A virtual enterprise (VE) is a platform that enables dynamic collaboration among manufacturers and service providers with complementary capabilities in order to enhance their market competitiveness. The performance of a VE as a system depends highly on the performance of its partner enterprises. Hence, choosing an appropriate methodology for evaluating and selecting partners is a crucial step toward creating a successful VE. In this paper, we begin by presenting an extensive review of articles that address the VE partner selection problem. To fill a significant research gap, we develop a new goal programming (GP)-based approach that can be applied in extreme bidding conditions such as tight delivery timelines for large demand volumes. In this technique, fuzzy analytic hierarchy process (F-AHP) is used to determine customer preferences for four main criteria: proposed unit price, on-time delivery reliability, enterprises' past performance, and service quality. These weights are then incorporated into the GP model to evaluate bidders based on customers' preferences and goals. We present a case study in which we implement the F-AHP-GP technique and verify the model's applicability, as it provides a more flexible platform for matching customers' preferences.