With rising urbanization and change in lifestyle and food habits of human beings, the amount of municipal solid wastes (MSWs) are now being increasing day by day, and the composition of wastes are now also being changed. Therefore, it is now becoming essential to develop a consistent mathematical model for managing those wastes in a systematic manner. In this context, fuzzy chance constrained programming (FCCP) model becomes useful to handle wastes efficiently through the process of selecting sorting stations, treatment facilities, etc. through an efficient way so that the net system cost of sorting and transporting the wastes would be minimized, and the revenue generated from different sorting stations and different treatment facilities would be to maximized. From that view point, in this chapter, a fuzzy chance constrained programming (CCP) model is developed for MSW management. Most of the parameters involved with this model are imprecisely defined and probabilistically uncertain. So, the parameters of the objectives are considered as FNs, and the right side parameters of the probabilistic constraints involve normally distributed fuzzy random variables (FRVs). To resolve the cases arising due to the multiple occurrences of fuzzy goals, a fuzzy goal programming (FGP) has been adopted. To expound the potential use of the approach, a modified version of a case example, studied previously, is considered and solved. The achieved model solution is discussed elaborately to illustrate the proposed methodology for MSW management.
TopEver since the ancient times, human and animals are using the resources of the earth to support life and disposing the wastes that are discarded as useless or unwanted. In those days, the disposal of wastes did not pose significant problems as the population size was small and a vast expanse of land was available for the assimilation of such wastes.
However, in recent years due to accelerated urbanization and growing population, waste management has become challenging to urban communities (Cheng et al., 2009). Also environmental protection has challenged many regional planners and decision makers. Such challenges are complicated by the rapid socio-economic development associated with increasing contaminant emissions and decreasing resources availabilities (Maqsood and Huang, 2003). As the capacity of the landfill areas gradually decreases, there is arising an increasing demand of other waste treatment facilities such as incinerator, composting facility and recycling facility. Thus those facilities are becoming an integrated part of waste management systems (Tang et al., 2008; Guo et al., 2008; Guo et al., 2009). Also, balancing the conflicts among various system components and considering limitations of the constraints of resources, it is necessary to develop acceptable planning techniques to effectively allocate the available resources (Maqsood et al., 2004). In 2015, Soltani et al. developed a review article in multi-criteria decision-making in the context of MSW management. Mir et al. (2016) developed an optimized MSW management model based on multi criteria decision analysis. Tozlu et al. (2016) proposed a technology to convert waste into energy for MSW management in Gaziantep.
In the context of modelling MSW management problems, probabilistic or possibilistic uncertainties are frequently involved with the amount of disposal of wastes and the costs related to collections, transportations, treatment of wastes, etc. Moreover, these uncertainties may further affect not only interactions among these complex, dynamic and uncertain parameters, but also their associations with economic penalties if the promised targets are violated (Howe et al., 2003). Consequently, various methods have been developed to deal with such uncertainties for planning MSW management systems. Most of them can be dealt with fuzzy, stochastic and interval mathematical programming approaches (Kirca and Erkip, 1988; Zhu and Revelle, 1993; Leimbach, 1996; Chang and Wang, 1994).
Charnes and Cooper (1962, 1963) first introduced the concept of CCP for dealing with probabilistic uncertainties. A bibliographical study has been presented by Infanger (1993) on stochastic programming. Several researchers (Kataoka, 1963; Geoffrion, 1967) further extended the concept of CCP technique for solving different real life problems. With this advancement in computational resources and scientific computing techniques, many complicated optimization models can now be solved efficiently. Guo et al.(2008) presented an interval stochastic quadratic programming approach to MSW management.