Optimal placement of a deposit between markets: Riemann-Finsler geometrical approach (Q1014026)

The paper considers a single-facility Weber location problem with unit weights on Riemann-Finsler manifolds. Finsler distances are used to measure the cost of travel between the existing facilities and the new facility. As an example, a single-facility Weber problem on an inclined plane is considered where, due to the gravity acting on the vehicle, the transportation cost depends on the direction of travel. Some existence, uniqueness and multiplicity results are proven. Specific problem settings are considered (for example, all existing facilities may be located on the same geodesic), and examples are provided to illustrate the results. A genetic algorithm is presented for the solution of the problem.