$2)$ Solve the mathematical model using a solver of your choice.

$3)$ Build a heuristic or metaheuristic to solve the above problem. Show two consecutive iterations. 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 following Table given: Settlement

Truck

VnCs

Rover VnCs Air VnCs

Pioneers $1583$

The Martians $462$

New New York $331$

Finally Alone $111$

Humans Only $110$

Robots Welcome $100.$ THE MATHEMATICAL MODEL IS GIVEN IN THE PICTURE. min${\displaystyle \underset{i}{\overset{n}{}}}{\displaystyle \underset{j}{\overset{n}{}}}{\displaystyle \underset{K_T}{\overset{N_T}{}}}{\displaystyle \underset{K_R}{\overset{N_R}{}}}{\displaystyle \underset{K_H}{\overset{N_H}{}}}\frac{c_{\text{i}\text{j}\text{T}}*x_{ij1K_T}}{40}+\frac{c_{\text{i}\text{j}\text{R}}*x_{ij}{K}_R}{20}+\frac{c_{\text{i}\text{j}\text{H}}*x_{ij}{K}_{K_H}}{300}$

${\displaystyle \underset{j}{\overset{n}{}}}{x}_{1j1k}=1,AA{k}_T\{1,$dots,$N_4\}$ All Tracks leave main settement

${\displaystyle \underset{j}{\overset{n}{}}}{x}_{1j3k}=1AA{K}_k\{\begin{array}{c}1\\ \text{d}\text{o}\text{t}\text{s}\\ N_A\end{array}$ All Helicopter leave main setelement

${\displaystyle \underset{i}{\overset{n}{}}}{x}_{i11k}=1AA{K}_i\{1,$dots,$k_i\}$ All trucks go to main settlement

${\displaystyle \underset{i}{\overset{n}{}}}{x}_{i12k}=1AA{K}_R\{1,$dots,$N_k\}$ All Rovers go to main Setelement

${\displaystyle \underset{i}{\overset{n}{}}}{x}_{i13k}=7k_H\{1,$dots,$N_H\}$ All Helicarers go to main seztemeny

${\displaystyle \underset{j=2}{\overset{N}{}}}{\displaystyle \underset{K_T}{\overset{M_T}{}}}{\displaystyle \underset{K_R}{\overset{N_R}{}}}{\displaystyle \underset{K_H}{\overset{NH}{}}}{x}_{ij1}{K}_T+x_{ij2}{K}_R+x_{ij}{K}_H=1,$AAi,$1,$dots,$n3$ all setelementer

Had Vnc leave once

$\{$:$x_{ij1}{k}_T,x_{ij2}{k}_R,x_{ij3}{k}_H\}0,1$ binary constraine