A multi-cover routing problem for planning rapid needs assessment under different information-sharing settings

Abstract

In this paper, we introduce a multi-cover routing problem (MCRP), which is motivated by post-disaster rapid needs assessment operations performed to evaluate the impact of the disaster on different affected community groups. Given a set of sites, each carrying at least one community group of interest, the problem involves selecting the sites to be visited and constructing the routes. In practice, each community group is observed multiple times at different sites to make reliable evaluations; therefore, the MCRP ensures that pre-specified coverage targets are met for all community groups within the shortest time. Moreover, we assume that the completion time of the assessment operations depends on the information-sharing setting in the field, which depends on the availability of information and communication technologies (ICT). Specifically, if remote communication is possible, each assessment team can share its findings with the central coordinator immediately after completing the site visits; otherwise, all teams must return to the origin point to share information and finalize the assessments. To address these different information-sharing settings, we define two MCRP variants with different objectives and present alternative formulations for these variants. We propose two constructive heuristics and a tabu search algorithm to solve the MCRP, and conduct an extensive computational study to evaluate the performance of our heuristics with respect to different benchmark solutions. Our results show that the proposed tabu search algorithm can achieve high-quality solutions for both MCRP variants quickly. The results also highlight the importance of considering the availability of ICT in the field while devising assessment plans.

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Acknowledgements

The authors thank the editors and the review team for their valuable suggestions. This research has been funded by the Scientific and Technological Research Council of Turkey Career Award (Grant no: 213M414). The authors thank Selene Silvestri for her help and guidance in programming.

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Appendices

Appendix A. Summary comparison of MCRPrd and MCRPna solutions obtained by different methods

Table 6 Comparison summary for MCRPrd and MCRPna solutions
Table 7 Solutions obtained by using with different ICH versions for the MCRPrd and MCRPna

Table 6 presents relative gaps (%) between the best solutions obtained by CPLEX by using different formulations with different parameter settings and our heuristics. We present the average relative gap values, where the relative gap \(\varDelta \) is calculated by subtracting the solution value obtained by CPLEX from that of the heuristic, and then diving the resultant by the solution value of the CPLEX. Therefore, the negative \(\varDelta \) values indicate superior heuristic solutions, and vice versa. For each pairwise comparison, the relative gaps are calculated and presented separately over the set of instances, which provided negative and positive \(\varDelta \) values. We also present the percentage of instances (denoted by p), for which our heuristics could obtain equivalent or better solutions than the best CPLEX solutions.

Appendix B. Comparison of ICH solutions with different vehicle assignment methods

Table 7 presents the solutions obtained by using different versions of the ICH. In \(\text {CH}^{\text {rd}}_{\text {I}}\), we assign the nodes to the vehicles in a greedy way, and in \(\text {CH}^{\text {rd}}_{\text {K}}\), the assignments are made via a k-means algorithm. The initial solutions obtained by \(\text {CH}^{\text {rd}}_{\text {I}}\) and \(\text {CH}^{\text {rd}}_{\text {K}}\), and the final solutions obtained by TS, which are initialized by \(\text {CH}^{\text {rd}}_{\text {I}}\) and \(\text {CH}^{\text {rd}}_{\text {K}}\), respectively, are presented.

Appendix C. Comparison of optimal solutions obtained by using different objective functions

In this section, we compare the optimal solutions obtained by MCRPrd and MCRPna with the solutions of an alternative formulation that minimizes total route duration, which is called the MCRPtrd. We compare the assessment completion times for the 25-node instances, which could be solved optimally by CPLEX for all these formulations within the given solution time. Table 8 presents the assessment completion time values, in terms of the maximum route duration and the maximum arrival time, achieved by different formulations. The last two columns present how much longer the assessment completion times would be (in percentages) if the problem is solved by minimizing total route duration; specifically, \(\varDelta _{\mathrm{rd}}=[Z_{\mathrm{rd}}-Z^*_{\mathrm{rd}}]/Z^*_{\mathrm{rd}}\) and \(\varDelta _{\mathrm{na}}=[Z_{\mathrm{na}}-Z^*_{\mathrm{na}}]/Z^*_{\mathrm{na}}\).

Table 8 Comparison of optimal solutions for 25-node instances

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Pamukcu, D., Balcik, B. A multi-cover routing problem for planning rapid needs assessment under different information-sharing settings. OR Spectrum 42, 1–42 (2020). https://doi.org/10.1007/s00291-019-00563-y

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Keywords

  • Rapid needs assessment
  • Information sharing
  • Location-routing
  • Multi-set covering
  • Tabu search