COMPUTATIONAL RESULTS FOR WATER POLLUTION TAXATION USING MULTILEVEL APPROACH1

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Abstract
A regional authority is postulated as the pollution abatement agency. The authority's task is to minimize the total cost of waste treatment to the region. Data from the Miami River in Ohio are used to model a twenty‐seven reach river with fifteen BOD dischargers. The description of the system model is given in terms of linear inequality constraints and a quadratic objective function. The multilevel approach with a two level optimization hierarchy in then applied. The river system model is decomposed into twenty‐seven subsystems (reaches). At the first level (local level), each subsystem is “independently” optimized. At the second level (regional level) the subsystems' solutions are coordinated to yield an overall optimum to the whole region. Two types of second level coordination schemes are presented for the decentralized decision making process. The first assumes a knowledge of the local treatment cost functions by the regional authority; the other assumes no such knowledge. A discussion of the multilevel optimization approach and the coordination algorithms for both schemes is presented. In addition, the physical interpretation of effluent charges imposed by the regional authority on each user (polluter) is given. This paper presents computational results to complement the theoretical discussions on the multilevel approach [Haimes, 1971a].

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