Optimizing Cost and Revenue for Solid Waste Management in Nyamira Municipality Using Fuzzy Goal Programming Mathematical Model

Abstract

Waste in urban areas is growing rapidly everywhere in the world. Effective methods to address challenges of solid waste management are critical in achieving an environment that is clean and healthy. The problem of waste growth in urban areas has been brought about by low collection of waste, illegal and uncontrolled dumping sites and the absence of sewer lines. In Kenya for instance the growth of economy has resulted in the development of cities and emergence of towns leading to waste management challenges. Efforts have been directed towards addressing the problem of waste management by various county governments. This study sought to address solid waste disposal and management challenges in Nyamira Municipality. The methods which are being employed to address this challenge was costly and had not yielded desirable results as was evident with the scattered waste in the streets of Nyamira Municipality. Currently the management does not carry out any waste recycling and has hired one landfill which is paid for monthly. This Study formulated solid waste management tool that involved construction of a fuzzy goal programming model with two objective functions. The model was solved analytically by simplex method. The obtained results for first objective function of minimizing the cost of solid waste management is ksh. 26,557,125 which gives a membership function of 0.6 and the second objective function of maximizing revenue is ksh 9,500,000 that is 0.5 membership function. This findings has reduced the net system cost of solid waste management in Nyamira Municipality by 36%. Numerical simulation and sensitivity analysis was carried by varying the operation cost of recycling facility and on the capacity of recycling facility parameters and then the graphs drawn using MATLAB software. The utility of the model was tested using data from Nyamira municipality. The research advocates for waste recycling as one of the ways of managing waste so as to earn revenue from these recycled waste. The findings of this study is useful in formulating policies such setting up of waste management projects and establishment of recycling industries. Furthermore the findings forms the basis for future research in related fields.