Trading Discharge Permisions in Rivers and Reallocating the Treatment Costs: Application of the Normalized Nucleolus Game

This paper presents a Trading Discharge Permisions (TDP) model for equitable treatment cost
allocation among dischargers in rivers. The model consists of two principal steps. In the first step, a
trade-off curve between objectives is developed using a recently developed multi-objective technique
namely Nondominated Sorting Genetic Algorithm-II (NSGA-II). The objective functions are average
value of the treatment levels of dischargers and a fuzzy risk of violating the water quality standards.
The best non-dominated solution on the trade-off curve, which shows an initial treatment cost
allocation, is defined using the Young conflict resolution theory. In the second step, using the
Normalized Nucleolus cooperative game, the maximum saving cost of cooperating dischargers in a
coalition is allocated to them fairly. This saving cost allocation provides a fair optimal trading
discharge permisions policy. To illustrate applicability of the proposed methodology, it is applied to
the Zarjub river system in north of Iran. The efficiency of the methodology is also evaluated using
some well-know criteria in the field of trading discharge permisions such as existence of hot spots and
free riders.