Stochastic Integer Waste Management Problem Solved by a Modified Progressive Hedging Algorithm

  • Martin Malek Brno University of Technology, Faculty of Mechanical Engineering, Institute of Mathematics
  • Radovan Somplak Brno University of Technology, Faculty of Mechanical Engineering, Institute of Process Engineering
  • Pavel Popela Brno University of Technology, Faculty of Mechanical Engineering, Institute of Mathematics
  • Jakub Kudela Brno University of Technology, Faculty of Mechanical Engineering, Institute of Automation and Computer Science https://orcid.org/0000-0002-4372-2105
Keywords: waste management decision making, stochastic programming, facility location problem, progressive hedging algorithm

Abstract

In this paper we describe a real-world large-scale stochastic integer waste-management decision making problem. The problem consists of choosing the optimal locations and capacities of new incineration plants, that will be used for the disposal of waste. To solve this problem, we implement a modied version of the progressive hedging algorithm. The presented case study with real-world data concerns the situation in the Czech Republic.

References

Bazaraa, M.S., Jarvis, J.J., and Sherali, H.D.: Linear programming and network flows. John Wiley and Sons, New York (1990)

Birge, J.R., Louveaux, F.: Introduction to Stochastic Programming. Springer, New York (1997)

Dolezel, P., Heckenbergerova, J., Mariska, M., and Skrabanek, P.: Transportation schedule-respected production planning using genetic algorithm based approach. Mendel 21(1), 31–38 (2015)

Gade, D., Hackebeil, G., Ryan, S.M., Watson, J.-P., Wets, R.J.-B., and Woodruff, D.L.: Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs. Mathematical Programming 157(1), 47–67 (2016)

Hrabec, D., Popela, P., Roupec, J., Jindra, P., and Novotny, J.: Hybrid algorithm for wait-and-see transportation network design problem with linear pricing:. Mendel 21(1), 183–188 (2015)

Hrabec, D., Viktorin, A., Somplak, R., Pluhacek, M., and Popela, P.: A heuristic approach to the facility location problem for waste management: A case study. Mendel 22(1), 61–66 (2016)

Hrabec, D., Somplak, R., Nevrly, V., and Smejkalova, V.: Sustainable model integration of waste production and treatment process based on assessment of GHG. Chemical Engineering Transactions 70(1), 1603–1608 (2018)

Janostak, F., Pavlas, M., Putna, O., Somplak, R., and Popela, P.: Heuristic approximation and optimization for waste-to-energy capacity expansion problem. Mendel 22(1), 123–130 (2016)

Kudela J., Popela P.: Two-stage stochastic facility location problem: GA with benders decomposition. Mendel 21(1), 53–58 (2015)

Kudela, J., Popela, P., Somplak, R., Malek, M., Rychtar, A., and Hrabec, D.: The L-shaped method for large-scale mixed-integer waste management decision making problems. Chemical Engineering Transactions 61(1), 1087–1092 (2017)

Kudela, J., Popela, P.: Warm-start cuts for generalized benders decomposition. Kybernetika 53(6), 1012–1025 (2017)

Kudela, J., Somplak, R., Nevrly, V., and Lipovsky, T.: Robust waste transfer station planning by stochastic programming. Chemical Engineering Transactions 70(1), 889–894 (2018)

Marada, T., Matousek, R., and Zuth, D.: Design of linear quadratic regulator (LQR) based on genetic algorithm for inverted pendulum. Mendel 23(1), 149–156 (2017)

Nevrly, V., Somplak, R., Popela, P., Pavlas, M., Osicka, O., and Kudela, J.: Heuristic challenges for spatially distributed waste production identication problems. Mendel 22(1), 109–116 (2016)

Osicka, O., Hrdina, J., Somplak, R., Popela, P., and Pavlas, M.: Shapley value approximation for games with distant players. Mendel 22(1), 103–108 (2016)

Pavlas, M., Nevrly, V., Popela, P., and Somplak R.: Heuristic for generation of waste transportation test networks. Mendel 21(1), 189–194 (2015)

Pavlas, M., Somplak, R., Smejkalova, V., Nevrly, V., Zaviralova, L., Kudela, J., and Popela, P.: Spatially distributed production data for supply chain models - Forecasting with hazardous waste. Journal of Cleaner Production 161(10), 1317–1328 (2017)

Rardin, R.L.: Optimization in Operations Research. Second edition, Person, Hoboken, New Jersey (2015)

Smejkalova, V., Somplak, R., Nevrly, V., and Pavlas, M.: Heuristic methodology for forecasting of quantities in waste management. Mendel 23(1), 185–192 (2017)

Published
2018-12-21
How to Cite
[1]
Malek, M., Somplak, R., Popela, P. and Kudela, J. 2018. Stochastic Integer Waste Management Problem Solved by a Modified Progressive Hedging Algorithm. MENDEL. 24, 2 (Dec. 2018), 17–22. DOI:https://doi.org/10.13164/mendel.2018.2.017.
Section
Research articles