A Humanitarian Logistics Model Integrating Heterogeneous Vehicle Routing, Time-Based Transportation Mode Switching, and Overtime Penalties for Disaster Pharmaceutical Logistics

Abstract

Earthquakes are sudden, unpredictable disasters that disrupt transportation infrastructure while generating surges in medical demand, posing critical challenges to last-mile pharmaceutical logistics. Existing humanitarian logistics models rarely integrate heterogeneous transportation modes, time-dependent mode switching, and operational constraints within a unified framework. This study develops a cost-optimised pharmaceutical distribution model based on a heterogeneous vehicle routing problem (VRP) that incorporates post-disaster infrastructure disruption, time-based mode switching, and overtime penalties. Using the 2022 Cianjur Earthquake (Indonesia) as a case study, three strategies are evaluated: a baseline, a Mixed-Integer Linear Programming (MILP) optimisation model, and a two-phase heuristic combining a savings algorithm with local search. The model distributes 550 pharmaceutical packages to 47 primary healthcare centres (PHCs) under a 480-minute daily operating constraint. The MILP model reduces total cost by 5.89% relative to the baseline (IDR 430,052,945), while the two-phase heuristic achieves the lowest cost (IDR 391,811,960;?8.89%) at a 100% service level. Sensitivity analysis indicates a four-day emergency duration gives the most cost-efficient transition from fast-response modes to consolidated truck distribution. The findings provide a practical optimisation framework and decision-support insights for efficiency, responsiveness, and resilience in disaster pharmaceutical logistics.