Rick K. Acosta-Vega (Universidad del Magdalena, Santa Marta;
Faculty of Industrial Engineering, Antonio Nariño University), Encarnación Algaba (Department of Applied Mathematics II and IMUS, University of Sevilla) and Joaquín Sánchez-Soriano (R.I. Center of Operations Research (CIO), Miguel Hernández University of Elche)


Water pollutants can be classified into three categories, each of which includes several classifications of substances. In this paper, we present a methodology based on bankruptcy models to determine the emission limits of polluting substances belonging to more than one category. We model the problem as a multi-issue allocation problem with crossed claims and introduce the constrained proportional awards rule to obtain the emission limits. This rule is based on the concept of proportionality and extends the proportional rule for bankruptcy problems. We also provide an axiomatic characterization of this rule. Moreover, this allocation rule is illustrated by means of a numerical example based on real-world data. Finally, managerial and policy implications of this approach for water pollution control are given.