A location-routing problem for the design of an asteroid mining supply chain network. (April 2019) - Dorrington, S.; Olsen, J.
Abstract: This paper considers the design of a supply chain network for the delivery of asteroid-derived resources to customers in Earth orbit. The network features orbital nodes consisting of an asteroid source, an orbital propellant depot, arrival and departure parking orbits, and customer spacecraft. Edges between nodes represent transfer trajectories modelled as impulsive manoeuvres. Two classes of spacecraft vehicles are assigned to transport the product through various edges in the network. We determine the optimal location of nodes, and vehicle routes through the network (a location-routing problem) with the objective of maximizing either the total sellable mass delivered to customers, or the total net present value of the asteroid mining venture. The depot and parking orbit locations are to be selected from a discrete set of candidate locations with variable orbital radius and orientation. Vehicle routes are to be chosen from two candidate routes that ensure reusability over multiple mining trips. A mathematical formulation is presented to describe the objective function as a function of the candidate node locations and vehicle routes. We develop a set of constrained optimization problems to determine the optimal location and orientation of parking orbits, depot location, and vehicle routes though the network. Solution methods are developed using integer programming. A numerical example is presented to illustrate the method for the case of maximizing total sellable mass delivered from a near-Earth asteroid to a single customer in Geostationary Orbit. The results showed that the maximum sellable mass is achieved with a delivery route in which the mining spacecraft remains in a highly elliptical parking orbit before returning to the asteroid, while a small transport spacecraft retrieves the load of material and delivers it to an orbital propellant depot and customers. The optimal location of a propellant depot is found to be at the same orbital radius and orbital plane as the customers. This depot location and vehicle routing can deliver between 33.15 and 52.63% of the mass extracted from the asteroid in a single trip (depending on the trajectories to/from the target asteroid), with the ability to conduct numerous return trips to the asteroid. Highlights: The optimal location of the depot was found to be in the same orbit as the customer. The optimal route was found to be Route 2 with an Elliptical parking orbit. The mining spacecraft performs an apo-twist manoeuvre at apoapsis of 768, 798 km. This strategy can deliver between 33.15 and 52.63% of the extracted mass to the customer.