Abstract
This paper’s aim is to develop a model for the household waste collection and transportation problem in the city of Sousse, one of the largest cities in Tunisia. Several vehicles with a finite capacity are located at the depot. The vehicles must collect the waste accumulated in all bins. The waste is then delivered to a transfer center, before vehicles return to the depot. The proposed model determines the routes of the vehicles and the number of bins to be assigned to each potential location, while minimizing the collection costs and the environmental impact. The problem can be considered as a bi-objective optimization problem, as cost minimization will be ensured by the optimal assignment of the determined minimum number of bins. We also consider the stochastic aspect of population size, which is supposed to follow a normal distribution. Our model is then a stochastic bi-objective programming model. A solution is obtained with reasonable computational effort using a hierarchical approach consisting of two stages as “cluster-first route-second”. In the first stage, a set of n locations of bins is assigned into k disjoint clusters using the K-means clustering algorithm. In the second stage, a certainty equivalent program to the bi-objective stochastic program is proposed, based on a chance-constrained, recourse and a goal programming approach. The model is tested and implemented using real data from the municipality of Sousse. The study shows that our model leads to lower environmental impact and an almost 38% reduction in the economic costs.
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References
Abdelaziz FB, Aouni B, Fayedh RE (2007) Multi-objective stochastic programming for portfolio selection. Eur J Oper Res 177(3):1811–1823
Alizadeh M, Ma J, Marufuzzaman M, Yu F (2019) Sustainable olefin supply chain network design under seasonal feedstock supplies and uncertain carbon tax rate. J Clean Prod 222:280–299
Badran MF, El-Haggar SM (2006) Optimization of municipal solid waste management in Port Said-Egypt. Waste Manag 26(5):534–545
Behdad S, Williams AS, Thurston D (2012) End-of-life decision making with uncertain product return quantity. J Mech Des 134(10):100902
Bellman R (1954) The theory of dynamic programming. Bullet Am Math Soc 60:503–515
Bereketli I, Erolgenevois M, Albayrak YE, Ozyol M (2011) WEEE treatment strategies evaluation using fuzzy LINMAP method. Expert Syst Appl 38(1):71–79
Berkhin PP (2006) A survey of clustering data mining techniques. Springer, Berlin
Charnes A, Cooper WW (1959) Chance-constrained programming. Manage Sci 6(1):73–79
Clark RM, Gillean JI (1975) Analysis of solid waste management operations in Cleveland Ohio: a case study. Interfaces 6(1):32–42
Costi P, Minciardi R, Robba M, Rovatti M, Sacile R (2004) An environmentally sustainable decision model for urban solid waste management. Waste Manag 24(3):277–295
Fiorucci P, Minciardi R, Robba M, Sacile R (2003) Solid waste management in urban areas development and application of a decision support system. Resour Conserv Recycl 37:301–328
Ganesh K, Narendran TT (2007) CLOVES: a cluster-and-search heuristic to solve the vehicle routing problem with delivery and pick-up. Eur J Oper Res 178(3):699–717
Grefenstette JJ, Gopal R, Rosmaita BJ, Gucht D (1985) Genetic algorithms for the traveling salesman problem. Ann Oper Res 63(3):337–370
Hemmelmayr VC, Doerner KF, Hartl RF, Vigo D (2013) Models and algorithms for the integrated planning of bin allocation and vehicle routing in solid waste management. Transp Sci 48(1):103–120
Kall P, Wallace SW (1994) Stochastic programming. Wiley, Chichester
Kara SS, Onut S (2010) A stochastic optimization approach for paper recycling reverse logistics network design under uncertainty. Int J Environ Sci Technol 7(4):717–730
Lee CKM, Yeung CL, Xiong ZR, Chung SH (2016) A mathematical model for municipal solid waste management—a case study in Hong Kong. Waste Manag 58:430–441
Letcher TM, Vallero DA (2011) Waste: a handbook for waste management. Chemistry International
Listeş O, Dekker R (2005) A stochastic approach to a case study for product recovery network design. Eur J Oper Res 160(1):268–287
Lund JR, Tchobanoglous G, Anex RP, Lawver RA (1994) Linear programming for analysis of material recovery facilities. J Environ Eng 120(5):1082–1094
MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the 5th Berkeley symposium on mathematical statistics and probability, pp 281–297
Masri H, Abdelaziz FB, Alaya H (2016) A recourse stochastic goal programming approach for the multi-objective stochastic vehicle routing problem. J Multi Criteria Decis Anal 23(1):3–14
Meyer AD, Cattrysse D, Orshoven JV (2015) A generic mathematical model to optimise strategic and tactical decisions in biomass-based supply chains (OPTIMASS). Eur J Oper Res 245(1):247–264
Mostafa N, Eltawil A (2017) Solving the heterogeneous capacitated vehicle routing problem using K-means clustering and valid inequalities. In: Proceedings of the international conference on industrial engineering and operations management rabat, Morocco
Muttiah RS, Engel BA, Jones DD (1996) Waste disposal site selection using GIS-based simulated annealing. Comput Geosci 22(9):1013–1017
Praveen V, Hemalatha V, Gomathi P (2018) A nearest centroid classifier- based clustering algorithm for solving vehicle routing problem. In: Innovations in Electronics and Communication Engineering, pp 575–586
Purkayastha D, Majumder M, Chakrabarti S (2015) Collection and recycle bin location-allocation problem in solid waste management: a review. Pollution 1(2):175–191
Sackmann D, Hinze R, Michael B, Krieger C, Halifeoglu E (2018) A heuristic for the solution of vehicle routing problems with time windows and multiple dumping sites in waste collection. Investig Oper 38(3):206–215
Sahoo S, Kim S, Kraas BI, Popov A (2005) Routing optimization for waste management. Interfaces 35(1):24–36
Simic V (2016) End-of-life vehicles allocation management under multiple uncertainties: an interval-parameter two-stage stochastic full-infinite programming approach. Resour Conserv Recycl 114:1–17
Singh V, Singh RM, Rawal N (2019) Municipal solid waste management using multiobjective optimization with uncertain parameters. Toxic Radioact Waste 23:4019020
Sreelekshmi V, Nair JJ (2017) Dynamic vehicle routing for solid waste management. IEEE Region 10(3):1–5
Thiessen AH (1911) Precipitation averages for large areas. Mon Weather Rev 39:1082–1089
Toso EAV, Alem D (2014) Effective location models for sorting recyclables in public management. Eur J Oper Res 234(3):839–860
Tralhao L, Coutinho-Rodrigues J, Alcada-Almeida L (2010) A multiobjective modeling approach to locate multi-compartment containers for urban-sorted waste. Waste Manag 30(12):2418–2429
Vadenbo C, Hellweg S, Guillen-Gosalbez G (2014) Multi-objective optimization of waste and resource management in industrial networks-Part I: model description. Resour Conserv Recycl 89:52–63
William JB (1961) Management models and industrial applications of linear programming. Naval Res Logist Q 9(1):63–64
Wu Y, Yang HB, Zhang KF, Chen Y, Wang Y (2016) Optimal site selection of electric vehicle charging stations based on a cloud model and the promethee method. Energies 9(3):2032
Xu R, Wunsch D (2005) Survey of clustering algorithms. Interfaces 16(3):645–678
Zhang X, Huang G (2013) Optimization of environmental management strategies through a dynamic stochastic possibilistic multiobjective program. J Hazard Mater 246:257–266
Acknowledgements
We would like to thank Eco-Tunisie, Polyservice and Municipality of Sousse, for their help to improvise data and for their cooperation and logistic support during the works. We thank Simon and Caroline Durk of the ōbex project for providing language editing support.
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Jammeli, H., Argoubi, M. & Masri, H. A Bi-objective stochastic programming model for the household waste collection and transportation problem: case of the city of Sousse. Oper Res Int J 21, 1613–1639 (2021). https://doi.org/10.1007/s12351-019-00538-5
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DOI: https://doi.org/10.1007/s12351-019-00538-5