Operations Research Model Formulation for Road Maintenance Case
Abstract
Operations research can be used to apply analytical methods that help make precise and reasonable decisions. In road maintenance, basic principles of operations research are used to create model formulation that could help lower costs in case of an inaccurately made decision. First, the paper provides a literature review on different model formulations. Afterward, hypotheses are proposed regarding the model formulation, and then the model that minimises total generalised costs from wrong duty orders for road maintenance is offered. In conclusion, the paper evaluates the hypotheses and the process of improving the mathematical model.
Keywords: |
Model formulation; operations research; road maintenance
|
Full Text: |
References
J. Grabis, Ž. Bondars, J. Kampars, Ē. Dobelis, and A. Zaharčukovs, “Context-Aware Customizable Routing Solution for Fleet Management,” in Proceedings of the 19th International Conference on Enterprise Information Systems - Volume 1: ICEIS, Porto, Portugal, 2017, pp. 638–645. https://doi.org/10.5220/0006366006380645
R. S. Pindyck and D. L. Rubinfeld, Econometric Models and Economic Forecasts: Tsp Handbook, vol. 4. Irwin/McGraw-Hill Boston, 1997.
J. Zdravkovic, J. Kampars, and J. Stirna, “Using open data to support organizational capabilities in dynamic business contexts,” in Lecture Notes in Business Information Processing, LNBIP, vol. 316, 2018, pp. 28–39. https://doi.org/10.1007/978-3-319-92898-2_3
J. Grabis and V. Minkēviča, “Context-aware multi-objective vehicle routing”, in Proceedings of 31st European Conference on Modelling and Simulation, pp. 235–239, 2017. https://doi.org/10.7148/2017-0235
J. B. Edwards, “Speed adjustment of motorway commuter traffic to inclement weather,” Transp. Res. Part F: Traffic Psychol. Behav., vol. 2, no. 1, pp. 1–14, Mar. 1999. https://doi.org/10.1016/S1369-8478(99)00003-0
Y. Y. Nguwi and A. Z. Kouzani, “Detection and classification of road signs in natural environments,” Neural Comput. Appl., vol. 17, no. 3, pp. 265–289, Jun. 2008. https://doi.org/10.1007/s00521-007-0120-z
S. J. Jeffrey, J. O. Carter, K. B. Moodie, and A. R. Beswick, “Using spatial interpolation to construct a comprehensive archive of Australian climate data,” Environ. Model. Softw., vol. 16, no. 4, pp. 309–330, 2001. https://doi.org/10.1016/S1364-8152(01)00008-1
T. R. Willemain, “Model Formulation: What Experts Think About and When,” Oper. Res., vol. 43, no. 6, pp. 916–932, 1995. https://doi.org/10.1287/opre.43.6.916
H. Y. Feng and C. H. Menq, “The prediction of cutting forces in the ballend milling process-II. Cut geometry analysis and model verification,” Int. J. Mach. Tools Manuf., vol. 34, no. 5, pp. 711–719, 1994. https://doi.org/10.1016/0890-6955(94)90053-1
D. Kraay, P. T. Harker, and B. Chen, “Optimal Pacing of Trains in Freight Railroads: Model Formulation and Solution,” Oper. Res., vol. 39, no. 1, pp. 82–99, 1991. https://doi.org/10.1287/opre.39.1.82
R. Daley, C. Girard, J. Henderson, and I. Simmonds, “Short-term forecasting with a multi-level spectralprimitive equation model part II - Hemispheric prognoses and verification,” Atmosphere, vol. 14, no. 2, pp. 117–135, 1976. https://doi.org/10.1080/00046973.1976.9648406
H. P. Williams and R. G. Jeroslow, “Logic-Based Decision Support: Mixed Integer Model Formulation,” The Journal of the Operational Research Society, vol. 41, no. 4. 1990. https://doi.org/10.2307/2583807
D. P. Rowell, “A demonstration of the uncertainty in projections of UK climate change resulting from regional model formulation,” Clim. Change, vol. 79, no. 3–4, pp. 243–257, 2006. https://doi.org/10.1007/s10584-006-9100-z
P. J. Zwaneveld et al., “Routing trains through railway stations: Model formulation and algorithms,” Transp. Sci., vol. 30, no. 3, pp. 181–194, 1996. https://doi.org/10.1287/trsc.30.3.181
J. M. Martel and B. Aouni, “Diverse Imprecise Goal Programming Model Formulations,” J. Glob. Optim., vol. 12, no. 2, pp. 127–138, 1998.
Y. Shafahi and A. Khani, “A practical model for transfer optimization in a transit network: Model formulations and solutions,” Transp. Res. Part A Policy Pract., vol. 44, no. 6, pp. 377–389, 2010. https://doi.org/10.1016/j.tra.2010.03.007
B. Wagner, “Model formulations for hub covering problems,” J. Oper. Res. Soc., vol. 59, no. 7, pp. 932–938, 2008. https://doi.org/10.1057/palgrave.jors.2602424
D. Battini, A. Persona, and F. Sgarbossa, “A sustainable EOQ model: Theoretical formulation and applications,” Int. J. Prod. Econ., vol. 149, pp. 145–153, 2014. https://doi.org/10.1016/j.ijpe.2013.06.026
H. Yan, Z. Yu, and T. C. E. Cheng, “A strategic model for supply chain design with logical constraints: Formulation and solution,” Comput. Oper. Res., vol. 30, no. 14, pp. 2135–2155, 2003. https://doi.org/10.1016/S0305-0548(02)00127-2
J. Blazewicz, M. Dror, and J. Weglarz, “Mathematical programming formulations for machine scheduling: A survey,” Eur. J. Oper. Res., vol. 51, no. 3, pp. 283–300, 1991. https://doi.org/10.1016/0377-2217(91)90304-E
A. Alfieri, P. Brandimarte, and S. D’Orazio, “LP-based heuristics for the capacitated lot-sizing problem: The interaction of model formulation and solution algorithm,” Int. J. Prod. Res., vol. 40, no. 2, pp. 441–458, 2002. https://doi.org/10.1080/00207540110081461
R. J. I. Basten, J. M. J. Schutten, and M. C. van der Heijden, “An efficient model formulation for level of repair analysis,” Ann. Oper. Res., vol. 172, no. 1, pp. 119–142, 2009. https://doi.org/10.1007/s10479-009-0516-5
D. A. Saville and O. A. Palusinski, “Theory of electrophoretic separations. Part I: Formulation of a mathematical model,” AIChE J., vol. 32, no. 2, pp. 207–214, 1986. https://doi.org/10.1002/aic.690320206
M. De Domenico et al., “Mathematical formulation of multilayer networks,” Phys. Rev. X3, p. 41022, 2014. https://doi.org/10.1103/PhysRevX.3.041022
D. Kraay, P. T. Harker, and B. Chen, “Optimal Pacing of Trains in Freight Railroads: Model Formulation and Solution,” Oper. Res., vol. 39, no. 1, pp. 82–99, 1991. https://doi.org/10.1287/opre.39.1.82
R. Hammami, Y. Frein, and A. B. Hadj-Alouane, “A strategic-tactical model for the supply chain design in the delocalization context: Mathematical formulation and a case study,” Int. J. Prod. Econ., vol. 122, no. 1, pp. 351–365, 2009. https://doi.org/10.1016/j.ijpe.2009.06.030
M. J. Vrhel and H. J. Trussell, “Color device calibration: A mathematical formulation,” IEEE Trans. Image Process., vol. 8, no. 12, pp. 1796–1806, 1999. https://doi.org/10.1109/83.806624
L. Mockus and G. V. Reklaitis, “Mathematical programming formulation for scheduling of batch operations based on nonuniform time discretization,” Comput. Chem. Eng., vol. 21, no. 10, pp. 1147–1156, 1997. https://doi.org/10.1016/S0098-1354(96)00325-0
A. I. Zacharof and A. P. Butler, “Stochastic modelling of landfill leachate and biogas production incorporating waste heterogeneity. Model formulation and uncertainty analysis,” Waste Manag., vol. 24, no. 5, pp. 453–462, 2004. https://doi.org/10.1016/j.wasman.2003.09.010
C. E. Miller, R. A. Zemlin, and A. W. Tucker, “Integer Programming Formulation of Traveling Salesman Problems,” J. ACM, vol. 7, no. 4, pp. 326–329, 1960. https://doi.org/10.1145/321043.321046
B. K. Stone, “A Linear Programming Formulation of the General Portfolio Selection Problem,” J. Financ. Quant. Anal., vol. 8, no. 4, pp. 621–636, 1973. https://doi.org/10.2307/2329828
A. Bellabdaoui and J. Teghem, “A mixed-integer linear programming model for the continuous casting planning,” Int. J. Prod. Econ., vol. 104, no. 2, pp. 260–270, 2006. https://doi.org/10.1016/j.ijpe.2004.10.016
S. Benati and R. Rizzi, “A mixed integer linear programming formulation of the optimal mean/value-at-risk portfolio problem,” Eur. J. Oper. Res., vol. 176, no. 1, pp. 423–434, 2007. https://doi.org/10.1016/j.ejor.2005.07.020
B. Bilgen and I. Ozkarahan, “A mixed-integer linear programming model for bulk grain blending and shipping,” Int. J. Prod. Econ., vol. 107, no. 2, pp. 555–571, 2007. https://doi.org/10.1016/j.ijpe.2006.11.008
K. L. Croxton, B. Gendron, and T. L. Magnanti, “A Comparison of Mixed-Integer Programming Models for Nonconvex Piecewise Linear Cost Minimization Problems,” Manage. Sci., vol. 49, no. 9, pp. 1268–1273, 2003. https://doi.org/10.1287/mnsc.49.9.1268.16570
P. Refalo, “Linear formulation of constraint programming models and hybrid solvers,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1894, pp. 369–383, 2000. https://doi.org/10.1007/3-540-45349-0_27
DOI: 10.7250/itms-2019-0005
Refbacks
- There are currently no refbacks.
Copyright (c) 2019 Jānis Pekša, Kristaps-Pēteris Rubulis
This work is licensed under a Creative Commons Attribution 4.0 International License.