A severe earthquake has struck a remote region, causing extensive damage and leaving $20$ communities in urgent need of humanitarian aid. Each community has a specific demand for emergency kits, which include water, food, and medical supplies. These kits are stocked in the central warehouse, located at Location $1,$ and the Humanitarian Relief Agency $($HRA$)$ is tasked with distributing them as efficiently and equitably as possible. This week, the HRA has $1,000$ emergency kits available in the warehouse, but the total demand across all affected communities amounts to $1,370$ kits. Unfortunately, not all demands can be fully met. Demand of all communities are given in file $$Demand$.$ To deliver these emergency kits, the HRA has two vehicles available. The vehicles travel at a constant speed of $1$ km$/$minute$,$ and the time required to unload a single kit at any location is $3$ minutes. Vehicles operate under time constraints, working $5$ days a week $($Monday to Friday$)$ from $08$:$00$ to $17$:$00,$ with a $1-$hour lunch break each day, resulting in a total of $8$ working hours daily. The distances between the central warehouse and the $20$ locations, as well as between locations, are provided in the file named $$Distance$.$ Due to earthquake$-$ related road damage, certain routes are inaccessible: Unfortunately Location $1($warehouse of HRA$)$ does not have direct access to locations $3,6,11,15,17$ and $18.$ Vehicles must follow alternative routes to ensure delivery. Develop a mathematical model and create routing plans for the two vehicles in a week with the objective of minimizing total distance travelled while ensuring the distribution of all $1,000$ emergency kits to designated locations under four specific scenarios; $1)$ there is no fairness or equity. $2)$ incorporate a minimum service level requirement, where the percentage of demand satisfied for any community must be at least $50\%.$ Here, the service level for a community is defined as the ratio of kits delivered to the community$$s demand. $3)$ Besides minimizing distance, maximize the minimum service level $4)$ Besides minimizing distance, ensure that the maximum difference between any service level does not exceed $0\mathrm{.}1($or $10\%).$ Assume that all the roads are repaired. Analyze the $4$ scenarios again and assess how this affects routing efficiency and service levels. Assume that in locations $5,10$ and $15$ there are small kids. Prioritize these communuties by satisfying all their demand in all scenarios. Analyze the $4$ scenarios again. Write a report for this case by introducing the problem. Then give the solution approach you propose $($the mathematical model$)$ and make all required analysis.

Could you solve it with using GAMS