## 4 Review of Literature
### Rescue in Routing Optimisation Problems
#### 4.3.2 Exact Methods in Rescue VRPs
These variables consisted of input variables representing the distance of the arc, the risk of travelling along the arc, as well as the output variable that represents the affected population, the level of damages sustained by buildings at the site, and the possibility of a second disaster occurrence. Taking the missing of information and data from the experts into account, the ILGCC model was developed and adopted in developing the DEA model. The ILGCC reflected the expert opinions and decisions that are often incomplete and vague as a first response when a disaster occurred. A rescue efficiency could be computed and applied to the IP model with the five decision variables and by applying the DEA model with ILGCC. Furthermore, in the dynamic setting, the changes of data are expected and applied for every period. In the IP model, the total rescue efficiency is maximised with an ongoing decrease of efficiency, as the operation time is prolonged. The case study of Wenchuan earthquake that hit Sincluan, China is taken to generate instances in order to verify the model. The efficiency of SAR is highlighted as compared to the time-based solution approach. The problem of saving victims that are trapped in various critical locations due to a disaster that occurred by allocating and routing the SAR team in the post disaster phase is addressed in [146]. In reflecting a realistic scenario, both dynamic and stochastic elements are presented in the proposed model. The SAR team is heterogeneous with different operation capacities. Additionally, two versions of the online problems are proposed with two different objectives. The first problem tried to minimise the operation time (known as makespan) as well as minimising the total weighted latency before the victim is finally rescued. The weights are computed based on the percentage of numbers of victims at a critical nodes. The second proposed online model tried to minimise the total waiting time of the victim until they are finally rescued. These two online models are then compared to the corresponding offline model, where all of the information is known. Finally, a deterministic online strategy is proposed, making use of the solution obtained through the offline MIP version of the problem. Ten generated networks are applied to validate the model; they are obtained from Gorubi, each with instances up to 500 nodes. More recently, the problem of both allocating resources and routing the resources for SAR operation via a two-stage decomposition approach was studied by [147]. The model also addressed the risk of a secondary disaster occurrence. Furthermore, the uncertainties are also considered through the environment setting, which is addressed by the interval based robust optimisation approach. In the first stage, there are several affected districtsthat consist of several demand locations with varying demands, depending on the damage afflicted. The model addresses the fairness in distributing allocation by computing the minimum total demand coverage through estimating the SAR demand in each afflicted district. Each demand is weighted by its importance weight and the objective is to maximise the weighted sum of the demand minimum's coverage for all types of demand, which, in turn, maximises the fairness allocation. The output of the first stage, namely the optimal SAR resource allocation is then forwarded to the second stage in the routing problem model. The total weighted demand completion time is minimised. Solving both of the MIP problems, an interval data robust optimisation is adopted as a solution approach, where each robust counterpart is defined for each problem model to address the uncertain parameters. A few scenarios are considered from the case study of earthquake in Iran in order to verify the models where the robust models are compared with a deterministic counterpart in terms of the solutions obtained.