Check this model, it should gave the output for AGV assignment such that one AGV can carry only one rack. Please check your answer before sending. I have already tried the solutions such as changing $(<=)$ to $(=)$ or using only one constraint for AGV. In all those cases there is zero assignment of AGV which is not true.

Also answer the upcoming question at the end of the model.

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$]$;

QUESTION: 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?