A new technique, called the mixed-integer-chance-constrained programming (MICCP) method is developed in this research. This technique considers uncertainty in all linear programming constraint coefficients and does not require a priori knowledge of the distribution. A groundwater remediation problem serves as an example. The method is developed to find the globally optimal trade-off curve for maximum reliability versus a minimum pumping objective. As the fields became more heterogeneous, the pumping rate of a reliable solution increases. Four simple ''rule of thumb'' methods are compared to the MICCP technique. In general, the performance of such methods decreases as the heterogeneity of the hydraulic conductivity field increases. ¿ American Geophysical Union 1993