Chebyshev Optimal Waste Discharges

Liquid wastes are often stored for some time before being discharged into a water resource. Storage capacity determines the set of feasible discharge schedules and, therefore, limits the levels of water quality that are attainable. Thus motivated, the paper considers the following discrete-time deterministic problems: (a) For a given storage capacity, what discharge schedule maximizes the minimum water quality during a finite horizon? (b) For a given minimum water quality during a finite horizon, what is the smallest storage capacity for which there exists a feasible discharge schedule? A characterization is provided for optimal solutions to (a) and (b). The characterization is exploited computationally to obtain exact solutions to (b) and approximate solutions to (a).