Please, help me build mathmatecal model only.
The year is 2103. Humans have reached Mars and have established some habitable autonomous settlements/colonies on the planet. Together, these settlements formed a Human Mars Exploration (HME) initiative to conduct exploration operations for the rest of the planet in a coordinated way. The main task of HME is to identify potential locations where humans can settle and/or extract any valuable resources, as resources are still scarce on the planet, and more exploration is necessary. HME decided it is best to gather data and determine which locations are suitable or ideal for establishing temporary outposts with habitats for researchers, engineers and doctors and their families. Once establish, and since they are new, supplies need to be delivered to these temponry outposts from one or some of the main settlements. Furthermore, the outposts will need to be maintained. In the future, these outposts may then end up becoming permanent even after they have fulfilled their scientific purpose. HME needs the help of Industrial Engineers (IEs) to help in organizing the logistics of this undertaking. Objective-1: Design the optimal tours for the supply of resources As mentioned above, each human settlement will be responsible for a number of outposts. Each settlement will send resources to all the other outposts that it is responsible for. Typically, a settlement has access to all 3 modes of transportation. Furthermore, every settlement has a limited number of VnCs. It is not wise to use all the available VnCs. Thus, the task is to find the best combination of VnCs that can be used for distributing the resources. However, finding the combination of VnCs is not obvious, and has to be made by decision-makers at HME. Therefore, HME would like to know from your team, the minimum time required to visit all outposts of a settlement and return to the settlement. For each settlement, you are given the number of VnCs available. The coordinates of all the outposts and corresponding details are provided in the Excel sheet titled Coordinates under the excel workbook DATA321.xls. Requirements (Objective-1): 1) Make a mathematical model that will identify the minimum time to visit all outposts of a human settlement and return to the settlement. Relevant data and details are provided in the following pages of this document. Since the onganization is unaware of the methodologies that you will be using to design the plan, you are allowed to make reasonable assumptions for the missing data. You are expected to use standands and speciffications wherever applicable (please cite any references you use). The primary goal of HME is to provide a constant supply of sustainable resources for the current outpost developed by major countries. The scientists and researchers of HME have discovered many locations that can be used for scientific and mineral extraction purposes. After lengthy discussions and many rounds of voting, the given list of outposts were peacefully constructed. The list of outposts that they have selected to be established and corresponding details are provided in the excel sheet. The main issues now are the sustenance and maintenance of the outposts. Apparently, it will take at least another 25 years for developing an underground and insulated transportation system that protects humans from the dangers of exposure to cosmic radiation as they travel between settlements and/or outposts. Meanwhile, transportation will have to be surface-based, but care must be taken due to the presence of dangerous dust storms, the terrain, and the cosmic radiation. HME has available to them some basic modes of transportation: i) Land Transport using Trucks: They have two models of trucks: a. Biggest Truck (BT) and b. Motber of all Trucks (MT). Both of them have an average speed of 40kph. ii) Land Transport using Rovers: They have two models of rovers: a. Please Read Instructions (PRI) and b. Insert Name Here (INH). Both of them have an average speed of 20kmph. iii) Air Transport: They have two models of Martian helicopters: a. I Hate the Grond ( IHG ) and b. Fby Like a Martian Eagle (FLME). Both of them have an average speed of 300kmph. The above vehicles and carriers ( VnCs ) are designed to withstand the harsh Martian climate. Not all the outposts will have access to all the three modes (depends on the terrain, the nature of the outpost, and other design considerations). However, there will be at least one mode of transportation available at each outpost. In addition to that, these modes will also be used for tourism and all other movements within settlements on the planet. The primary challenge is to continuously supply the outposts with enough resources food, water, clothes, basic needs, etc. It is estimated that at least for the next 20 years, the resources must be shipped and replenished to the outposts on a regular basis. The plan is to make cach human settlement responsible for supplying and maintaining a set of outposts. The primary challenge can be divided into the following objectives
