Fixed route delivery inventory calculation

Hi all,

For a group project we are trying to model a tram line, however we come across an infeasible model when adding constraints.

The problem arises when we try to add constraint 8 and 9, but we think the problem is in constraint 6 and 7. It is basicly a inventory counter which adds up the fixed value from a table and inventory that was not used in a previous 'time step'. 

I have added the code we have used, hopefully someone can help us and thanks in advance!

import numpy as np 
import math
from gurobipy import *
import pandas as pd
import gurobipy as gp
import matplotlib.pyplot as plt
#%%
Q = [700,700,700]
c_x = 10
c_y = [100,100,100]
c_t = [150,275,375]

d = [
    (5, 8, 14, 20, 25),
    (10, 12, 15, 18, 20),
    (15, 18, 12, 10, 13),
    (20, 14, 20, 15, 10),
    (22, 25, 16, 12, 18),
    (12, 10, 8, 14, 15),
    (10, 5, 10, 8, 12),
    (8, 15, 18, 22, 16),
    (18, 20, 25, 16, 14),
    (5, 3, 8, 12, 10)
]


summed_values = [sum(i) for i in zip(*d)]
sum2 = [sum(j) for j in zip(*d)]


print(sum2)
print(summed_values)

M = 100000

#%%
model = gp.Model(name = 'Tram_parcel')

#%%
I = [0,1,2,3,4,5,6,7,8,9] #Stops
I_min = [0,1,2,3,4,5,6,7,8]
J = [0,1,2,3,4] #Tours
J_min = [1,2,3,4]
T = [0,1,2]

x = {} 
for i in I:
    for j in J:
        x[i,j] = model.addVar(lb=0, vtype= GRB.BINARY, name='X[' + str(i) + str(j) + ']')
        
y = {}
for j in J:
    for t in T:
        y[j,t] = model.addVar(lb=0, vtype= GRB.BINARY, name='Y[' + str(j) + ']')
    
v = {}
for i in I:
    for j in J:
        for t in T:
            v[i, j, t] = model.addVar(lb=0, vtype=GRB.INTEGER, name='X[' + str(i) + str(j) + ']')
        
l = {}
for i in I:
    for j in J:
        for t in T:
            l[i,j,t] = model.addVar(lb=0, vtype = GRB.CONTINUOUS, name ='L[' + str(i) + str(j) + ']')
        
e = {}
for i in I:
    for j in J:
        e[i,j] = model.addVar(lb=0, vtype = GRB.CONTINUOUS, name = 'L[' + str(i) + str(j) + ']')

u = {}
for t in T:
    u[t] = model.addVar(lb=0, vtype = GRB.CONTINUOUS, name = 'U[' + str(i) + str(j) + ']')


model.update()
#%%
obj_expr = (
    quicksum(x[i, j] * c_x for i in I for j in J) +
    quicksum(y[j, t]*c_y[t] for j in J for t in T) +
    quicksum(y[j,t] * c_t[t] for t in T))

model.setObjective(obj_expr, sense=GRB.MINIMIZE)

model.update()
#%%


con0 = {}
for i in I:
    con0[i,t] = model.addConstr(
        quicksum(v[i, j,t] * x[i, j] for j in J for t in T) == quicksum(d[i][j] for j in J))

con1 = {}
for j in J:
    for t in T:
        con1[j] = model.addConstr(
            quicksum(v[i, j,t] * x[i, j] for i in I) <= Q[t] * y[j, t] )

con2 = {}
for i in I_min:
    for j in J:
        for t in T:
            con2[i,j,t] = model.addConstr(l[i+1,j,t] == l[i,j,t] - v[i,j,t]*x[i,j])
           
con3 = {}
for i in I:
    con3 = model.addConstr(quicksum(x[i,j] for j in J) <= 1)
           
con4 = {}
for j in J:
    con4 = model.addConstr(quicksum(y[j,t] for t in T) <= 1) 
           
con5 ={}
for i in I:
    for j in J:
        for t in T:
            con5 = model.addConstr(v[i,j,t] <= M*x[i,j])

con6 = {}
for i in I:
    con6 = model.addConstr(e[i,0] == d[i][0] - quicksum(v[i,0,t] for t in T))

con7 = {}
for i in I:
    for j in J_min:
        con7 = model.addConstr(e[i,j] == d[i][j] + e[i,j-1]- quicksum(v[i,j-1,t] for t in T))
        
con8 = {}
for i in I:
    for j in J_min:
        con8[i, j] = model.addConstr(quicksum(v[i, j, t] for t in T) <= e[i, j-1] + d[i][j])
        
con9 = {}
for i in I:
    con9[i, 0] = model.addConstr(quicksum(v[i, 0, t] for t in T) <=  d[i][0])