(Solved): 1. Introduction 1.1. Solid Waste management Management of solid waste (SWM) is remained as one of ...

1. Introduction 1.1. Solid Waste management Management of solid waste (SWM) is remained as one of the most important issues due to the growth in economy and population (Solano, Ranjithan, Barlaz, \& Brill, 2002). Increasing efforts are being put to develop realistic solutions to SWM problems for decades (Holkcanen \& Salminen, 1997). Optimum way of solving SWM issues highly depends on the conditions of each community. This is because of that available resources, landfill, recycling capacity, economic growth, and population increase may differ from region to region. Although there are general models or frameworks which are applicable for the majority of the SWM issues (Sabbas et al., 2003; Clift, Doig, \& Finnveden, 2000), some local problems are needed to be addressed specifically considering the local constraints, conditions, goals. Moreover, SWM is intrinsically complex and it contains numerous connected problems. Hence, it is not easy to evaluate the various alternatives towards gatisfying the needs of sustainable development (Caruso, Colomi, \& Paruccini, 1993). In this regard, most of the studies addressing SWM are conducted by utilizing mathematical models to provide optimum solutions. 1.2.Problem description The Lower Rio Grande Valley (LRGV) is a 9,324 km2 area in the southernmost part of Texas formed by Cameron, Hidalgo, Willacy, and Starr counties. It is one of the fastest growing regions in Texas and the Nation. Population growth, induatrial development, proximity to the border with Mexico, and other North American Free Trade Agreement-induced (NAFTA induced) factors are behind the explosion in Valley development. The area's population has increased by \( 39.8 \% \) in the last ten years. It is expected to continue growing at an estimated rate of \( 4 \% \) per year in the coming years. The population is projected to be over \( 1.7 \) million people by 2022 (LRGVDC, 2002). The growth in the population in the region is influenced by immigration from Mexico, high-birth rates in the Valley, and the growing employment opportunities in the Valley. The Office of Management and Budget (OMB) ranks Metropolitan Statistical Area (MSA) according to their population and economic growth. Cameron County contains the 28th MSA Brownsville-Harlingen-San Benito- while Hidalgo County, with roughly half of the LRGV area, is mostly urbanized and has the fourth fastest growing area in the nation: the McAllen Edinburg Mission MSA. Synonymous with this economic development is an alarming rise in the solid waste generation that leaves the area with only 12 more years of landfill life. With receding landfill space and limited agents equipped to meet the solid waste management (SWM) demands, public and private landfills compete for municipal clients to ensure capital to extend landfill life or apply for new permits. The main SWM competitors observed in the LRGV are the City of Edinburg landfill and the BrowningFerris Industries (BFI) landfill over the solid waste management market of the Valley although some other small landifills are still in operation. The cities selected for this solid waste management analygis that lie in \( t \) in Hidalgo County are Edinburg, Mission, Pharr, McAllen, San Juan, Alamo, Donna, Weslaco, and Mercedes. The geographical location of the open landfills in the Valley is illustrated with the study area ghown in Fig. 1. Fig. 1: The geographical location of the open landfills in the Valley This solid waste management systems analysis is designed to identify the waste management altematives for Hidalgo County only. Table 1 indicates the ghipping distance between sources and 4 landfill facilities and associated unit shipping cost. Table 2 lists the capacity and disposal fee of four landfills. In 2004 , the waste streams generated are 87 tons (Edinburg), 81 tons (Misaion), 84 tons (Pharr), 191 tons (ULacAllen), 47 tons (San Juan), \( 26.5 \) tons (Alamo), 30 tons (Donna), 48 tons (Weslaco), and 25 tons (Mercedes). The annual growth of waste generation rate is \( 5 \% \) (Chang 2011). Table 2 : The capacity and disposal fees of four landfills 2. Method The goal of this project is to formulate a linear programming model for dynamic planning that may minimize the total operating cost over a 9-year time horizon subject to the capacity limitation constraint and mass balance constraint in the system and search for the optimal waste management pattem. Decision variables and parameters are defined clearly and appropriately, and the problem is formulated with a mathematical model. The problem is solved by using LINGO software package. Figure 2 illustrates the analysis work flow. Firstly a dynamic (time dependent) dynamic cost matrix is calculated. Next, solid waste generation amounts by the years are calculated for each city. Then, the objective function is formulated. After defining the objective function, constraints are formulated based on the collected data. Finally, the LP model is pan and the results are obtained. 2.1. Developing the dynamic cost matrix Considering that the problem is for a time period, the variables within the problem are also subject to time. Accumulation of trangportation and disposal costs for each combination of cities and landfills are calculated for the 2004. Later, the future values of these money flows are calculated by assuming \( \% 1.5 \) inflation and \( 1 \% \) nominal discount rate. Table 3 represents the dynamic cost matrixes. Due to large volume of cost variables the time horizon is divided into three equal periods; period 1,2 , and 3 , which are the periods between 2005-2007, 2008-2010, and 2011-2013.ragnectivaly. Table 4 shows the modified costs over the 3 periods. Table 4. Modified dynamic cost matrix over the selected time periods 2.2. Estimating the waste generation amounts Considering that the waste generation is increasing with a rate of \( 5 \% \) annually. The year 2004 is selected as a base year. Table 5 ghows the solid waste generation amounts by the years. Table 5 . Solid waste amount by the years Similarly this table is also shirked and grouped under the same three time periods. Table 6 shows the solid waste generation amount by the selected time periods. Table 6 . Dynamic solid waste generation amount by the selected time periods 2.3. Formulating the Objective function and constraints In the objective function, we want to minimize overall digposal shipping and digposal cost for each time period*. a) Please formulate the LP model [45 points] b) Solve the LP in using both Excel solver and LINDO software [ 40 points] c) Interpret the software outputs (e.z. Binding \& nonbinding constraints, sensitivity results, dual price \& reduced costs, etc. [15 points] Note*: The LP model will be formulated for three combined periods: 2005-07, 2008-10, and 2011-13. 1. Word file; To describe the problem briefly, how you model the problem as LP model (decision variables, constraints, parameter efch), LP model itself, Explanation of the excel model with snapshots from the excel model, Excel output report, LINDO model, LINDO output report, Explanation of the interpretation part, analysis etc. 2. Excel file of your model (Word file will be graded, not excel file. Excel file is needed in case we want to check it)