Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

This study deals with an aircraft-to-target assignment (ATA) problem considering the modern air operation environment, such as the strike package concept, multiple targets for a sortie, and the strike packages' survivability. For the ATA problem, this study introduces a novel mathematical model in which a heterogeneous vehicle routing problem (HVRP) and a weapon-to-target assignment (WTA) problem are conceptually integrated. The HVRP generates the flight routes for strike packages because this study confirms that the survivability of a strike package depends on the path, and the WTA problem evaluates the likelihood of successful target destruction of assigned weapons. Although the first version of the model is developed as a mixed-integer nonlinear programming (MINLP) model, this study attempts to convert it to a mixed-integer linear programming (MILP) model using the logarithmic transformation and piecewise linear approximation methods. For an ATA problem, this activity could provide an opportunity to use the excellent existing algorithms for searching the optimal solution of LP models. To maximize the operational effectiveness, the MILP model simultaneously determines the following for each strike package: (a) composition type, (b) targets, (c) flight route, (d) types, and (e) quantity of weapons for each target.