## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.2 Exact Methods in Supply and Delivery VRPs  
In [30], a Generalised VRP with flexible fleet size (GVRP-flex) is addressed. Common assumptions are made, such that the vehicles are homogeneous with one depot and several demand nodes that are clustered into a number of clusters. Only one vehicle is allowedper cluster and the trip to demand nodes should only be made once. The problem is solved while using a Column Generation (CG) and the performance is evaluated and compared with two metaheuristics that are inspired by the iterative local search (ILS). Ref. [30] addressed the problem that is inspired by HL, where the road conditions are often poor, due to the effect of disaster that requires the trip to be done by aeroplane. As opposed to [31], which allows for multiple trips, the trip needs to be done once at each disaster location, thus being ideal for the delivery problem with flexible fleet size, although it is somewhat unrealistic when considering the limited amount of transport during the real world application. The application of exact method solutions, particularly in the supply and delivery using VRPs, are comparable in number when compared to heuristic and metaheuristic solution approaches (Table A4). Nonetheless, some work, such as [32] (mark with two stars, \(\star\star\)), only addressed a single vehicle for the humanitarian delivery operation involving only 20 to 40 affected locations at the maximum. The problem of multi-trip Cumulative Capacitated Single VRP (mt-CCSVRP) is inspired by the response phase of humanitarian operations operation allowing for a single vehicle with limited capacity to perform successive trips to destinations in order to meet the urgency of delivering medical supplies. For a small instance of 20 sites to visit, ref. [32] proposed two Mixed Integer Linear Programming (MILP) model, while, for a larger instance, a resourced constrained shortest path problem model is adopted to minimise the sum of total arrival time. It is evident that the exact method can actually only be applied up to a certain number of instances based on their complexity in terms of constraints and objectives. A complex representation of a VRP as inter-modal networks is described by [33]. The problem is inspired from the joint effort of relief distribution coming from both local and international participants in the humanitarian operations. This translates into a routing problem for an inter-modal network that includes maritime and land transport. Applying GAMS solver, ref. [33] is also able to address a multi-objective problem, which further increases the complexity of their model. Moreover, they also stressed the importance and potential of inter-modal transport in delivering relief aid supplies during a disaster event by also considering the vulnerability of the road during the disaster, which is based on a case of the aftermath of an earthquake at the Istanbul seaport. Ref. [34], in his work, also considered multi-objective by adopting fuzzy and crisp formulation in solving the routing problem consists of multiple depots that are assigned with dispatch vehicles, distribution points, and emergency shelters. The problem of split delivering supply towards shelters is addressed while using a heterogeneous fleet during the response phase of disaster. However, due to limited resources of vehicles, the model aims to minimise the numbers of vehicle, while also minimising the total arrival time of vehicle to a depot or to the emergency shelter. Unlike the common VRP, which deals with network involving depots and shelters, this study dealt with three layers of network consisting of depot, distribution centre, as well as emergency shelters, thereby making sure that the distribution centre is able to accommodate deliveries to emergency shelters with vehicles only allowed to go to any one shelters and remain stationary. Thus, the TH method is applied to solve for the objectives introduced in the model. Similarly, the multi-objective problem is also addressed by [35].