Bi-objective bilevel optimization of distribution center locations considering user equilibria

• We develop a bi-objective bilevel model for the location of distribution centers.
• On the upper level, the objectives are cost and uncovered demand.
• On the lower level, a user equilibrium for the choices by customers is computed.
• The exact Pareto frontier is determined.
• An application to humanitarian logistics is outlined.

We propose a bi-objective, bilevel optimization model for the location of relief distribution centers (DCs) in humanitarian logistics. The upper-level decision-maker (an aid-providing organization) selects locations for capacitated DCs. On the lower level, beneficiaries choose a DC according to distance and amount of supply to be expected. This effects a user equilibrium on the lower decision level. Upper level objectives are to minimize total opening cost for the DCs and total uncovered demand. We develop an exact algorithm for determining the Pareto frontier of the problem, integrating the adaptive epsilon-constraint method, a branch-and-bound procedure, and the Frank–Wolfe procedure.