The Lightly Robust Max-Ordering Solution Concept for Uncertain Multiobjective Optimization Problems: An Ambulance Location Problem with Unavailability

Abstract

This study introduces a robust concept for considering uncertain multiobjective optimization problems, called the lightly robust max-ordering solution. This introduced solution concept offers the best option for solving issues based on the maximum cost in the worst-case scenario. Introducing a tolerable relaxation parameter can be used to increase the robustness of the solution but, at the same time, the desirable property of such a solution with respect to the nominal scenario might be decreased. Subsequently, the two measurements, which are the ‘gain in robustness’ and the ‘price to be paid for robustness’, are considered. These measurements are needed to support a decision maker to find more desirable lightly robust max-ordering solutions with a beneficial trade-off between the robustness of solutions and the quality of solutions in an undisturbed situation. Moreover, an algorithm for finding the proposed solution is presented and discussed. An instance of the benefits of the suggested solution concept is used on an example of ambulance location planning if ambulances may be unavailable.