The collection of solid waste from third class communities in most devel-oping countries is by skip containers, however, the location of these facilities has been done arbitrary without any mathematical considerations as to the number of customers the facility is serving, the distance one has to travel to access it and thereby making some of these residences to dump their refuse in gutters, streams and even burn them. In this paper we proposed an improved probabilistic distance, capacity clustering location model which takes into consideration the weight of solid waste from a customer and the capacity of the skip container to locate the skip container to serve a required number of customers based on the capacity constraint of the container. The model was applied on a real world situation and compared with the existing practice in terms of average distance customers had to travel to access the facility. Our results gave a well shorter average travel distance by customers, gave a number of skip containers needed in an area based on their waste generation per capita.
References
[1]
Barbati, M. (2013) Models and Algorithms for Facility Location Problems with Equity Considera-tions.
Shiripour, S., Mahdavi, I., Amiri-Aref, M., Mohammadnia-Otaghsara, M. and Mahdavi-Amiri, N. (2012) Multi-Facility Location Problems in the Presence of a Probabilistic Line Barrier: A Mixed Integer Quadratic Programming Model. International Journal of Production Research, 50, 3988-4008.
https://doi.org/10.1080/00207543.2011.579639
[4]
Erkut, E. and Neuman, S. (1989) Analytical Models for Locating Undesirable Facilities. European Journal of Operational Research, 40, 275-291.
https://doi.org/10.1016/0377-2217(89)90420-7
[5]
Erkut, E. and Neuman, S. (1992) A Multiobjective Model for Locating Undesirable Facilities. Annals of Operations Research, 40, 209-227.
https://doi.org/10.1007/BF02060478
[6]
Drezner and Wesolowsky, G.O. (1983) The Location of an Obnoxious Facility with Rectangular Distance. Journal of Regional Science, 23, 241-248.
https://doi.org/10.1111/j.1467-9787.1983.tb00800.x
[7]
Wyman, M. and Kuby, M. (1993) A Multiobjective Loca-tion-Allocation Model for Assessing Toxic Waste Processing Technologies. Studies in Locational Analysis, 4, 193-196.
[8]
Wyman, M. and Kuby, M. (1995) Proactive Optimization of Toxic Waste Transportation, Location and Tech-nology. Location Science, 3, 167-185.
https://doi.org/10.1016/0966-8349(95)00014-3
[9]
Ghiani, G., Laganà, D., Manni, E. and Triki, C. (2012) Capacitated Location of Collection Sites in an Urban Waste Management System. Waste Management, 32, 1291-1296. https://doi.org/10.1016/j.wasman.2012.02.009
[10]
Costa, M.G., Captivo, M.E. and Clímaco, J. (2008) Capacitated Single Allocation Hub Location Problem—A Bicriteria Approach. Computers & Operations Research, 35, 3671-3695. https://doi.org/10.1016/j.cor.2007.04.005
[11]
Cappanera, P., Gallo, G. and Maffioli, F. (2004) Discrete Facility Location and Routing of Obnoxious Facilities. Discrete Applied Mathematics, 133, 3-28.
https://doi.org/10.1016/S0166-218X(03)00431-1
[12]
Fonseca, M.C. and Captivo, M.E. (2007) Analysis of Bicriteria Semi Obnoxious Location Models. Paper Presented at Tercer Encuentro de la Red Iberoamericana de Evaluación Decisión Multicriterio, R.E.D.-M. 2007, Culiacán.
[13]
Shen, Z., Zhan, R. and Zhang, J. (2011) The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms. INFORMS Journal on Computing, 23, 470-482. https://doi.org/10.1287/ijoc.1100.0414
[14]
Li, X., Tomasgard, A. and Barton, P.I. (2011) Nonconvex Generalized Benders Decomposition for Stochastic Separable Mixed-Integer Nonlinear Programs. Journal of Optimization Theory and Applications, 151, 425.
https://doi.org/10.1007/s10957-011-9888-1
[15]
Li, Q., Zeng, B. and Savachkin, A. (2012) Reliable Facility Location Design under Disruptions. Computers & Operations Research, 40, 901-909.
https://doi.org/10.1016/j.cor.2012.11.012
[16]
An, Y., Zeng, B., Zhang, Y. and Zhao, L. (2014) Reliable p-Median Facility Location Problem: Two-Stage Robust Models and Algorithms. Transportation Research Part B: Methodological, 64, 54-72. https://doi.org/10.1016/j.trb.2014.02.005
[17]
An, Y., Zhang, Y. and Zeng, B. (2015) The Reliable Hub-and-Spoke Design Problem: Models and Algorithms. Transportation Research Part B: Methodological, 77, 103-122. https://doi.org/10.1016/j.trb.2015.02.006
[18]
Farahani, R.Z., SteadieSeifi, M. and Asgari, N. (2010) Multiple Criteria Facility Location Problems: A Survey. Applied Mathematical Modelling, 34, 1689-1709.
https://doi.org/10.1016/j.apm.2009.10.005
