MODIFY THESE CODES TO RUN ON AMPLE AND ANSWER THE FOLLOWING QUESTIONS BASED ON THAT

Project aim: Since the AGVs move only along the x$,$y$-$axes, the distance between two locations in the warehouses is given by the $$Manhattan distance$,$ i$.$e$.$ the $`1$ norm, where the distance between two points $($x $(1),$ y$(1))$ and $($x $(2),$ y$(2))$ is defined as $||$x $(1),$ y$(1))($x$(2),$ y$(2))||=|$x$(1)$ x $(2)|+|$y$(1)$ y$(2)|.$

Our objective, which we intend to minimise, is a weighted combination of the total distance of the rack from their assigned AGV $($with weight $\backslash$alpha $1=1),$ the total distance of the rack from their assigned workstation $($with weight $\backslash$alpha $1=1\mathrm{.}3),$ and the total number of orders that will be left unfulfilled $($with weight $\backslash$alpha $1=3).($Note that it makes sense to assign larger weight in the objective to the distance the

AGV travel when carrying a rack, since they will be slower and consume more energy.$)$

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

# Parameters

param rack$\_$location$\{$Racks$\}$ symbolic;

param rack$\_$status$\{$Racks$\}$ symbolic;

param agv$\_$location$\{$AGVs$\}$ symbolic;

param workstation$\_$location$\{$Workstations$\}$ symbolic;

param sku$\_$inventory$\{$Racks$,1.\mathrm{.}10\}>=0$;

param demands$\{$Workstations$,1.\mathrm{.}40\}>=0$;

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

# Decision variables

var AssignRackToAGV$\{$Racks$,$ AGVs$\}$ binary;

var AssignRackToWorkstation$\{$Racks$,$ Workstations$\}$ binary;

# 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$\}$ AssignRackToAGV$[$r$,$ a$]*$ abs$($rack$\_$location$[$r$]-$ agv$\_$location$[$a$])+$

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

alpha$3*$ sum$\{$w in Workstations, sku in $1.\mathrm{.}40\}$ max$(0,$ demands$[$w$,$ sku$]-$ sum$\{$r in Racks$\}$ AssignRackToWorkstation$[$r$,$ w$]*$ sku$\_$inventory$[$r$,$ sku$])$;

# Constraints

subject to RackAssignmentConstraint:

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

subject to WorkstationAssignmentConstraint:

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

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

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

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

DATA:

param rack$\_$location:$=$

R$1"103"$ "stationary"

R$2"105"$ "stationary"

R$3"107"$ "stationary"

R$4"109"$ "stationary"

R$5"1011"$ "stationary"

R$6"1013"$ "stationary"

R$7"1015"$ "stationary"

R$8"1017"$ "stationary"

R$9"1019"$ "stationary"

R$10"1021"$ "stationary"

R$11"1023"$ "stationary"

R$12"1025"$ "stationary"

R$13"00"$ "AGV$7"$

R$14"1029"$ "stationary"

until

R$80"1033"$ "stationary"

param agv$\_$location:$=$

AGV$1"1522"$ "active"

AGV$2"91"$ "idle"

AGV$3"2518"$ "active"

AGV$4"111"$ "idle"

AGV$5"121"$ "idle"

AGV$6"181"$ "idle"

AGV$7"3511"$ "active"

AGV$8"201"$ "idle"

AGV$9"211"$ "idle"

AGV$10"1540"$ "active"

AGV$11"281"$ "idle"

AGV$12"291"$ "idle"

AGV$13"301"$ "idle"

AGV$14"523"$ "active"

AGV$15"321"$ "idle"

AGV$16"381"$ "idle"

AGV$17"391"$ "idle"

AGV$18"4539"$ "active"

AGV$19"411"$ "idle"

AGV$20"421"$ "idle"

;

param workstation$\_$location:$=$

W$1"00"$

W$2"050"$

W$3"500"$

W$4"5050"$

;

param sku$\_$inventory: S$1$ S$2$ S$3$ S$4$ S$5$ S$6$ S$7$ S$8$ S$9$ S$10$ S$11$ S$12$ S$13$ S$14$ S$15$ S$16$ S$17$ S$18$ S$19$ S$20$ S$21$ S$22$ S$23$ S$24$ S$25$ S$26$ S$27$ S$28$ S$29$ S$30$ S$31$ S$32$ S$33$ S$34$ S$35$ S$36$ S$37$ S$38$ S$39$ S$40$:$=$

R$17519$ until S$40$

R$2201510$ until S$40$

the rows continues until R$80$ each with S$1$ to S$40$ column data;

param demands: S$1$ S$2$ S$3$ S$4$ S$5$ S$6$ S$7$ S$8$ S$9$ S$10$ S$11$ S$12$ S$13$ S$14$ S$15$ S$16$ S$17$ S$18$ S$19$ S$20$ S$21$ S$22$ S$23$ S$24$ S$25$ S$26$ S$27$ S$28$ S$29$ S$30$ S$31$ S$32$ S$33$ S$34$ S$35$ S$36$ S$37$ S$38$ S$39$ S$40$:$=$

W$116131101$ until S$40$

W$223684$ until S$40$

W$321591021$ until S$40$

W$4492291021$ until S$40$ ;

param berths:$=$

W$14$

W$25$

W$37$

W$49$;