Si as the starting point $($settlement$)$ for the tour

Tij as the time required to travel from outpost I to outpost $j$ using

specific mode of transportation

Dijk as the decision variable representing whether vehicle type Kt or

KrKa

$($t refers to Truck $VnCs$ and $r$ represents Rover $VnCs$ and a represents

Air $VnCs$

is used for the tour from outpost I to outpost $j$ starting from si

Objective function:

Minimize Z$={\displaystyle \underset{i}{\overset{?}{}}}{\displaystyle \underset{j}{\overset{?}{}}}*{\displaystyle \underset{k}{\overset{?}{}}}$Dijk$**Tij$

S$.$t

Each outpost should be visited exactly once, and the number of

vehicles used should not exceed the available $VnCs$ for each

settlement:

${\displaystyle \underset{j}{\overset{?}{}}}{\displaystyle \underset{k}{\overset{?}{}}}$Dijk$=1$ for all $i$

${\displaystyle \underset{i}{\overset{?}{}}}{\displaystyle \underset{k}{\overset{?}{}}}$Dijk$$ VnCsik for all $j$

Write the Subtour elimination constraint based on these variables