Abstract
Effectively sharing resources requires solving complex decision problems. This requires constructing a mathematical model of the underlying system, and then applying appropriate mathematical methods to find an optimal solution of the model, which is ultimately translated into actual decisions. The development of mathematical tools for solving optimization problems dates back to Newton and Leibniz, but it has tremendously accelerated since the advent of digital computers. Today, optimization is an inter-disciplinary subject, lying at the interface between management science, computer science, mathematics and engineering. This chapter offers an introduction to the main theoretical and software tools that are nowadays available to practitioners to solve the kind of optimization problems that are more likely to be encountered in the context of this book. Using, as a case study, a simplified version of the bike sharing problem, we guide the reader through the discussion of modelling and algorithmic issues, concentrating on methods for solving optimization problems to proven optimality.
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References
Miller C, Tucker A, Zemlin R (1960) Integer programming formulations and traveling salesman problems. J Assoc Comput Mach 7:32–329
Toth P, Vigo D (eds) (2002) The vehicle routing problem. SIAM
Toth P, Vigo D (eds) (2014) Vehicle routing: problems, methods, and applications. SIAM
Wolsey LA, Nemhauser GL (1999) Integer and combinatorial optimization. Wiley
Lee J, Leyffer S (Eds) (2012) Mixed integer nonlinear programming. The IMA volumes in mathematics and its applications. Springer
Desaulniers G, Desrosiers J, Solomon MM (eds) (2005) Column generation. Springer
Conforti M, Cornuejols G, Zambelli G (2014) Integer programming. Springer
Korte B, Vygen J (2018) Combinatorial optimization—theory and algorithms. Springer
Fliege J, Kaparis K, Khosravi B (2012) Operations research in the space industry. Eur J Oper Res 217(2):233–240
Galli L (2011) Combinatorial and robust optimisation models and algorithms for railway applications. 4OR 9(2):215–218
Boyd S, Vandenberghe L (1997) Semidefinite programming relaxations of non-convex problems in control and combinatorial optimization. In: Paulraj A, Roychowdhuri V, Schaper C (eds) Communications, computation, control and signal processing. Kluwer, pp 279–288
van Ackooij W, Lopez ID, Frangioni A, Lacalandra F, Tahanan M (2018) Large-scale unit commitment under uncertainty: an updated literature survey. Ann OR 271(1):11–85
Frangioni A, Galli L, Stea G (2014) Optimal joint path computation and rate allocation for real-time traffic. Comput J 58(6):1416–1430
AMPL. https://ampl.com/
GAMS. https://www.gams.com/
Coliop. http://www.coliop.org/
ZIMPL. http://zimpl.zib.de/
FlopC++. https://projects.coin-or.org/FlopC++
Pyomo. http://www.pyomo.org/
YALMIP. https://yalmip.github.io/
GuRoBi. http://www.gurobi.com/
MOSEK. https://www.mosek.com/
SCIP. http://scip.zib.de/
LocalSolver. http://www.localsolver.com/
COIN-Reharse. https://github.com/coin-or/Rehearse
Acknowledgements
The first author acknowledge the financial support of the University of Pisa under the grant PRA_2017_33 “Distretti urbani a zero impatto energetico ed ambientale”. The authors acknowledge the financial support of the Italian Ministry for Education, Research and University (MIUR) under the project PRIN 2015B5F27W “Nonlinear and Combinatorial Aspects of Complex Networks” and of the Europeans Union’s EU Framework Programme for Research and Innovation Horizon 2020 under the Marie Skłodowska-Curie Actions Grant Agreement No 764759 “MINOA – Mixed-Integer Non Linear Optimisation: Algorithms and Applications”.
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Frangioni, A., Galli, L. (2020). Optimization Methods: An Applications-Oriented Primer. In: Crisostomi, E., Ghaddar, B., Häusler, F., Naoum-Sawaya, J., Russo, G., Shorten, R. (eds) Analytics for the Sharing Economy: Mathematics, Engineering and Business Perspectives. Springer, Cham. https://doi.org/10.1007/978-3-030-35032-1_2
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DOI: https://doi.org/10.1007/978-3-030-35032-1_2
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