Despite the overwhelming food supply, people still go hungry. This project is a way to come up with a part of the solution to a global problem.
Restaurants produce food in abundance to meet their demands. Some of this food gets wasted or thrown. We are modelling a scenario where we take the food from these restaurants and give it to the ones in need through our tie-ups. The tie-ups are organisations (NGOs) or religious places where the poor come to be served free food.
We model this as a sequential decision modelling problem where we implement 3 policies. The span of this problem occurs over a 12 hour day where we are the food bank in charge of allocating food resources to multiple tie-ups. Each tie-up has it's own demand (D_t) which we know the forecast of.
Over the 12 hour day, we send out food to one tie-up in one hour. Therefore, we have 12 tie-ups to send food out to. We have R_0 amount of food in our storage initially that keeps decreasing as we keep sending the food out. Problem sequence:
- Collect food amount R_0 from restaurants at night and store in food bank storage units.
- In the morning, the 12 hour day starts.
- At t=0, allot food amount x_t to the first tie-up 't_1'where food is distributed throughout the hour. (The demand is not known until the end of the hour)
- Once the first hour is up, at t=t+1, send out x_{t+1} to the next tie-up and so on....
Note: Keep updating the amount of food you have in storage as R_{t+1} = R_t - x_t
But there is a catch to this problem!! You can only send out food that is fresh. To quantify freshness, we introduce a freshness factor f_F where F= A,B We assume there to be 2 kinds of food in the storage.
- Type A is the kind of food that deteriorates faster with time.
- Type B is the kind of food that deteriorates with time but at a rate that is much slower than type A.
f_{F,t+1} = f_{F,t} - E_{F,t+1}
where E_{F,t+1} is a decreasing function. The rates at which type A and B deteriorate are:
E_{A,t+1} = {1,5,10}
E_{B,t+1} = {1,2,3}
The decreasing function E_{F,t+1} can take on any of the 3 values with equal probability. We start off by assuming the food in storage initially is f_F = 500 for both type A and B. This value decreases as every hour passes.
State variables: R_A , R_B , f_A , f_B
Exogenous information: E_A , E_B , D
Transition function:
R_{F,t+1} = R_{F,t} - x_{F,t}
f_{F,t+1} = f_{F,t} - E_{F,t+1}
where F = A,B
Decision variables:
Decision 1: How much quantitiy of food to send to one tie-up? x_t = ?
Decision 2: How much of it should be type A and type B? x_{A,t} = ? x_{B,t} = ?
Constraints:
For F= A,B
x_F <= R_F........you can only send as much as you have
f_F > 0 ............you can only serve fresh food, i.e, if freshness factor becomes 0, the food must be thrown away
Decision 1: Divide the amount of food to every tie-up equally irrespective of the demand. Send the demand needed if below equal or send equal.
Decision 2 Type A should be 60% of the demand and type B should be 40% of demand.
global fa
global fb
global x
global Ra
global Rb
global R
global T
global t
global d
import random
T=12
fa=50
fb=50
Ra=500
Rb=500
d=0
R = Ra+Rb
def demandcalc(T):
global D
D= random.normalvariate(100,20) #random.choice(50,100)
equal=(R//T) #use t as start index while T comes from the other way
Dmu= 100
if equal-D>=0:
x=D
else:
x=equal #what if actual demand is much greater than equal
print("The calculated demand is : %r" %x)
return x
def send(x, t):
global fa
global fb
global D
global d
global Ra
global Rb
global R
fa = fa
fb = fb
D = D
d = d
Ra = Ra
Rb = Rb
R = R
Eaa= [1,5,10];
Ea= random.choice(Eaa)
Ebb= [1,2,3];
Eb= random.choice(Ebb)
fa= fa - Ea
fb= fb - Eb
print("The freshness is : %r / %r" %(fa,fb))
xa= int(0.6*x)
xb= int(0.4*x)
print("The expected amount of A and B to be sent : %r / %r" %(xa,xb))
if fa>0:
if Ra>=xa:
Ra= Ra-xa
else:
d= xa-Ra #d is deficit
xa=Ra
Ra=0
else:
Ra=0
xa=0
xb=x
print("The amount of A sent: %r" %xa)
print("The amount of A left: %r" %(Ra))
if fb>0:
xb=xb+d
d=0
if Rb>=xb:
Rb= Rb-xb
else:
xb=Rb
Rb=0
else:
Rb=0
xb=0
print("The amount of B sent: %r" %xb)
print("The amount of B left: %r" %(Rb))
x= xa+xb
print("The total amount sent : %r" %x)
R= Ra+Rb
print("The Total amount left is : %r" %(R))
T = 12
Sum = 0
for i in range(1,13):
print("For tie-up %r" %i)
x = demandcalc(T)
Sum = int(Sum + x)
send(x, i)
T = T-1
print("The total demand in all the tie-ups is %r" %Sum)For tie-up 1
The calculated demand is : 73.76513778957445
The freshness is : 49 / 49
The expected amount of A and B to be sent : 44 / 29
The amount of A sent: 44
The amount of A left: 456
The amount of B sent: 29
The amount of B left: 471
The total amount sent : 73
The Total amount left is : 927
For tie-up 2
The calculated demand is : 84
The freshness is : 39 / 48
The expected amount of A and B to be sent : 50 / 33
The amount of A sent: 50
The amount of A left: 406
The amount of B sent: 33
The amount of B left: 438
The total amount sent : 83
The Total amount left is : 844
For tie-up 3
The calculated demand is : 84
The freshness is : 29 / 45
The expected amount of A and B to be sent : 50 / 33
The amount of A sent: 50
The amount of A left: 356
The amount of B sent: 33
The amount of B left: 405
The total amount sent : 83
The Total amount left is : 761
For tie-up 4
The calculated demand is : 84
The freshness is : 19 / 43
The expected amount of A and B to be sent : 50 / 33
The amount of A sent: 50
The amount of A left: 306
The amount of B sent: 33
The amount of B left: 372
The total amount sent : 83
The Total amount left is : 678
For tie-up 5
The calculated demand is : 84
The freshness is : 18 / 42
The expected amount of A and B to be sent : 50 / 33
The amount of A sent: 50
The amount of A left: 256
The amount of B sent: 33
The amount of B left: 339
The total amount sent : 83
The Total amount left is : 595
For tie-up 6
The calculated demand is : 85
The freshness is : 17 / 41
The expected amount of A and B to be sent : 51 / 34
The amount of A sent: 51
The amount of A left: 205
The amount of B sent: 34
The amount of B left: 305
The total amount sent : 85
The Total amount left is : 510
For tie-up 7
The calculated demand is : 72.82279477997855
The freshness is : 16 / 39
The expected amount of A and B to be sent : 43 / 29
The amount of A sent: 43
The amount of A left: 162
The amount of B sent: 29
The amount of B left: 276
The total amount sent : 72
The Total amount left is : 438
For tie-up 8
The calculated demand is : 78.68784005811696
The freshness is : 6 / 37
The expected amount of A and B to be sent : 47 / 31
The amount of A sent: 47
The amount of A left: 115
The amount of B sent: 31
The amount of B left: 245
The total amount sent : 78
The Total amount left is : 360
For tie-up 9
The calculated demand is : 90
The freshness is : -4 / 36
The expected amount of A and B to be sent : 54 / 36
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 90
The amount of B left: 155
The total amount sent : 90
The Total amount left is : 155
For tie-up 10
The calculated demand is : 51
The freshness is : -5 / 35
The expected amount of A and B to be sent : 30 / 20
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 51
The amount of B left: 104
The total amount sent : 51
The Total amount left is : 104
For tie-up 11
The calculated demand is : 52
The freshness is : -10 / 34
The expected amount of A and B to be sent : 31 / 20
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 52
The amount of B left: 52
The total amount sent : 52
The Total amount left is : 52
For tie-up 12
The calculated demand is : 52
The freshness is : -15 / 32
The expected amount of A and B to be sent : 31 / 20
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 52
The amount of B left: 0
The total amount sent : 52
The Total amount left is : 0
The total demand in all the tie-ups is 889
Decision 1: Send whatever the forecasted demand is
Decision 2: Send 60% A and 40% B
global fa
global fb
global x
global Ra
global Rb
global R
global T
global t
global d
import random
T=12
fa=50
fb=50
Ra=500
Rb=500
d=0
R = Ra+Rb
def demandcalc(T):
global D
D= random.normalvariate(100,20) #random.choice(50,100)
x=D
print("The calculated demand is or the amount to be sent : %r" %x)
return x
def send(x, t):
global fa
global fb
global D
global d
global Ra
global Rb
global R
fa = fa
fb = fb
D = D
d = d
Ra = Ra
Rb = Rb
R = R
Eaa= [1,5,10];
Ea= random.choice(Eaa)
Ebb= [1,2,3];
Eb= random.choice(Ebb)
fa= fa - Ea
fb= fb - Eb
print("The freshness is : %r / %r" %(fa,fb))
xa= int(0.6*x)
xb= int(0.4*x)
print("The expected amount of A and B to be sent : %r / %r" %(xa,xb))
if fa>0:
if Ra>=xa:
Ra= Ra-xa
else:
d= xa-Ra #d is deficit
xa=Ra
Ra=0
else:
Ra=0
xa=0
xb=x
print("The amount of A sent: %r" %xa)
print("The amount of A left: %r" %(Ra))
if fb>0:
xb=xb+d
d=0
if Rb>=xb:
Rb= Rb-xb
else:
xb=Rb
Rb=0
else:
Rb=0
xb=0
print("The amount of B sent: %r" %xb)
print("The amount of B left: %r" %(Rb))
x= xa+xb
print("The total amount sent : %r" %x)
R= Ra+Rb
print("The Total amount left is : %r" %(R))
T = 12
Sum = 0
for i in range(1,13):
print("For tie-up %r" %i)
x = demandcalc(T)
Sum = int(Sum + x)
send(x, i)
T = T-1
print("The total demand in all the tie-ups is %r" %Sum)For tie-up 1
The calculated demand is or the amount to be sent : 113.47276058265248
The freshness is : 40 / 47
The expected amount of A and B to be sent : 68 / 45
The amount of A sent: 68
The amount of A left: 432
The amount of B sent: 45
The amount of B left: 455
The total amount sent : 113
The Total amount left is : 887
For tie-up 2
The calculated demand is or the amount to be sent : 129.50822402473636
The freshness is : 30 / 44
The expected amount of A and B to be sent : 77 / 51
The amount of A sent: 77
The amount of A left: 355
The amount of B sent: 51
The amount of B left: 404
The total amount sent : 128
The Total amount left is : 759
For tie-up 3
The calculated demand is or the amount to be sent : 67.29426109936557
The freshness is : 25 / 42
The expected amount of A and B to be sent : 40 / 26
The amount of A sent: 40
The amount of A left: 315
The amount of B sent: 26
The amount of B left: 378
The total amount sent : 66
The Total amount left is : 693
For tie-up 4
The calculated demand is or the amount to be sent : 135.8241952550827
The freshness is : 20 / 40
The expected amount of A and B to be sent : 81 / 54
The amount of A sent: 81
The amount of A left: 234
The amount of B sent: 54
The amount of B left: 324
The total amount sent : 135
The Total amount left is : 558
For tie-up 5
The calculated demand is or the amount to be sent : 72.108346041468
The freshness is : 15 / 39
The expected amount of A and B to be sent : 43 / 28
The amount of A sent: 43
The amount of A left: 191
The amount of B sent: 28
The amount of B left: 296
The total amount sent : 71
The Total amount left is : 487
For tie-up 6
The calculated demand is or the amount to be sent : 71.70163352520441
The freshness is : 5 / 37
The expected amount of A and B to be sent : 43 / 28
The amount of A sent: 43
The amount of A left: 148
The amount of B sent: 28
The amount of B left: 268
The total amount sent : 71
The Total amount left is : 416
For tie-up 7
The calculated demand is or the amount to be sent : 61.760037654801984
The freshness is : -5 / 34
The expected amount of A and B to be sent : 37 / 24
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 61.760037654801984
The amount of B left: 206.23996234519802
The total amount sent : 61.760037654801984
The Total amount left is : 206.23996234519802
For tie-up 8
The calculated demand is or the amount to be sent : 70.85288966963763
The freshness is : -6 / 31
The expected amount of A and B to be sent : 42 / 28
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 70.85288966963763
The amount of B left: 135.38707267556038
The total amount sent : 70.85288966963763
The Total amount left is : 135.38707267556038
For tie-up 9
The calculated demand is or the amount to be sent : 69.87171423224845
The freshness is : -7 / 28
The expected amount of A and B to be sent : 41 / 27
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 69.87171423224845
The amount of B left: 65.51535844331192
The total amount sent : 69.87171423224845
The Total amount left is : 65.51535844331192
For tie-up 10
The calculated demand is or the amount to be sent : 105.69993805474734
The freshness is : -8 / 25
The expected amount of A and B to be sent : 63 / 42
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 65.51535844331192
The amount of B left: 0
The total amount sent : 65.51535844331192
The Total amount left is : 0
For tie-up 11
The calculated demand is or the amount to be sent : 95.7307162498553
The freshness is : -13 / 23
The expected amount of A and B to be sent : 57 / 38
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 0
The amount of B left: 0
The total amount sent : 0
The Total amount left is : 0
For tie-up 12
The calculated demand is or the amount to be sent : 101.17679849874155
The freshness is : -14 / 20
The expected amount of A and B to be sent : 60 / 40
The amount of A sent: 0
The amount of A left: 0
The amount of B sent: 0
The amount of B left: 0
The total amount sent : 0
The Total amount left is : 0
The total demand in all the tie-ups is 1088
Optimization over the freshness (We maximize the number of people having fresh food where fresh food is limited to a value of 35 and above)
Decision 1: Send whatever the forecasted demand is
Decision 2: Send the type A quantity as j% of demand such that maximum number of people get fresh food
global fa
global fb
global x
global Ra
global Rb
global R
global T
global t
global d
global D
global aa
global bb
global ff
global s
global j
global v
global sum
import random
import matplotlib.pyplot as plt
fa=50
fb=50
Ra=500
Rb=500
d=0
aa=0
bb=0
sum=0
s=[]
j=[]
R = Ra+Rb
for j in range(0,101,1):
fa=50
fb=50
Ra=500
Rb=500
d=0
aa=0
bb=0
for T in range(0,13):
D=random.normalvariate(100,20) #random.choice(50,100)
x=D
#print("The calculated demand is or the amount to be sent : %r" %x)
Eaa= [1,5,10];
Ea= random.choice(Eaa)
Ebb= [1,2,3];
Eb= random.choice(Ebb)
fa= fa - Ea
fb= fb - Eb
#print("The freshness is : %r / %r" %(fa,fb))
xa= int((j/100)*x)
xb= int(((100-j)/100)*x)
#print("The expected amount of A and B to be sent : %r / %r" %(xa,xb))
if fa>=0:
if Ra>=xa:
Ra= Ra-xa
else:
d= xa-Ra #d is deficit
xa=Ra
Ra=0
if fa>=35:
aa=aa+xa
else:
aa=aa
else:
Ra=0
xa=0
xb=x
#print("The amount of A sent: %r" %xa)
#print("The amount of A left: %r" %(Ra))
if fb>0:
xb=xb+d
d=0
if Rb>=xb:
Rb= Rb-xb
else:
xb=Rb
Rb=0
if fb>=35:
bb=bb+xb
else:
bb=bb
else:
Rb=0
xb=0
#print("The amount of B sent: %r" %xb)
#print("The amount of B left: %r" %(Rb))
x= xa+xb
#print("The total amount sent : %r" %x)
R= Ra+Rb
#print("The Total amount left is : %r" %(R))
ff=aa+bb
s.append(ff)
#print("The number of people eating fresh food is:%r" %ff)
v=max(s)
print("The maximum number of people that can get fresh food is: %r" %v)
jj=s.index(v)
print("The percentage of A that should be sent for every demand is: %r"%jj)
j= range(101)
plt.plot(s,j)
plt.ylabel('Percentage of demand that is fulfiled by A')
plt.xlabel('Number of people eating fresh food')
plt.show()
The maximum number of people that can get fresh food is: 981
The percentage of A that should be sent for every demand is: 73
- It is not a very good policy if the goal is to maximize the number of people fed.
- Should a scenario arise, where the demand is consistently way above the equal amount that is allocated, there will be a food deficit at the tie-ups when the we have the food at the storage.
- There is a high possibility of food being wasted due to the freshness falling to 0 before it could get allocated.
- The food bank has to make multiple trips to various tie-ups when it could have allocated as much as the tie-up needed and finished the food faster.
- This policy is good if we want to meet the demand but there is difficulty when we go to decide the % of demand that should be of type A and B.
- The stock finishes up faster which also means lesser number of trips to tie-ups compared to policy 1.
- This policy gives the optimum percent of demand that should be fulfilled by type A and thus, type B (Type B% = 100-type A %) if the goal in mind is to maximize the amount of fresh food consumed.