PLEASE SOLVE CORRECTLY,

Solve the mathematical model using a solver of your choice BY PYTHON

Build a heuristic or metaheuristic to solve the above problem. Show two consecutive iterations.

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 Kr Ka

$($ 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$=\_$i$\_$j$.\_$k$$Dijk$*$Tij$$

S$.$t

Each outpost should be visited exactly once, and the number of vehicles used should not exceed the available VnCs for each settlement:

$\_$j$.\_$k$$Dijk$=1$ for all i$$

$\_$i$.\_$k$$Dijk$<=$VnCsik for all j$$

$3.$ Flow conservation:$-$

$\backslash$Sigma $\_$i D$\_$ij $=\backslash$Sigma $\_$j D$\_$ji$,$ for all i

$4.$ Start and end at the settlement:$-$

$\backslash$Sigma $\_$j D$\_1$j $=$ V$,\backslash$Sigma $\_$i D$\_$ij $=$ V

$5.$ Non$-$negativity:$-$

dij$>=0,$ for all i and j

Subtour breaking constraint:

Ui $+1<=$ Uj $+($n$-1)(1-$Dij$)$ Ai$,$ j $=2,3,,,$ n $,$ i$=/$j

Ui $>=0$ Ai $=2,3..,$ n