Waste Processing Facility Location Problem by Stochastic Programming: Models and Solutions
The paper deals with the so-called waste processing facility location problem (FLP), which asks for establishing a set of operational waste processing units, optimal against the total expected cost. We minimize the waste management (WM) expenditure of the waste producers, which is derived from the related waste processing, transportation, and investment costs. We use a stochastic programming approach in recognition of the inherent uncertainties in this area. Two relevant models are presented and discussed in the paper. Initially, we extend the common transportation network flow model with on-and-off waste-processing capacities in selected nodes, representing the facility location. Subsequently, we model the randomly-varying production of waste by a scenario-based two-stage stochastic integer linear program. Finally, we employ selected pricing ideas from revenue management to model the behavior of the waste producers, who we assume to be environmentally friendly. The modeling ideas are illustrated on an example of limited size solved in GAMS. Computations on larger instances were realized with traditional and heuristic algorithms, implemented within MATLAB.
KeywordsWaste processing Facility location problem Stochastic programming Two decision stages Uncertainty modeling Scenarios Mathematical programming algorithms Heuristics Genetic algorithms GAMS MATLAB Pricing related ideas
This work was supported by the Programme EEA and Norway Grants for funding via grant on Institutional cooperation project nr. NF-CZ07-ICP-4-345-2016 and by the specific research project “Modern Methods of Applied Mathematics for the Use in Technical Sciences”, no. FSI-S-14-2290, id. code 25053. The authors gratefully acknowledge further support from the NETME CENTRE PLUS under the National Sustainability Programme I (Project LO1202) and support provided by Technology Agency of the Czech Republic within the research project No. TE02000236 “Waste-to-Energy (WtE) Competence Centre.
- 2.Blumenthal, K.: Generation and treatment of municipal waste. Technical report KS-SF-11-031 (2011)Google Scholar
- 7.Hrabec, D., Popela, P., Roupec, J., et al.: Hybrid algorithm for wait-and-see network design problem. In: 20th International Conference on Soft Computing MENDEL 2014, pp. 97–104. Brno University of Technology, VUT Press, Brno (2014)Google Scholar
- 15.Steenbrink, P.A.: Optimization of Transport Network. Wiley, New York (1974)Google Scholar
- 16.Stodola, P., Mazal, J., Podhorec, M., Litvaj, O.: Using the ant colony optimization algorithm for the capacitated vehicle routing problem. In: 16th International Conference on Mechatronics - Mechatronika (ME), pp. 503–510 (2014)Google Scholar
- 17.Šenkeřík, R., Pluháček, M., Davendra, D., Zelinka, I., Janoštík, J.: New adaptive approach for multi-chaotic differential evolution concept. In: Hybrid Artificial Intelligent Systems, pp. 234–243. Springer (2015)Google Scholar
- 18.Šoustek, P., Matoušek, R., Dvořák, J., Bednář, J.: Canadian traveller problem: a solution using ant colony optimization. In: 19th International Conference on Soft Computing MENDEL 2013, Brno, Czech Republic, pp. 439–444 (2013)Google Scholar
- 20.Štěpánek, P., Lániková, I., Šimůnek, P., Girgle, F.: Probability based optimized design of concrete structures. In: Life-Cycle and Sustainability of Civil Infrastructure System, pp. 2345–2350. Taylor & Francis Group, London (2012)Google Scholar
- 21.Štětina, J., Klimeš, L., Mauder, T., Kavička, F.: Final-structure prediction of continuously cast billets. Mater. Tehnol. 46(2), 155–160 (2012)Google Scholar
- 22.Yo, H., Solvang, W.D.: A general reverse logistics network design model for product reuse and recycling with environmental considerations. Int. J. Adv. Manuf. Technol. 87, 1–19 (2016)Google Scholar