modeling the M(t)/M/s(t) Queue with Exhaustive Discipline. Fonte: http://www.bus.ualberta.ca/aingolfsson/working_papers.htm
Ingolfsson, A., Akhmetshina, E., Budge, S., Li, Y., & Wu, X. (2007). A Suvey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline. INFORMS Journal on Computing, 19(2), pp. 201-214. DOI: https://doi.org/10.1287/ijoc.1050.0157
Ingolfsson, A., Campello, F., Wu, X., & Cabral, E. (2010). Combining integer programming and the randomization method to schedule employees. European Journal of Operational Research, 202, pp. 153-163. DOI: https://doi.org/10.1016/j.ejor.2009.04.026
Ingolfsson, A., Haque, A., & Umnikov, A. (2002). Accounting for time-varying queueing effects in workforce scheduling. European Journal of Operational Research, 139, pp. 585-597. DOI: https://doi.org/10.1016/S0377-2217(01)00169-2
Jarvis, J. P. (1985). Approximating the Equilibrium Behavior of Multi-Server Loss Systems. Management Science, 31(2), pp. 235-239. DOI: https://doi.org/10.1287/mnsc.31.2.235
Kim, S.-H., & Whitt, W. (2014). Are Call Centers and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes. Manufacturing & Service Operations Management, 16(3), pp. 464-480. DOI: https://doi.org/10.1287/msom.2014.0490
Larson, R. (1974). A Hypercube Queueing Model for Facility Location and Redistricting in Urban Emergency Services. Computers & Operations Research, 1, pp. 67-95. DOI: https://doi.org/10.1016/0305-0548(74)90076-8
Larson, R. (1975). Approximating the Performance of Urban Emergency Service Systems. Operations Research, 23(5), pp. 845-868. DOI: https://doi.org/10.1287/opre.23.5.845
Mandelbaum, A., & Zeltyn, S. (2009). Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers. Operations Research, 57(5), pp. 1189-1205. DOI: https://doi.org/10.1287/opre.1080.0651
Marianov, V., & ReVelle, C. (1996). The Queueing Maximal Availability Location Problem: A model for the siting of emergency vehicles. European Journal of Operational Research, 93, pp. 110-120. DOI: https://doi.org/10.1016/0377-2217(95)00182-4
Owen, S. H., & Daskin, M. S. (1998). Strategic facility location: A review. European Journal of Operational Research, 111, pp. 423-447. DOI: https://doi.org/10.1016/S0377-2217(98)00186-6
Patrick, J., Puterman, M. L., & Queyranne, M. (2008). Dynamic Multipriority Patient Scheduling for a Diagnostic Resource. Operations Research, 56(6), pp. 1507-1525. DOI: https://doi.org/10.1287/opre.1080.0590
Rajagopalan, H. K., Saydam, C., & Xiao, J. (2008). A multiperiod set covering location model for dynamic redeployment of ambulances. Computers & Operations Research, 35, pp. 814-826. DOI: https://doi.org/10.1016/j.cor.2006.04.003
Rodrigues, L. F., Morabito, R., Chiyoshi, F., Iannoni, A. P., & Saydam, C. (2017). Towards hypercube queuing models for dispatch policies with priority in queue and partial backup. Computers & Operations Research, 84, pp. 92-105. DOI: https://doi.org/10.1016/j.cor.2017.02.021
Schwarz, J. A., Selinka, G., & Stolletz, R. (2016). Performance analysis of time-dependent queueing systems: Survey and classification. Omega, 63, pp. 170-189. DOI: https://doi.org/10.1016/j.omega.2015.10.013
Souza, R., Morabito, R., Chiyoshi, F., & Iannoni, A. (2015). Incorporating priorities for waiting customers in the hypercube queuing model with application to an emergency medical service system in Brazil. European Journal of Operational Research, 242, pp. 274-285. doi:10.1016/j.ejor.2014.09.056 DOI: https://doi.org/10.1016/j.ejor.2014.09.056
Taha, H. A. (2008). Operations Research: An Introduction (8th ed.). Prentice Hall.
Takeda, R. A., Widmer, J. A., & Morabito, R. (2007). Analysis of ambulance descentralization in an urban emergency medical service using the hypercube queueing model. Computers & Operations Research, 34, pp. 727-741. DOI: https://doi.org/10.1016/j.cor.2005.03.022
Downloads
Publicado
Como Citar
Edição
Seção
Licença
O(s) autor(es) do artigo autorizam a publicação do texto na revista e garantem que a contribuição é original e inédita, não estando em processo de avaliação em outra(s) revista(s). As opiniões, ideias e conceitos emitidos nos textos são de inteira responsabilidade do(s) autor(es), não sendo a revista responsável por tais conteúdos.
Os editores da revista reservam o direito de efetuar ajustes textuais e de adequação às normas da publicação, caso necessário.
Os autores mantêm os direitos autorais sobre o trabalho e concedem à revista o direito de primeira publicação, sendo o trabalho simultaneamente licenciado sob a Attribution 4.0 International (CC BY 4.0), o que permite o compartilhamento do trabalho com reconhecimento da autoria e publicação inicial nesta revista.
Os autores têm autorização para firmar contratos adicionais, separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
