A lexicographic maximin approach to the selective assessment routing problem

Abstract

Max-min approaches have been widely applied to address equity as an essential consideration in humanitarian operations. These approaches, however, have a significant drawback of being neutral when it comes to solutions with the same minimum values. These equivalent solutions, from a max-min point of view, might be significantly different. We address this problem using the lexicographic maximin approach, a refinement of the classic max-min approach. We apply this approach in the rapid needs assessment process, which is carried out immediately after the onset of a disaster, to investigate the disaster's impact on the affected community groups through field visits. We construct routes for an assessment plan to cover community groups, each carrying a distinct characteristic, such that the vector of coverage ratios are maximized. We define the leximin selective assessment problem, which considers the bi-objective optimization of total assessment time and coverage ratio vector maximization. We solve the bi-objective problem by a heuristic approach based on the multi-directional local search framework.

A Bi-Objective Field-Visit Planning Problem for Rapid Needs Assessment under Travel-Time Uncertainty

“…In this study, we extend the literature on humanitarian relief by considering both bi-objectives and uncertainty of travel times during the RNA stage, which addresses the two conflicting objectives of minimizing the total route duration and maximizing the vector of coverage ratio during the RNA stage. Specifically, we extend the study by Hakimifar et al [15] by investigating the impact of different levels of travel-time uncertainty on the Pareto frontier and the impact on route infeasibility. We apply robust optimization to tackle travel-time uncertainty.…”

“…MDLS provides an approximation of Pareto-optimal solutions by generalizing the concept of local search to multiple objectives [23]. Hakimifar et al [15] compared the performance of the MDLS method with methods previously applied to the SARP and showed that the designed MDLS finds the same max-min coverage ratio in most of the runs and, in some cases, a value that is even higher than the previously best-known value. To apply MDLS, for each objective, we use specific Adaptive Large Neighborhood Search (ALNS) operators, which are introduced and detailed in Hakimifar et al's [15] paper, to lead our search towards better solutions.…”

“…They used a simulation environment to evaluate the performance of the presented heuristic algorithms. Hakimifar et al [15] considered the lexicographic maximin approach, which refines the classic max-min approach used by Balcik [10] by distinguishing solutions with the same max-min value. The goal of this differentiation is to provide a range of solutions with more sites to visit along the assessment routes.…”

“…The excess value is the difference between the number of site visits made per community group and the pre-specified target value. Our paper adopts the idea of travel-time uncertainty presented in Balcik and Yanıko glu [6] and integrates it with the deterministic study by Hakimifar et al [15], who considered a bi-objective optimization model that offers the best trade-off between the total route duration and coverage-ratio vector maximization to the SARP.…”

“…In Section 3.1, we describe the bi-objective SARP problem, starting with a brief description of the lexicographic maximin approach and its differences from the max-min approach. The lexicographic maximin approach and its bi-objective setting have been detailed in Hakimifar et al [15] and we only provide a summary of this approach and the corresponding main definitions in this section. In Section 3.2, we describe the robust optimization approach adopted to address travel-time uncertainty.…”