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Many states are actively involved with the load allocation phase of the Total Maximum Daily Load (TMDL) Program. The Environmental Protection Agency (EPA) directs that TMDLs must include establishment of reasonable and equitable load allocations among point sources that will, alone or in conjunction with other management and restoration activities, provide for the attainment of designated water uses (water quality standards) and the restoration of impaired waters(FDEP, 2002). Allocation of load reductions must include an evaluation of the most costeffective approach, however, specific guidelines do not address how this should be accomplished. The TMDL process is technically complex enough without the inclusion of cost optimization. What are the benefits to be derived from including cost into the allocation? Preliminary EPA reports project a median savings of 75% (with a range of 21% to 92%) in implementation cost for BOD and Nutrients reduction when a Cost-effective TMDL Program approach is followed (EPA, 2001). The EPA evaluation involved a simple linear comparison of allocation alternatives. Unfortunately, the highly non-linear nature of the implementation costs was not taken into consideration. With the potential for savings, it is imperative to develop a systematic optimization approach that seeks to minimize costs of implementation while incorporating the non-linear nature of the cost functions.

The objective of this paper is to present a mathematical model that that uses a mixed integer nonlinear optimization approach to reduce the potential costs associated with alternative allocation strategies. The mathematical model was developed for the fecal coliform TMDL allocation for the Muddy Creek sub-watershed (Muddy 3) located in Rockingham County, Virginia. The Virginia TMDL Program has historically allocated the fecal reductions as follows (ASAE, 2002):

90-100% direct deposits of cattle manure in streams

100% of all unpermitted point sources

0-95% in nonpoint sources

35-85% in wildlife fecal materials in streams

The mathematical model has the potential for considerable cost savings when a flexible (non-rule based) allocation strategy is adopted that focuses on maximum environmental contribution for a given expenditure.