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Screening weapon systems development projects is a complex, multicriteria decision problem that must be accomplished within a constrained resource environment. This paper presents a hybrid decision support methodology for use in the screening of weapon systems development projects. The hybrid methodology integrates the analytic hierarchy process (AHP) with a 0-1 integer portfolio optimization model. An AHP component allows the decision maker to incorporate qualitative and intangible criteria into the decision-making process and use the priority rankings of the AHP to represent a measure of value in the 0-1 integer model objective function. The hybrid methodology is extremely flexible and the decision maker can tailor both the AHP and the 0-1 integer optimization model to represent a specific decision-making situation. To fully appreciate the added value of implementing the hybrid screening methodology, a group of Air Force decision makers applied the hybrid methodology to a realistic weapon-systems project screening activity. Results indicate that decision support provided by the methodology could lead to substantial improvements in a weapon-systems portfolio value.