Annals of Operations Research

, Volume 220, Issue 1, pp 87–109 | Cite as

LP models for pricing diffuse nitrate discharge permits

  • R. A. Ranga Prabodanie
  • John F. Raffensperger
  • E. Grant Read
  • Mark W. Milke


Nitrate discharges from diffuse agricultural sources significantly contribute to groundwater and surface water pollution. Tradable permit programs have been proposed as a means of controlling nitrate emissions efficiently, but trading is complicated by the dispersed and delayed effects of the diffuse pollution. Hence, markets in nitrate discharge permits should be carefully designed to account for the underlying spatial and temporal interactions. Nitrate permit markets can be designed similar to the modern electricity markets which use LPs to find the equilibrium prices because the two trading problems have close analogy.

In this paper, we propose alternative LP models to find efficient permit prices for year-ahead markets. The model structure varies depending on the catchment hydro-geology and long-term goals of the community. We show how the market price structures are driven by the constraint structure under different environmental conditions. We discuss the physical and economic conditions required to assure consistent prices, the modeling of essential and optional constraints in an LP, and the problem of balancing resource allocation over time among delayed-response discharge units. We then extend the LP model to balance resource allocation over time and to improve the market performance.


Water quality markets Nitrate trading Non-point sources Tradable permits Linear programming 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • R. A. Ranga Prabodanie
    • 1
  • John F. Raffensperger
    • 1
  • E. Grant Read
    • 1
  • Mark W. Milke
    • 2
  1. 1.Department of ManagementUniversity of CanterburyChristchurchNew Zealand
  2. 2.Department of Civil and Natural Resources EngineeringUniversity of CanterburyChristchurchNew Zealand

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