The reasons why Operations Research (OR) techniques can be profitably used in waste management decision making are various.
For countries in the EU25 group, the municipal solid waste generated per year has
reached the value of approximately 100 millions of Mg at the end of XX century. Such waste production rate is expected to face an increasing trend in the next 15 years. Similar amounts are disposed in landfills (see Mazzanti and Zoboli [189]). It is clear that such a huge amount of waste have to be collected, transferred, transformed and disposed while taking into account a variety of factors, such as social, political, legal, economic, environmental and technical implications (Wilson et al. [253]).
Also, for what concerns the IW, regardless of the production rate, it is important to handle these flows with special care. As explained in Section 4.2.1.3, the waste treat- ment processes consist in complex operations performed by several plants, with large differences in input and output products (see also Singh et al. [229]). The production of liquid waste such as leachates or industrial sludges has to be specifically considered, since their treatment is affected by environmental and technical implications.
The waste managers are therefore facing complex and relevant issues for modern so- cieties. In this context, a mathematical model can describe the specific features of the network of waste treatment facilities and of the waste generation. OR methods will then help to determine the best planning strategy according to given optimization criteria. An extended and recent survey on the application of OR methodologies to Solid Waste Management is given by Ghiani et al. [113].
In problems in which the waste flow is a decision variable, one of the most important and used optimization criterion is that of minimizing the total transportation and pro- cessing cost, minus all revenue for reclaimed material and generated energy ([113]). Generally, the models proposed in literature can be considered as a multiperiod multi- commodity flow with multiple sources and sinks. When the selection of the operating facility in each period is taken into account, a facility location component can be also identified in the model. Because of the large number of waste facilities features an OR model for the waste management should be tailored to the characteristics of the case study. General purpose models would be too hard to formulate or solve.
A major aspect to be taken into account in the model formulation is the time horizon in which the planning has to be made. Two planning levels are usually considered. In the strategic level, long-term decisions have to be made at a regional level. Generally, the problem is to select which facilities to use and how to ship the waste in each period of the time horizon in order to minimize waste processing and transportation costs. Furthermore, if the time horizon involves more than four or five years, the expansions of the existing plants as well as the building of new facilities may be considered (see, e.g., Baetz et al. [19], Li and Huang [173], Vigo et al. [247]).
At the tactical level, short and medium term decisions have to be performed. Although the literature is still relatively scarce in this area, OR models can be profitably applied to incorporate operational issues, such as: waste flow allocation according to short term forecasts and aggregation of waste sources and commodities (see section4.5.2for further details), the districting phase, the collection sites location (Ghiani et al. [114]), the selection of the collection days and the determination of fleet and crew composition that performs the waste collection (Ghiani et al. [112]). The present chapter addresses waste flow allocation problems.
Another factor that influences the mathematical formulations for waste management is the uncertainty that affects the data related to waste generation rates, processing and transportation costs and revenues at the time of the decision making. The reader can refer to Sun et al. [233] for a recent survey on inexact programming methods for solving waste management problems with uncertain data. Stochastic parameters can be expressed with interval data, random variables with given probability distributions, or fuzzy sets. In such stochastic context, the selection of the solution method to be applied is strongly dependent on the capability of the waste manager to adopt robust decisions or rather use flexible planning strategies and the modality in which uncertain parameters are available and how uncertainty is revealed in the planning horizon. For instance, a Two-Stage Stochastic Programming formulation (Birge and Louveaux [38]) is commonly adopted when the waste manager is able to take a recourse action when the flow waste turns out to exceed the forecasted amount (see, e.g., Li and Huang [173], Maqsood and Huang [187]).
In the present chapter, all problem parameters are deterministic data obtained by us- ing forecasting methods for the waste generation in the future planning period. The amount of historical data available in Optit is not sufficient for estimating stochastic tools such as probability distributions of uncertain parameters. A wide and general dissertation on demand forecasting techniques in logistic systems can be found in Ghi- ani et al. [111]. An accurate prediction of municipal solid waste generation is both an important and challenging task in a waste management problem (Dyson and Chang [84]). While traditional forecasting methods have taken into account demographic and economic factors on a per-capita basis, researches have shown that population growth and migration are not the only factors influencing the forecast. In addition to them, climate changes, employment status, education, social and public attitudes affect the waste generation interactively (Bandara et al. [21]). In developing countries, the waste forecast can be made with respect to the economic activity of the city by using re- gression modeling and time series analysis (Rimaityte et al. [215]). A vast survey on formulations for the municipal solid waste generation using economical, social, demo- graphic and management-orientated data can be found in Beigl et al. [28].
A common approach in literature is to describe the waste management system as a multi-echelon supply chain (see, e.g., Ghiani et al. [113], Zhang et al. [261]). According to this assumption, the waste network can be considered having a sources - facilities -
destinations hierarchy. Waste generation sources are network nodes in which munici- pal and industrial waste is generated in each period and has to be shipped inside the network. Waste treatment, separation and composting facilities are plants in which both ingoing and outgoing flow are allowed. Destination sites are landfills and disposal markets in which the waste is required to be disposed.