This study proposes an inexact semi-infinite programming (ISIP) method for dealing with engineering optimization problems. The ISIP problem is solved by dividing it into two interactive linear programming subproblems and then solved by conventional simplex method, respectively. The method is applied to a system for identifying optimal regional waste management strategies under uncertainty. The results indicate that the generated strategies obtained though ISIP would not increase the complexity in decision-making processes. Compared to interval linear programming (ILP), ISIP has the advantages of (i) better reflecting the association of the total system revenue with gas and power prices, (ii) generating more reliable solutions with a lower risk of system failure due to the possible constraints violation, and (iii) providing a more flexible management strategy since the capital availability can be adjusted with the variations in gas prices. Although only a hypothetical but representative system is applied in this study, the proposed ISIP method may be applicable to many other systems where the complex uncertainties in parameters should be taken into account.