$1.$ Modify the model and rewrite a better code such that each AGV should be assigned to only one Rack. Please do not suggest me changing $(<=)$ to $(=)$ or removing one constraint from AGV assignment. I have already did use these but not got the result. Check your final answer before sending.

$2.$ Write codes for this question as well:

Building an integrated order$-$dispatching system

Currently House.AI has a legacy system to assign orders to workstations. They would like to explore the benefit of integrating the order$-$dispatching decision into the AGV$-$dispatching model. In this second part of the project, the task is to include the assignment of orders to workstations in the optimisation model. How does the integrated model compare to the previous one? What is the difference in cost$?$ How many more orders are fulfilled?

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

# Objective function

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

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

param alpha$3$ :$=3$; # 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$\}$ AssignRackToWorkstation$[$r$,$ w$]*$ sku$\_$inventory$[$r$,$ s$])$;

# Constraints

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

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

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

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

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

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

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

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