An optimal aquifer remediation design model employing a nonlinear prog
ramming algorithm was developed to find the minimum cost design of a p
ump-and-treat aquifer remediation system. The mixed-integer nonlinear
programming model includes the discontinuous fixed costs of system con
struction and installation as well as operation and maintenance. The f
u;ed cost terms in the objective function have been approximated by co
ntinuous functions of the decision variables using a polynomial penalt
y coefficient method resulting in a nonlinear programming formulation
of an otherwise mixed-integer nonlinear programming model. Results of
applying the new polynomial penalty coefficient method to an example d
esign problem show that a combined well field and treatment process mo
del that includes fixed costs has a significant impact on the design a
nd cost of aquifer remediation systems, reducing system costs by using
fewer, larger flow rate wells. Previous pump-and-treat design formula
tions have resulted in systems with numerous, low flow rate wells due
to the use of simplified cost functions that do not exhibit economies
of scale or fixed costs. The polynomial penalty coefficient method res
ults were compared to two alternative approximate mixed-integer nonlin
ear programming methods for solving optimal aquifer remediation design
problems, the pseudo-integer method and the exponential penalty coeff
icient method. The polynomial penalty coefficient method obtains the s
ame solutions and performs as well as or better than the exponential p
enalty coefficient method. The polynomial penalty coefficient method a
lmost always results in better, less expensive designs and requires si
gnificantly less computer time than the pseudo-integer method.