Single aircraft mid-air refueling using spherical distances

This paper addresses the problem of a single military transport aircraft that must carry cargo from an origin base to a destination base. Refueling is required and performed by a tanker aircraft that originates from the returns to a third base. The objective is to determine the initial fuel required by each aircraft and the location of the refueling point so as to minimize the total fuel consumed subject to restrictions on the range of the transport and the tanker. Based on U.S. Air Force data, analytical relationships are dervied which allow the problem to be formulated similar to a constrained spherical Weber problem with two main differences: (1) the objective function is nonlinear, and (2) some of the constraints are a function of the decision variables. Spherical convexity of both the objective function and the feasible region is shown and used to develop a solution procedure. Computational experience is given.