Generalized Benders Decomposition for Location-Allocation of Wastewater Treatment Plants

Pollution of freshwater sources is a major problem in many developing economies. Environmental norms mandate that Industrial wastewater must be treated before releasing it in the environment or recycling. Apart from large enterprises, many medium and small-scale enterprises use water for industrial purposes. However, many of these enterprises do not have enough financial resources to set up their own wastewater treatment plant (WWTP). Government policies encourage establishing a common set of WWTPs that can service all the enterprises in an industrial cluster and will be more economical to operate. We formulate the problem of locating WWTPs of appropriate sizes and allocating polluting firms to them as a Mixed Integer Non-linear Program (MINLP). The model minimizes the setup cost and the operating cost for the network of WWTPs. For the operating cost, empirical evidence shows that there exist economies of scale with wastewater volume and dis-economies of scale with pollutant concentration. Hence, the operating cost function is non-convex. We provide an exact convexification strategy for this problem. Still, the commercial solvers are unable to solve practical size instances. Therefore, we propose a Generalized Benders decomposition based algorithm with many refinements. We exploit the structure of the problem to solve the sub-problem very efficiently. Our proposed method can solve this MINLP much more efficiently than commercial solvers.