Overview of decision problems addressed by optimization approaches in disaster patient flow logistics
| Reference | Focus | Objective | Method | Solution | Problem |
|---|---|---|---|---|---|
| Jin et al. (2015) | Effectiveness | No. survivors (max) | MIP | Exact | Resource allocation |
| Tlili et al. (2018) | Efficiency | Total travel cost (min) | Combinatorial optimisation | Genetic algorithm | Routing |
| Sun et al. (2021) | Effectiveness | No. casualties (min) | Robust LP | Exact | Location- allocation |
| Memari et al. (2020) | Efficiency | Costs (min) + waiting times (min) | Bi-objective problem | NSGA-II + MOICA | Location- allocation- routing |
| Niyazi and Behnamian (2023) | Effectiveness | No. survivors (max) | MIP | Exact | Allocation |
| Aringhieri et al. (2022) | Effectiveness + efficiency | Max completion time (min) + score urgent patients visited (max) | Hierarchical LP | Exact | Routing |
| Yassin et al. (2022) | Efficiency | Cost transport + facilities (min) | LP | Exact | Location- allocation |
| Dean and Nair (2014) | Effectiveness | No. expected survivals (max) | MIP | Exact | Location- allocation |
| Pınarbaşı et al. (2022) | Efficiency | Total waiting time (min) | LP | Exact | Scheduling |
| Liu (2020) | Fairness + efficiency | Coverage (max) + cost (min) | Combinatorial optimisation | Genetic algorithm (NSGA) | Location |
| Zhu et al. (2023) | Efficiency | Makespan (min) | MIP | Variable neighbourhood search | Scheduling |
| Ghasemi et al. (2019) | Effectiveness + efficiency | Costs facilities + transport (min) + casualties (min) | Multi- objective MIP | NSGA-II, ϵ-constraint, MMOPSO | Location- allocation |
| Munawar et al. (2023) | Efficiency | Total distance (min) + time required (min) 16 | Non-linear integer programming | Artificial bee colony | Routing- scheduling |
| Sirbiladze et al. (2024) | Efficiency | Reliability (max); total cost (min); time to evacuate (min); no. shelters (min) | Combinatorial optimisation | ϵ-constraint | Location- allocation |
| Pouralia et al. (2018) | Fairness + effectiveness + efficiency | Population covered (max); distance between health centres (min) | Multi-objective problem | NSGA-II | Location- allocation |
| Caunhye et al. (2015) | Efficiency | Reliability (max); total cost (min); time to evacuate (min); no. shelters (min) | Combinatorial optimisation | ϵ-constraint | Location- allocation |
| Liu et al. (2019) | Effectiveness + efficiency | Expected number of survivors (max); cost (min) | Bi-objective problem | ϵ-constraint method | Location- allocation |
| Gao et al. (2017) | Effectiveness + efficiency | Total travel time (min); total mortality risk (min) | Bi-objective problem | Genetic algorithm | Location- allocation |
| Xu et al. (2016) | Efficiency | Total transportation time (min); distance of distribution centres (min); resource gap (min) | Fuzzy multi-objective bi-level programming | Genetic algorithm | Location- routing |
| Salman and Gül (2014) | Efficiency | Total travel time of transported casualties (min) + total waiting time (min) + total setup cost (min) | LP | Exact | Location- allocation |
| Wilson et al. (2013b) | Effectiveness + efficiency | Number fatalities (min); suffering [waiting times (min); adequate match of hospital (max)]; efficiency [idleness (min); make-span (min)] | Multi- objective problem | Variable neighbourhood search | Scheduling |
| Li et al. (2020b) | Efficiency | Total rescue cost (min): fixed cost for opening facilities + emergency resource allocation cost, evacuation cost, and un-evacuated penalty | Stochastic programming: multi-stage scenario model | Progressive hedging algorithm | Location- distribution |
| Bronfman et al. (2022) | Efficiency | Minimize total time until patients are treated | LP | Exact | Allocation |
| Kaviyani-Charati et al. (2018) | Effectiveness + efficiency | Transportation time (min), untreated patients (min) | Robust optimisation | Monte carlo | Location- transportation |
| Babaqi and Vizvári (2023) | Efficiency | Make-span (min) | NP | EDDBF, EDDWF, LPTBF | Scheduling |
| Shavarani and Vizvari (2018) | Efficiency | Total travel time (min) | NP | Genetic algorithm | Routing |
| Caglayan and Satoglu (2021) | Effectiveness + efficiency | Unserved number of patients (min), no. ambulances (min), total time (min) | Multi- objective two-stage stochastic programming | ϵ-constraint: AUGMECON2 | Location-allocation |
| Aghaie and Karimi (2022) | Effectiveness + efficiency | Time of operations (min), cost of operations (min) [+robustness/ penalties] | Two-stage multi- objective multi-period scenario- based model | NSGA-II | Location-allocation- routing |
| Mousavi et al. (2022) | Efficiency | Total distance (min); cost of facilities (min); cost of treatment (min) | Bi-objective problem | ϵ-constraint | Location-allocation |
| Zhang et al. (2018) | Effectiveness | Number of victims transported (max) | Mixed- integer linear programming (MILP) | Exact | Allocation |
| Wilson et al. (2013a) | Effectiveness | Total time to adequate treatment (min) | LP | Exact | Allocation |
| Reference | Focus | Objective | Method | Solution | Problem |
|---|---|---|---|---|---|
| Effectiveness | No. survivors (max) | Exact | Resource allocation | ||
| Efficiency | Total travel cost (min) | Combinatorial optimisation | Genetic algorithm | Routing | |
| Effectiveness | No. casualties (min) | Robust | Exact | Location- allocation | |
| Efficiency | Costs (min) + waiting times (min) | Bi-objective problem | NSGA-II + | Location- allocation- routing | |
| Effectiveness | No. survivors (max) | Exact | Allocation | ||
| Effectiveness + efficiency | Max completion time (min) + score urgent patients visited (max) | Hierarchical | Exact | Routing | |
| Efficiency | Cost transport + facilities (min) | Exact | Location- allocation | ||
| Effectiveness | No. expected survivals (max) | Exact | Location- allocation | ||
| Efficiency | Total waiting time (min) | Exact | Scheduling | ||
| Fairness + efficiency | Coverage (max) + cost (min) | Combinatorial optimisation | Genetic algorithm ( | Location | |
| Efficiency | Makespan (min) | Variable neighbourhood search | Scheduling | ||
| Effectiveness + efficiency | Costs facilities + transport (min) + casualties (min) | Multi- objective | NSGA-II, ϵ-constraint, | Location- allocation | |
| Efficiency | Total distance (min) + time required (min) 16 | Non-linear integer programming | Artificial bee colony | Routing- scheduling | |
| Efficiency | Reliability (max); total cost (min); time to evacuate (min); no. shelters (min) | Combinatorial optimisation | ϵ-constraint | Location- allocation | |
| Fairness + effectiveness + efficiency | Population covered (max); distance between health centres (min) | Multi-objective problem | NSGA-II | Location- allocation | |
| Efficiency | Reliability (max); total cost (min); time to evacuate (min); no. shelters (min) | Combinatorial optimisation | ϵ-constraint | Location- allocation | |
| Effectiveness + efficiency | Expected number of survivors (max); cost (min) | Bi-objective problem | ϵ-constraint method | Location- allocation | |
| Effectiveness + efficiency | Total travel time (min); total mortality risk (min) | Bi-objective problem | Genetic algorithm | Location- allocation | |
| Efficiency | Total transportation time (min); distance of distribution centres (min); resource gap (min) | Fuzzy multi-objective bi-level programming | Genetic algorithm | Location- routing | |
| Efficiency | Total travel time of transported casualties (min) + total waiting time (min) + total setup cost (min) | Exact | Location- allocation | ||
| Effectiveness + efficiency | Number fatalities (min); suffering [waiting times (min); adequate match of hospital (max)]; efficiency [idleness (min); make-span (min)] | Multi- objective problem | Variable neighbourhood search | Scheduling | |
| Efficiency | Total rescue cost (min): fixed cost for opening facilities + emergency resource allocation cost, evacuation cost, and un-evacuated penalty | Stochastic programming: multi-stage scenario model | Progressive hedging algorithm | Location- distribution | |
| Efficiency | Minimize total time until patients are treated | Exact | Allocation | ||
| Effectiveness + efficiency | Transportation time (min), untreated patients (min) | Robust optimisation | Monte carlo | Location- transportation | |
| Babaqi and Vizvári | Efficiency | Make-span (min) | EDDBF, EDDWF, | Scheduling | |
| Efficiency | Total travel time (min) | Genetic algorithm | Routing | ||
| Effectiveness + efficiency | Unserved number of patients (min), no. ambulances (min), total time (min) | Multi- objective two-stage stochastic programming | ϵ-constraint: AUGMECON2 | Location-allocation | |
| Effectiveness + efficiency | Time of operations (min), cost of operations (min) [+robustness/ penalties] | Two-stage multi- objective multi-period scenario- based model | NSGA-II | Location-allocation- routing | |
| Efficiency | Total distance (min); cost of facilities (min); cost of treatment (min) | Bi-objective problem | ϵ-constraint | Location-allocation | |
| Effectiveness | Number of victims transported (max) | Mixed- integer linear programming ( | Exact | Allocation | |
| Effectiveness | Total time to adequate treatment (min) | Exact | Allocation |
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