## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.2 Exact Methods in Supply and Delivery VRPs
[45] is one of the few that studied the problem of preparing emergency supplies for a disaster instead of responding towards a disaster through the utilisation of a neighbourhood disaster station. The idea is to place the neighbourhood disaster station at a strategic location while restocking the station with emergency supplies that can be distributed to the affected neighbouring areas in the time of a disaster. However, it is unknown when a disaster would strike; thus, to prevent the supplies from expiring, they are to be sold to maximise returns. Once they are sold, the station would need to be replenished. Their objective is to maximise the profit by determining the optimal replenishment policy for each supply items as well as to provide an optimal route for the vehicles that will minimise the cost. A heterogeneous vehicle is considered and the replenishment of the stations is done according to their capacity from a single depot with time constraints. Here, the MIP formulation of the problem is solved by CPLEX solver for a small instance. Because all of the information is known, the problems are denoted as a deterministic problem. Ref. [46] addressed the scheduling and open vehicle routing of pick up and drop off aid delivery problem through the perspective of a humanitarian coordinator. The coordinator as the decision maker is to decide how many vehicles should be rented from the third party logistics service provider while taking into consideration the limited duration of the rent in the aftermath of a hurricane. This includes tasking each vehicle to a set of clients in an optimised manner and routing the vehicles optimally, such that the total transportation cost is minimised. The problem is considered to be an Open Vehicle Routing Problem with Time Window (OVRPTW). Two models are presented for the problem. The MIP model is formulated by defining an artificial source and sink, and it is solved via a commercial solver. The MIP model is further reformulated into a path based integer model. Here, the routing of vehicle along with the rent period constraint are addressed by the column generation approach. The obtained results indicate that the column generation approach outperformed the commercial solver, especially when the instance size grew. A DSS is proposed by [47] for aiding the distribution during a disaster event where an embedded VRP module is discussed, resulting in a model driven based decision support system. Here, a deterministic model addressing a heterogeneous fleet that performed split delivery as well as multi-trip is presented. In order to validate the model, a case study was done based on the earthquake and tsunami in the coast of central Chile on 2010, where the smaller instance version is solved by the GAMS solver as well as the prototype solver of the decision support system. Ref. [48] combined the commodities distribution in the LRP in order to ensure efficient aid distribution in the post disaster phase. However, the location of distribution centres as well as commodities distribution is done during the pre-disaster phase. The problem that focuses on time deprivation in emergency logistics model further reflects the critical scenario, where there is a shortage of supplies. The time deprivation serves as the loss cost incurred during the humanitarian operation. The optimisations are done where the commodities distribution and site selection are considered at pre-disaster phase. The first objective is then to minimise the all logistics cost, which includes the operating cost of the relief centre, the inventory cost, the transportation cost pre- and post-disaster, along with the deprivation cost that is incurred by the unmet demand. The second objective on the other hand is to minimise the total transport time for any edges used. The problem is initially modelled as two stage nonlinear bi-objective integer programming and was further simplified into a single objective integer programming model.