|
| Authors | Objective function | Constraints/decision | Problem type |
|
| Ahmadi et al. [31] | Minimize (distribution time, penalty cost of unsatisfied demand, fixed costs of opening local depot) | Arrival and destination, number of vehicles, demand, working time, depot capacity | Multidepot location-routing model |
|
| Yi and Kumar [78] | Minimize (weighted sum of unsatisfied demand) | Flow of wounded people, number of unserved wounded people, vehicle load and capacity, number of vehicles | Multicommodity network flow model |
|
| Vitoriano et al. [96] | Minimize (time, cost)
Maximize (equity, reliability) | Supply and demand balance at each node, vehicle type, subcycle elimination, vehicle capacity | Relief distribution model |
|
| Tzeng et al. [37] | Minimize (transportation cost, travel distance)
Maximize (minimum satisfaction) | Shipment period, selection of depot, uncertain demand | Relief distribution model |
|
| Chen et al. [42] | Minimize (decision making and equipment transportation time) | Balance of inflow and outflow at each node, vehicle routing | Relief equipment distribution model |
|
| Wang et al. [72] | Minimize (travelling time, relief distribution cost)
Maximize (route reliability) | Vehicle arrival and destination, quantity of relief, demand and supply of relief, vehicle capacity | Multiobjective open location-routing model |
|
| Jabbarzadeh et al. [33] | Minimize (costs of locating blood facilities, transportation, and holding) | Location and number of facilities, quantity of blood required at each facility, blood inventory level at the end of each period | Robust network design model |
|
| Balcik et al. [44] | Minimize (logistic costs, penalty cost, and shortage cost) | Demand fulfilment, vehicle capacity | Last mile relief distribution model |
|
| Tirado et al. [98] | Minimize (deviation of delivered aid with respect to the planned amount) | Dynamic flow balance at each node, flow balance for vehicle, vehicle availability, vehicle capacity, amount of load | Lexicographical dynamic flow model |
|
| Liberatore et al. [43] | Maximize (demand satisfaction) | Arrival time, total served demand, maximum ransack probability, arc reliability | Humanitarian aid distribution model |
|
| Campbell et al. [32] | Minimize (maximum and minimum average arrival time) | Subtour elimination, vehicle route destination, arrival time | Travelling salesman problem (TSP) and vehicle routing problem (VRP) |
|
| Sheu [38] | Maximize (collective resilience of survivors during emergency logistics operations) | Population size, number of affected areas, setup cost, transportation cost, relief demand and supply | Relief distribution model |
|
| Afshar and Haghani [39] | Minimize (total amount of weighted unsatisfied demand) | Commodity flow, vehicular flow, facility location, capacities for temporary facilities | Relief distribution model |
|
| Huang et al. [79] | Minimize (sum of arrival times to beneficiaries) | Number of vehicles, flow balance, subtour elimination, arrival time | Assessment routing model |
|
| Bozorgi-Amiri et al. [36] | Minimize (total cost of the relief chain, sum of the maximum shortages)
Maximize (satisfaction level) | Commodity flow, capacity limits of distribution centers, number of distribution centers | Relief distribution model |
|
| Özdamar and Demir [64] | Minimize (estimated total travel time) | Commodity flow balance, unmet demands, inventory level at warehouse, vehicle capacity, number of vehicles, number of routes | Vehicle routing model |
|
| Hu and Sheu [50] | Minimize (logistical costs, environmental and operational risk costs, and psychological costs) | Recycled amounts for use, stocks of the debris amounts stocked, recycled, transported, and disposed, debris transportation | Postdisaster debris reverse logistics model |
|
| Lin et al. [40] | Minimize (penalty function, unsatisfied demands, and total travel time) | Maximum service level, fairness, vehicle capacity, working hours | Relief distribution model |
|
| Wohlgemuth et al. [34] | Minimize (delays in delivery time) Maximize (equipment utilization) | Vehicle capacity, subtour elimination, time window, time consistency | Last mile relief distribution model |
|
| Vitoriano et al. [41] | Minimize (operation cost, maximum ransack probability)
Maximize (reliability in a link) | Availability of goods, vehicles flow, vehicle load, budget | Humanitarian aid distribution system |
|
| Shen et al. [35] | Minimize (unsatisfied demand) | Route feasibility, time, service, demand flow | Vehicle routing model |
|
| Chiou and Lai [51] | Minimize (travel time of rescue path, total detour travel time, number of unconnected trips of nonvictims, and number of police officers) | Access reliability, traffic capacity, degree of damage of transportation facility | Optimal rescue path and traffic control model |
|
| Berkoune et al. [71] | Minimize (total duration of all trips) | Relief goods availability, supply and demand, daily work time, vehicle type, vehicle capacity | Relief distribution model |
|
| Adıvar and Mert [52] | Maximize (minimum credibility with respect to every item)
Minimizing (total cost of procurement plus transportation) | Flow conservation, capacity limitations of the available transportation assets, time period in which the relief item arrives, available number of vehicles | International relief planning model |
|
| Camacho-Vallejo et al. [53] | Minimize (total response time for delivering aid, cost of transportation) | Available space in each storage center, relief goods quantity, demand and supply | International aid distribution model |
|
