Waste Load allocation Using Machine Scheduling: Model Formulation

In this paper a novel approach for effective utilization of river assimilative capacity has been proposed. The method, referred to as waste load scheduling (WLS) is based on the principle that by restricting the effluent discharge into the river to only one polluter at any given day will allow us to utilize the available river assimilative capacity in a more efficient manner. This is achieved by scheduling the dischargeable waste load among the polluters, such that a waste load schedule once developed will specify two things: (1) which polluter has to discharge his/her effluent on a given day; and (2) what is the quantity of effluent that he/she can discharge. By scheduling the waste load discharge into the river thus, will considerably reduce the total effluent discharge into the river and hence a greater degree of water quality level can be achieved when compared to traditional waste load allocation methods. For the mathematical development of the model, the WLS problem was envisaged as analogous to a machine scheduling problem. In a simple single MS problem n number of jobs are required to be scheduled on a single machine to minimize/maximize a pre-defined performance measure. In a WLS problem, the river can be treated as a machine and the polluters discharging effluent directly into the river are analogous to the jobs to be scheduled. Treating the waste load scheduling problem in an analogous way to a MS problem enables us to apply the solution methods used for solving standard sequencing and scheduling problems to the proposed waste load scheduling problem. Although the present paper discusses the special case of waste load scheduling in which only one polluter can discharge effluent at any given day (suitable when the number of point load sources is small), it is however, possible to extend it to a more general case involving a large number of polluters as easily. In the accompanying paper, the application of the developed model to a case study has been explained in detail. The proposed model and its application proved that the model is highly efficient in solving the waste load allocation problem in a more comprehensive way.