## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.2 Exact Methods in Supply and Delivery VRPs
Two objectives are considered in this problem: the total time travel per route is minimised for all vehicles as well as to minimise the arrival time to each demand nodes. These two objectives are solved based on priorities, as defined by the user. A small test instance based on hypothetical scenario was applied to validate the model where the problem is solved optimally. Meanwhile, ref. [40] considered the uncertainty of travel time and demand in CVRP with the robust optimisation approach. The objective is to minimise the total travel time as well as the unmet demand. In this model, two depots are iconsiderendstead of just one, whereas the rest of the formulation is similar to formal CVRP formulation. Finally, based on the robust counterpart obtained, the model is then converted into a deterministic MILP model, which is verified through the commercial solver Gurobi. As expected, the solver struggled for larger instance of the problem, which, according to [40], is largely due to the increasing sub-tour elimination constraints. An interesting approach of dynamically updating route condition is shown in [41], where a dynamic routing is executed during a disaster. In this problem, the realistic assumption that roads may be affected by disaster with no communication available is addressed. Two problems are specifically addressed in this problem: to obtain an optimal route in delivering relief aid, and to be informed on the route condition while performing the humanitarian operation. Two algorithms are proposed to be solved for the problem, namely the Information Gathering Algorithm (IGA) and Route Construction Algorithm (RCA). This process of information gathering is executed through the IGA. Meanwhile, based on the information that is gathered by IGA, RCA is then dynamically constructed at every query interval while using the Dijkstra shortest path algorithm. The objective is minimise the cost incurred for all vehicles when travelling. A simulation test is performed in order to validate the model and solution based on the rectangular area pivoted from the Nakagyo fire department in Kyoto. The results are compared with the existing method of Geocast, where an improvement can be observed in terms of gathering real time information and the arrival time. Ref. [42], on the other hand, addressed the stochastic problem of LRP under a fuzzy environment. In this problem a multi-commodity, multi-depot, with heterogeneous vehicle with different capacity and speed are considered. A split delivery is allowed, illustrating a more realistic version of the problem. In this problem, three objectives are addressed. The first objective is to minimise the total expenditure cost, including opening distribution centre, transportation cost, travel expanses, as well as the transportation cost, from suppliers and the distribution centre. The maximum travel time is minimised as the second objective, while the third addresses the unmet demand that should be minimised. Moreover, in this stochastic problem, the available traffic, transportation cost, volume of relief aid, fix cost of providing distribution centre, the distribution points, as well as the normal speed of the vehicle is uncertain. A MIP model is converted to its deterministic counterpart via a crisp model to further address the fuzzy parameters, which are the capacity of the distribution centre as well as the transportation cost. Finally, an exact solution approach is proposed that is based on the proposed crisp model as well as the method presented by [43], which is solved by the GAMS software while using the Baron Solver. The LRP with uncertain demand and travel time for distributing delivery aid in the event of a disaster is also addressed in [44]. With the objective of minimising the total arrival time of vehicles, the problem is formulated with the associated LRP constraints. This proposed model is applied to small experimental cases, where the commercial solver of LINGO is implemented in order to solve the problem. Ref.