## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.3 Heuristics and Local Search in Supply and Delivery VRPs
However, it is shown in their work that this algorithm may not be able to satisfy the operational constraint, such that the total cost is minimised. Instead, the fair division problem is assumed for the allocation problem, while the routing component of the problem is formulated as a MILP model. The bi-objective of the model is to minimise the maximum deviation of envy free allocation and the total travel cost respectively. In order to obtain an optimal solution, the problem is decomposed while using [PERSON]'s decomposition method, where the relaxed version of the original problem is obtained. However, for larger instances, a hybrid heuristic of local search and a greedy algorithm is proposed. This proposed method consists of pickup node clustering, assignment of delivery nodes, tour construction, and, finally, the improvement of the solution. A numerical experiment is based on the real case, showing the capability of the proposed heuristic in obtaining a balanced solution between quality and computation efforts. Ref. [58], in his work, argued the necessity of addressing the HL from the perspective of minimising the arrival time, rather than the cost minimising problem to reflect the real urgency of delivering critical supply to the victims. The problem is modelled as the selective cumulative multi-VRP with stochastic travel time, where the priority of the affected area is considered based on the destruction that is caused by the disaster as well as the population of the affected area. Because the fleet of vehicles is limited, only selective areas are served from a single depot. Unlike typical literature addressing the humanitarian problem, homogeneous vehicles are considered to have unlimited capacity. The objective is to maximise the utility that represents the decreasing function of the arrival time. To cater for the urgency of planning, an iterated greedy heuristic is proposed that consists of construction and destruction stages. Benchmark instances are used and the results shows good quality solutions that are computed within a reasonable and comparable time. The strategy to decompose VRP into multiple TSPs are proposed in [59] through the approach of cluster first and route second. The problem is formulated as a MIP with the objective to minimise the total transportation cost, the pipeline inventory cost, as well as holding cost with back order for the scenario of hurricane Irma in Florida, where the gas supplies for gas stations were urgently needed due to people fleeing from the storm. Prior to solving the routing decision, the optimal replenished amount of gas stations and inventory level or route served by the vehicle are first computed. The solution of the continuous approximation serves as a guidance for the clustering, which would decomposed the VRP into multiple TSPs. Two clustering methods are employed and compared, namely the local observation based clustering and the K-means clustering algorithm to determine the routes. Once the clustering is performed, the TSP is then solved using [PERSON]'s method. Ref. [60], on the other hand, used the ability of UAVs in order to aid land transport in transporting relief aid during flood. The min cost flow model is applied with a single source and a single destination to routing model, which would also account for the capacity of the arc. Furthermore, the Hortonion Overland flood model is applied to model the problem in a more realistic fashion. Two heuristics are employed to solve the model, depending on the phase of routing. Initially, the quickest flow algorithm is employ to construct the initial routing. However, when flood data affecting transport network are updated, the vehicle is forced to reroute to a new route computed by the earliest arrival flow algorithm. At this point, the model is converted into a multiple source single destination problem. Both the virtual network and real network of Bangalore were applied in order to validate the model.