Two-stage system of systems model by linking system design with resource allocation

Decomposition-based product design optimization under system of systems paradigm is linked with resource (i.e., product) allocation. A two-stage, system of systems approach to linking resource allocation (e.g., vehicle routing problem (VRP)) and system design optimization (e.g., vehicle design problem (VDP)) is presented. The problem inherently contains discrete variables from VRP, thus a practical formulation is presented to overcome convergence difficulty associated with shared discrete variables in a decomposed setting. Two examples, composed of four and eight air routes respectively with the introduction of a new air-craft to the existing fleet, are presented to demonstrate the effectiveness of the proposed approach. A new type of aircraft is designed and allocated to the currently existing VRP to meet the demand, while the direct operating cost of an airline is minimized.