## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.2 Exact Methods in Supply and Delivery VRPs
In this routing problem, the efficiency of maximising the delivered supplies through a short time window is considered. Furthermore, the fairness of delivery is also addressed among emergency points. Apart from having multiple depots, the model, known as dynamic continuous time flow network, tackled the complex problem through the dynamic constraint, which depends on time incorporating changes of demand, donation, as well as the condition of the road. In this problem, the decisions involved are the dispatching decision as well as the routing decision. Furthermore, a continuous-time dynamic network flow algorithm that is based on the augmentation of the continuous-time dynamic residual network (CTDRN) involving four steps is proposed in order solve the problem. Ref. [36] seeked to minimise the cost of travel, in the event of arc failure. The arc failure could be reflected in many scenarios, especially in times of disaster. This study also considered the condition where a route failure is unexpected, where the on board routing software is not available, as well as when communication with a control centre is difficult, due to the damage on communication facilities. It allows for a driver to pick a primary road along with its alternative should an arc failure occur. To solve the problem, ref. [36] proposed a modified label-correcting algorithm where the primary path and alternate secondary path are computed in two parts, respectively. Additionally, through the dominance rule proposed, the huge number of possible instances representing failure in each arc are effectively reduced. A more detailed model of delivering supplies in a disaster event that is addressed by the exact solution approach is shown in [37]. The Mixed Integer Programming (MIP) model highlights an interesting concept of sharing relief supply among emergency shelters. This concept works by allowing for sharing according to the assigned priorities as well as the number of evacuees. Ref. [37] addressed the problem criteria based on the Japan government's white paper on the Great East Japan Earthquake in 2011. The objective of the model is to minimise the total transportation cost as well as the penalty that is imposed for every failure in satisfying the demand. The goods' priority are represented by each weight that is associated with the good types. Unlike the typical VRP model, shelters that have homogeneous delivery cars with fixed capacity take the role of a depot, while also having their own demand. As such, the sharing concept among shelters could be modelled. Furthermore, each shelter is also associated with priority according to urgency. Here, real data of Chofu City in Japan are applied to generate real data for the parameter of the problem. The CPLEX solver is utilised for solving the problem. The fairness of relief distribution for event such as earthquake is studied in [38]. The fairness in this work is considered based on the arrival time of vehicle. The satisfaction level of the victims is considered as a utility function with the objective of minimising the range of delivery times from he transportation vehicle. The proposed model is then compared with model for different objectives, namely one that minimises the arrival time as well as the one that minimises the transportation cost. The 2011 Japan earthquake is taken as a case study focusing on the city of Fukushima and Noda village. The results shows that the satisfaction level of victims improved, even with a slight improvement in the time range of delivery. Furthermore, the proposed model improved the fairness of delivery at the price of a higher cost of operation as compared to the two models compared. Ref. [39] focused on the integration of VRP in the Decision Support System (DSS). However, the embedded VRP considers the extension of conventional VRP. such as the Heterogeneous VRP (HVRP), SDVRP, and the Multi Travel VRP (MTVRP). The prototype model in DSS also considered partitioning the deliveries, where the vehicle has the choice of not delivering all aid within its capacity.