This paper presents a formal mathematical framework for the use of the morphological matrix in a computerized conceptual design framework. Within the presented framework, the matrix is quantified so that each solution principle is associated with a set of characteristics such as weight, cost, performance, etc. Selection of individual solutions is modeled with decision variables and an optimization problem is formulated. The applications are the conceptual design of subsystems for an Unmanned Aerial Vehicle and an aircraft fuel transfer system. Both the system models and the mathematical framework are implemented in MS Excel.