For the following AMPL model $($data is not provided here due to lack of space$)$ an output is generated by AMPL. However, it is mostly zero and in an ideal situation it shouldnt be like this. Many Racks should be assigned to AGVs and workstations, respectively to meet the demand and lower cost. Modify the model where necessary and write the correct codes.

AMPL Model:

# The sets

set Racks; # Set of racks

set AGVs; # Set of AGVs

set Workstations; # Set of workstations

set SKUs; # Set of SKUs

set Axes$=\{"$x$","$y$"\}$; # Set of axes

# Parameters

param rack$\_$location$\{$Racks$,$ Axes$\}$; # Rack location

param rack$\_$status$\{$Racks$\}$ binary; # Rack status, $0$ for stationary and $1$ otherwise

param agv$\_$location$\{$AGVs$,$ Axes$\}$; # AGV location

param agv$\_$status$\{$AGVs$\}$ binary; # AGV status, $0$ for idle and $1$ for active

param workstation$\_$location$\{$Workstations$,$ Axes$\}$; # Workstation location

param sku$\_$inventory$\{$Racks$,$ SKUs$\}>=0$; # SKU inventory

param demands$\{$Workstations$,$ SKUs$\}>=0$; #Demands

param berths$\{$Workstations$\}>=0$; # Berths

# Decision variables

var AssignRackToAGV$\{$Racks$,$ AGVs$\}$ binary; # Rack to AGV assignment

var AssignRackToWorkstation$\{$Racks$,$ Workstations$\}$ binary; # Rack to workstation assignment

var AssignWorkstationToRack$\{$Workstations$,$ Racks$\}$ binary; # Workstation to rack assignment

# Objective function

param alpha$1$ :$=1$; # Weight for rack$-$AGV distance

param alpha$2$ :$=1\mathrm{.}3$; # Weight for rack$-$workstation distance

param alpha$3$ :$=1$; # Weight for unfulfilled orders

minimize TotalDistance:

alpha$1*$ sum$\{$r in Racks, a in AGVs, ax in Axes$\}$ AssignRackToAGV$[$r$,$ a$]*$ abs$($rack$\_$location$[$r$,$ ax$]-$ agv$\_$location$[$a$,$ ax$])+$

alpha$2*$ sum$\{$r in Racks, w in Workstations, ax in Axes$\}$ AssignRackToWorkstation$[$r$,$ w$]*$ abs$($rack$\_$location$[$r$,$ ax$]-$ workstation$\_$location$[$w$,$ ax$])+$

alpha$3*$ sum$\{$w in Workstations, s in SKUs$\}$ max$(0,$ demands$[$w$,$ s$]-$ sum$\{$r in Racks$\}$ AssignWorkstationToRack$[$w$,$ r$]*$ sku$\_$inventory$[$r$,$ s$])$;

# Constraints

subject to RackAssignmentConstraint$\{$r in Racks$\}$:

sum$\{$a in AGVs$\}$ AssignRackToAGV$[$r$,$ a$]=1$;

subject to WorkstationAssignmentConstraint$\{$w in Workstations$\}$:

sum$\{$r in Racks$\}$ AssignRackToWorkstation$[$r$,$ w$]=1$;

subject to WorkstationToRackAssignmentConstraint$\{$w in Workstations, r in Racks$\}$:

AssignWorkstationToRack$[$w$,$ r$]=$ AssignRackToWorkstation$[$r$,$ w$]$;

subject to BerthConstraint$\{$w in Workstations$\}$:

sum$\{$r in Racks$\}$ AssignRackToWorkstation$[$r$,$ w$]<=$ berths$[$w$]$;

$``````````````````````````````````````````````````````````````````$

AMPL output $($Gurobi$)$

ampl: include assignment$\_$run.run;

Gurobi $10\mathrm{.}0\mathrm{.}3$: Gurobi $10\mathrm{.}0\mathrm{.}3$: optimal solution; objective $3130\mathrm{.}6$

$31$ simplex iterations

$1$ branching nodes

AssignRackToAGV $[*,$the $*]$

: a$1$ a$10$ a$11$ a$12$ a$13$ a$14$ a$15$ a$16$ a$17$ a$18$ a$19$ a$2$ a$20$ a$3$ a$4$ a$5$ a$6$ a$7$ a$8$ :$=$

r$10000000000000010000$

r$101000000000000000000$

r$110000010000000000000$

upto r$80$

AssignRackToWorkstation $[*,*]$

: w$1$ w$2$ w$3$ w$4$ :$=$

r$10000$

r$100000$

r$110000$

upto r$80$

AssignWorkstationToRack $[*,*]($tr$)$

: w$1$ w$2$ w$3$ w$4$ :$=$

r$10000$

r$100000$

r$110000$

upto r$80$

Total distance traveled by AGVs: $3130\mathrm{.}600000$