## 4 Review of Literature
### Supply and Delivery in Routing Optimisation Problems
#### 4.1.4 Metaheuristics in Supply and Delivery VRPs
The problem is formulated while using the chance constraint programming approach and finally solved by GA. The sustainability issue concerning the social, economic, and environment concerns when relief aid delivery operation is performed in times of disaster is addressed by [78]. The sustainability issue is regarded in terms of the access, equity, and needs of fulfillment. What links these factors in the proposed VRP is the amount of relief, as well as the time of arrival, which is reflected by the Victim's Perception of Satisfaction (VPS) with regards to sustainability. As such, the objective is to maximise the minimum VPS as well as to minimise the largest difference of VPS among victims at an interval. The problem is formulated as a Mixed Integer Non Linear Programming (MINLP) model, where split delivery is allowed in delivering multi-commodities via heterogeneous vehicles from multi-Relief Distribution Center to multiple Affected Specific Areas. For this problem, a GA is adopted as the solution approach, due to its balanced trade-off between solution quality and computation time, which is shown in the test case of the Wenchuan Earthquake. Meanwhile, ref. [79] addressed the single layer LRP for relief commodity distribution, where priority is given to commodity and demand while considering the road damage. The priority to relief commodity is given through a set of real numbers that differentiate them from urgent relief material and general life relief material. The demand priority is reflected by the relationship between the urgency of demand and their time tolerance. A satisfaction function is introduced through a soft time window of each node and the time sensitivity coefficient where the link to urgency of demand is highlighted. Additionally, weight is assigned to each road signifying the level of damage sustained by the road. The two objective functions are to maximise the satisfaction level and the penalty incurred by violating time window is minimised. The formulated model is solved through the NSGA-II where the first objective function is simplified to ease the analysis. Two layers of coding are introduced with regards to the location decision as well as the routing decision. Finally, [PERSON]'s instance is applied in order to validate and evaluate the model and solution. Ref. [80] focused on the location inventory routing problem (LIRP) to prepare for both pre and post disaster by looking into three stages of the supply chain. This problem focuses on the earthquake in Tehran as a case study. The model is divided into two addressing the pre- and post-DM. In the first stage, the ideal location of warehouses is considered noting the hospital as a relief points as well as potential affected areas due to disaster. The cost of setting up warehouses, the cost of transporting the supplies from supplier to warehouses, as well as the inventory cost are addressed. Meanwhile, in the second stage, the distribution of the relief aid is considered based on the Multi-Echelon, Multi-Depot VRP (MEMDVRP). The first echelon reflects transporting the supply between warehouses and hospitals. The second echelon focuses on the transport and routing between hospitals and the affected areas. Three objective functions have been considered for the problem, namely to minimise: (i) the operational cost caption in the pre-disaster operation, (ii) the cost that is incurred by the post-disaster humanitarian operation, and (iii) the total relief time during the relief operation in the post-disaster phase. The problem is formulated as a MILP model, where the small instance is solved by the \(\epsilon\) constraint method. The larger scale of the problem is solved by the NSGA-II as well as the Reference Point Based NSGA-II (RPBNSGA-II), where they outperformed each other for the case of smaller instance and larger instance, respectively. The LIRP to supply multi-commodity to disaster sites is addressed in [81] while using two proposed models.