Capacitated facility location–allocation problem for wastewater treatment in an industrial cluster

Abstract

We present a location–allocation problem for wastewater treatment in a cluster of processing units. The problem involves installing wastewater treatment plants of appropriate capacities at suitable locations and allocating processing units to these plants. The operational cost of treatment plants is a nonconvex function of wastewater volume and pollutant concentration. This problem is formulated as a non-convex mixed integer nonlinear programming (MINLP) problem. For the general class of this problem, solution strategies based on adapted McCormick envelopes and also piece-wise linear approximation are presented. For a special case of this problem, an exact convexification strategy is proposed and an outer approximation based branch-and-cut approach is presented as an exact solution method. For solving larger instances, we present a matheuristic solution method based on multi-start neighborhood search incorporated into a MINLP solution approach. A real-world case study is presented to illustrate the results of the model along with a multi-objective analysis.