System-of-Systems Inspired Aircraft Sizing and Airline Resource Allocation via Decomposition

The phrase "system-of-systems" describes a large system of multiple systems, each capable of independent operation, which have been brought together to provide capabilities beyond those of each individual constituent system. Formulating and solving a system-of-systems design problem has become increasingly important in the aerospace and defense industries as customers have begun to ask contractors for broad capabilities and solutions rather than for specific individual systems. Part of a system-of-systems design problem is determining the appropriate mix of both existing and yet-to-be-designed systems. Whereas determining an appropriate mix of existing systems falls into the category of resource allocation, including features of a yet-to-be-designed system complicates the problem by requiring the allocation of a variable resource. In this paper, an airline wishing to investigate how a new, yet-to-be-designed aircraft will impact the fleet operating costs provides a simple example of this type of problem. The resulting statement is a mixed-integer, nonlinear programming problem. Both a traditional approach and a new decomposition approach were used to solve the problem. The traditional approach is a mixed-integer nonlinear branch-and-bound. The decomposition approach applied to the problem is analogous to those of multidisciplinary optimization, in which there is an allocation domain and an aircraft sizing domain. When the problem size increases to the point where the traditional mixed-integer, nonlinear programming approaches cannot obtain a solution, the decomposition approach can find solutions for these larger problems. The multidisciplinary design optimization-motivated decomposition approach appears to have promise for the allocation of variable resources challenge presented by many system-of-systems design problems.