<![CDATA[This paper tackles the multi-depot heterogeneous-fleet vehicle-routing problem with time windows and simultaneous pickup and delivery (MDHF-VRPTW-SPD), a variant that mirrors he growing complexity of modern healthcare logistics. The primary purpose of this study is to model this complex routing problem as a mixed-integer linear program and to develop and validate a novel hybrid metaheuristic, B-ALNS, capable of delivering robust, high-quality solutions. The proposed B-ALNS combines a discrete Bat Algorithm with Adaptive Large Neighborhood Search, where the bat component supplies frequency-guided diversification, while ALNS adaptively selects destroy and repair operators and exploits elite memory for focused intensification. Extensive experiments were conducted on twenty new benchmark instances (ranging from 48 to 288 customers), derived from Cordeau’s data and enriched with pickups and a four-class fleet. Results show that B-ALNS attains a mean cost 1.15 % lower than a standalone discrete BA and 2.78 % lower than a simple LNS, achieving the best average cost on 17/20 instances and the global best solution in 85% of test instances. Statistical tests further confirm the superiority of the hybrid B-ALNS, a Friedman test and Wilcoxon signed-rank comparisons give p-value of 0.0013 versus BA and p-value of 0.0002 versus LNS, respectively. Although B-ALNS trades speed for quality (182.65 seconds average runtime versus 54.04 seconds for BA and 11.61 seconds for LNS), it produces markedly more robust solutions, with the lowest cost standard deviation and consistently balanced routes. These results demonstrate that the hybrid B-ALNS delivers statistically significant, high-quality solutions within tactical planning times, offering a practical decision-support tool for secure, cold-chain-compliant healthcare logistics]]>
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