I am trying to solve the following problem.
How to build a deterministic optimization model for the following fc
we have $x_1,x_2,...,x_365$ are the order shipped from an FC to a customer for 365 days We have $o_1,..,o_365$ the amount that we ship from the DC to the FC. We have the parameter $d1,d2,d3,...,d365$ is the the demand for the day.
We have $l_1,l_2,l_3,l_4,l_5,...,l_365$ is the lost sales for the day.
We also have $I_1,I_2,I_3,...,I_(365)$ is the inventory stored in the FC.
I have the following definition for my lost sales
$l_i=d_i-x_i$
and we have inventory is
$I_1=50-x_1$ starting iventory is 50
$I_2=i_1-x_2$
$i_3=i_2-x3$
$i_4=i_3-x_4+o_1$ [take 3 day for an order to reach ]
$i_365=i_{364}-x_{365}+o_{362}$
Problem is I am not sure how to code this in python pulp.
I have the following objective function I want to minimize $50(x_1+..+x365)+2(o_1+...+o_365$)+3(ls_1+...+l_365)+1(o_1+..+o_365$)
I got final which is a csv file which shows how much I ordered for the 365 days of the year. It is where I get my demand
But my model return all the zeroes and this cannot be right because my lost sales constraint is not satisfied.
days orders
1 0
2 4
3 1
4 4
5 0
6 1
7 2
8 0
9 5
10 2
11 5
mport pandas as pd
from pulp import LpMaximize, LpProblem, LpStatus, lpSum, LpVariable,LpMinimize,LpInteger
from pulp import LpBinary
from pulp import LpSolverDefault
import pulp
k3=pd.read_csv("final.csv")
w2=k3["orders"]
demandStore=w2.tolist()
#DAY shipped
#WE HAVE ONE DAY MAY HAVE MULTIPLE ORDERS
xArray=[]
model = LpProblem(name="small", sense=LpMinimize)
xs = [LpVariable("xs{}_var".format(i+1),lowBound=0,upBound=50, cat="Integer") for i in range(0,365)]
#ORDERS
os= [LpVariable("os{}_var".format(i+1),lowBound=0,upBound=50, cat="Integer") for i in range(0,365)]
#lost sale
ls= [LpVariable("ls{}_var".format(i+1),lowBound=0,upBound=50, cat="Integer") for i in range(0,365)]
#inventory
iv=[LpVariable("iv{}_var".format(i+1),lowBound=0,upBound=50, cat="Integer") for i in range(0,365)]
k=[]
#we have here the lost sales
for i in range(0,365):
#lost sales constraint is demand-orders
w=ls[i]==demandStore[i]-xs[i]
k.append(w)
for i in range(0,365):
model+=k[i]
cons1=iv[0]==50-xs[0]
cons2=iv[1]==iv[0]-xs[1]+os[0]
cons3=iv[2]==iv[1]-xs[2]+os[1]
model+=cons1
model+=cons2
model+=cons3
k2=[]
for i in range(0,365):
cool2=xs[i]<=iv[i]
k2.append(cool2)
for i in range(0,365):
model+=k2[i]
k3=[]
for i in range(3,365):
cool=iv[i]==iv[i-1]-xs[i]+os[i-1]
k3.append(cool)
for i in range(0,362):
model+=k3[i]
One=pulp.lpSum([50*xs[i]+2*os[i]+60*ls[i]+1*iv[i] for i in range(0,365)])
#Two=pulp.lpSum([os[i]*2 for i in range(0,365)])
#Three=pulp.lpSum([iv[i]*1 for i in range(0,365)])
#four=pulp.lpSum([ls[i]*30 for i in range(0,365)])
model+=One
#model+=Two
#model+=Three
#model+=four
model.solve()
#model.solve()
name=[]
value=[]
for var in model.variables():
print(var.name, " ",var.value())
name.append(var.name)
value.append(var.value())
