## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.4 Metaheuristics in Supply and Delivery VRPs
Because of the uncertain demand during chaos, triangular fuzzy numbers are applied in order to estimate the demand centring around the most optimistic, pessimistic, and, most likely, demand. A penalty cost is incurred in the model should the delivery be insufficient, due to the limited capacity of vehicles per delivery. Moreover, the carbon emissions are derived from the fuel consumption, which is dependent on the vehicle speed, vehicle load, the inclination of the roads, as well as the travelled distance. A combined PSO and TS metaheuristic mechanism is applied in order to solve the problem. The initial solution is first computed by the PSO, which is later improved by the TS. Although the mechanism is regarded as hybrid in their work, the method is considered as two separate metaheuristics, since no internal operator of respective metaheuristic is changed in any manner. The problem of LRP in post disaster phase is addressed by [89], where the medical facilities need to be setup or located at an optimal location within the vicinity of disaster affected area along with their fixed emergency medical vehicle. It then needs to route each medical fleet respectively in an optimal manner such that the delivery aid is delivered to the demand nodes minimising the time spent on providing humanitarian aid. Each fleet belonging to each \(k\) erected site is heterogeneous allowing for a more complex representation of the real case. The Emergency \(k\)-Location Routing Problem (EkLRP) next deals with routing the heterogeneous vehicle with varying capacity in such a way that the wait time is minimised. In order to execute the proposed SA algorithm, the initial solution is first obtained through the Greedy Randomised Algorithm (GRA) that decomposed the problem into two sub-problem namely the location problem and the routing problem. The GRA is also applied to adjust or improve the solution that is computed by SA in the consequent steps. Ref. [90] focused on the shortage of supplies scenario, where fairness in distributing relief aid is demanded. The problem is modelled as LRP where the distribution centres are built just after the occurrence of a disaster. Partial road damage is addressed in the model as well as the inclusion of urgent window constraint. In this problem, the maximum demand loss is minimised, along with the total loss of all the nodes. In order to account for efficiency in delivery, another objective is to consider where the maximum duration of demand points in receiving relief aid is minimised. The problem is formulated through the lexicographic order multi-objective method. A Hybrid Heuristic Algorithm (HHA) is employed that consists of a greedy algorithm as well as ACO. Here, the fair allocation distribution is done by a greedy algorithm where the loss of demand nodes are computed iteratively. The demand nodes are also allocated to the each distribution centre via a greedy algorithm, which is also employed in order to determine the mode of delivery. Finally both the helicopter and land vehicle routing are solved by the ACO. The case of Great Wenchuan Earthquake was chosen as the study case. In [91], the issue of relief distribution and redistribution is highlighted during a disaster to ensure that there are no severe shortages of supplies in the needed area. An IRP is used to address both distribution and redistribution issues. The first period of the operation is distribution by routing vehicles utilising the VRPPD to assign locations where the redistribution is done next according to the Network Flow Problem (NFP). Dynamic changes of updated data are considered at each multi-period planning increasing distribution and redistribution efficiency and ensure fairness in the case of increase casualties of destruction, due to the ongoing disaster. A Specialised Simulated Annealing (SSA) is proposed in order to solve the problem. The partial solution is obtained by partially solving the problem (turning it into a sub-problem due to some feasible variable fixing).