import pandas as pd

import numpy as np

import math

np$.$random.seed$(21069925)$

RandomFtoD$1=$np$.$round$($np$.$random.uniform$($low$=1,$high$=10,$size$=12),0).$astype$($int$)$

RandomFtoD$2=$np$.$reshape$($RandomFtoD$1,(4,3))$

CostFtoD$=$pd$.$DataFrame$($RandomFtoD$2,$columns$=["$Atlas$",$"Nebulae","Azure"$],$

index$=["$Tonoz$",$"White Kiosk","Quarterage","Middle Yard"$])$

RandomDtoS$1=$np$.$round$($np$.$random.uniform$($low$=1,$high$=10,$size$=15),0).$astype$($int$)$

RandomDtoS$2=$np$.$reshape$($RandomDtoS$1,(3,5))$

CostDtoS$=$pd$.$DataFrame$($RandomDtoS$2,$columns$=["$Venus$",$"Minerva","Neptunus","Mars","Cere"$],$

index$=["$Atlas$",$"Nebulae","Azure"$])$

RandomFtoS$1=$np$.$round$($np$.$random.uniform$($low$=1,$high$=10,$size$=20),0).$astype$($int$)$

RandomFtoS$2=$np$.$reshape$($RandomFtoS$1,(4,5))$

CostFtoS$=$pd$.$DataFrame$($RandomFtoS$2,$columns$=["$Venus$",$"Minerva","Neptunus","Mars","Ceres"$],$

index$=["$Tonoz$",$"White Kiosk","Quarterage","Middle Yard"$])$

print$("$The shipment cost from factory to distribution center"$)$

print$($CostFtoD$)$

print$("$

The shipment cost from distribution center to store"$)$

print$($CostDtoS$)$

print$("$

The shipment cost from factory to store"$)$

print$($CostFtoS$)$

# The data

warehouses $=["$Tonoz$",$ "White Kiosk", "Quarterage", "Middle Yard"$]$

distribution$\_$centers $=["$Atlas$",$ "Nebula", "Azure"$]$

stores $=["$Venus$",$ "Minerva", "Neptunus", "Mars", "Ceres"$]$

warehouse$\_$capacity $=[3000,5000,10000,7000]$

store$\_$demand $=[5500,4750,6550,4000,4200]$

# The solver

solver $=$ pywraplp.Solver.CreateSolver$(\text{'}$CBC$\text{'})$

# Defining decision variables

x $=\{\}$

for i in warehouses:

for k in distribution$\_$centers:

x$[$i$,$ k$]=$ solver.IntVar$(0,$ solver.infinity$(),$ f$\text{'}$x$[\{$i$\},\{$k$\}]\text{'})$

y $=\{\}$

for k in distribution$\_$centers:

for j in stores:

y$[$k$,$ j$]=$ solver.IntVar$(0,$ solver.infinity$(),$ f$\text{'}$y$[\{$k$\},\{$j$\}]\text{'})$

z $=\{\}$

for i in warehouses:

for j in stores:

z$[$i$,$ j$]=$ solver.IntVar$(0,$ solver.infinity$(),$ f$\text{'}$z$[\{$i$\},\{$j$\}]\text{'})$

# Objective function

objective $=$ solver.Objective$()$

for i in warehouses:

for k in distribution$\_$centers:

objective.SetCoefficient$($x$[$i$,$ k$],$ CostFtoDC.at$[$i$,$ k$])$

for k in distribution$\_$centers:

for j in stores:

objective.SetCoefficient$($y$[$k$,$ j$],$ CostDCtoS.at$[$k$,$ j$])$

for i in warehouses:

for j in stores:

objective.SetCoefficient$($z$[$i$,$ j$],$ CostFtoS.at$[$i$,$ j$])$

objective.SetMinimization$()$

# Constraints

# Warehouse capacity

for i$,$ cap in zip$($warehouses$,$ warehouse$\_$capacity$)$:

constraint $=$ solver.Constraint$(0,$ cap$)$

for k in distribution$\_$centers:

constraint.SetCoefficient$($x$[$i$,$ k$],1)$

for j in stores:

constraint.SetCoefficient$($z$[$i$,$ j$],1)$

# Flow balance at distribution centers

for k in distribution$\_$centers:

solver.Add$($sum$($x$[$i$,$ k$]$ for i in warehouses$)==$ sum$($y$[$k$,$ j$]$ for j in stores$))$

# Demand satisfaction

for j$,$ demand in zip$($stores$,$ store$\_$demand$)$:

constraint $=$ solver.Constraint$($demand$,$ demand$)$

for k in distribution$\_$centers:

constraint.SetCoefficient$($y$[$k$,$ j$],1)$

for i in warehouses:

constraint.SetCoefficient$($z$[$i$,$ j$],1)$

# Solution of the problem

status $=$ solver.Solve$()$

# Results

if status $==$ pywraplp.Solver.OPTIMAL:

print$(\text{'}$Objective value $=\text{'},$ solver.Objective$().$Value$())$

print$(\text{'}$x$[$i$,$k$]$ values:$\text{'})$

for i in warehouses:

for k in distribution$\_$centers:

print$($f$\text{'}$x$[\{$i$\},\{$k$\}]=\{$x$[$i$,$ k$].$solution$\_$value$()\}\text{'})$

print$(\text{'}$x$[$k$,$j$]$ values:$\text{'})$

for k in distribution$\_$centers:

for j in stores:

print$($f$\text{'}$y$[\{$k$\},\{$j$\}]=\{$y$[$k$,$ j$].$solution$\_$value$()\}\text{'})$

print$(\text{'}$y$[$i$,$j$]$ values:$\text{'})$

for i in warehouses:

for j in stores:

print$($f$\text{'}$z$[\{$i$\},\{$j$\}]=\{$z$[$i$,$ j$].$solution$\_$value$()\}\text{'})$

else:

print$(\text{'}$The problem does not have an optimal$$solution$.\text{'})$

Answer these questions according to the code sent above using CBC solver

b$)(3$p$)$ What is value of the objective function?

c$)(3$p$)$ What is the value of decision variables? According to this values, evaluate the supply

chain and flow in this supply chain?

d$)(3$p$)$ If we change the capacity of warehouse Quarterage from $10000$ to $7500,$ and the

demand of Ceres from $4200$ to $1700,$ how do the objective value and the values of the

decision variables change?

e$)(4$p$)$ If we change the shipment cost from warehouse Tonoz to distribution center Atlas as

$10$ and Azure to Minerva as $5,$ how the objective function is affected. Give new objective

value and number of shipments, and then explain your answer with few sentences.

f$)(7$p$)$ If we change the capacity of the warehouse Middle Yard from $7000$ to $5000,$ what

should we expect? Can we obtain optimal solution? Please explain your conclusion clearly.

If it is necessary make some arrangement and give the results with explanations.