Table 1.

Summary of the previous efforts that combine aircraft design and airline allocation

Methods	Approach	Pros	Cons
Sequential design-allocation with a top-level subspace	One MINLP (top-level) using complete/pseudo enumeration, one NLP (design) using gradient-based approach, and one MILP (allocation) using linear integer programming	Breaks the large problem into smaller easy-to-solve problems via subspace decomposition	Could capture only one-way coupling i.e. design affects allocation but not vice-versa, leads to sub-optimal solution
Simultaneous mission-allocation	one MINLP using branch-and-bound and gradient-based approach	Captures two-way coupling	Difficult to obtain a valid upper bound of the problem objective, limited global exploring capability, computationally inefficient
Simultaneous allocation-mission-design	One NLP using gradient-based approach within a computational analysis framework	Captures two-way coupling, capable of solving a larger network problem	Treats integer types variables as continuous – yields very little useful information to the allocation solution