Multi-period VRP Inventory stuck

Hi Gurobi Team,

I am working on my undergraduate thesis on multi period VRP in collection scheduling and routing. The inventory will be the fundamental point to trigger the multiperiod method. I want to make sure in scheduling selection will consider the demand satisfaction.

Indexes:

• k is index for set period [T]
• i is index for set vehicle [m]
• j is index for set nodes [n]

Notes:

• I[k] = inventory in period k
• e[i,j,k] = amount of goods picked up by vehicle i, from node j, in period k
• d[k] = demand in period k
• initial_inventory = initial inventory in the beginning of period
• ss = safety stock

This multi period will work in 2 days period of pickup routing. But, the demand (d[k]) will need to be 3 period data because d[k] is needed for calculating I[k] and e[i,j, k-1]. It is like this because the pickup today is aiming to fulfill the next day's demand. 

Hence, in period T=3 there will be no outcome of e[i,j,3] because there's no data of d[4]. Also, d[1] is needed because we need to calculate I[1]. So, I'm confused in calling list 'T', because variable 'e' and 'd' are having different number of period (e only have 2, d have 3). 

This is the code that I'm using:

    "constraint pickup minimal quantity - considering multi period inventory" 
    for k in range (t+1):
        if k == 0:
            M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= initial_inventory - d[k] - ss) #apakah ga masalah d[k] aja?
        if k <= t:
            M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= I[k-1] - d[k] - ss) #not really sure penggunaannya
    M.update()

Now I'm confused in using:

for t in range (T+1):
#or 
for t in range (T):

Also, in the variable definiton I put it like this for calling the list 't'. From the df_dm, the T is having length 3 period. 

T = df_dm.shape[0] -1 # number of days to run --> because collection only needs 2 periods

Here's the code (also inputting code that are corelated):

"constraint pickup minimal quantity" 
    for k in range (T+1):
        if k == 0:
            M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - initial_inventory) 
        if k <= T:
            M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - I[k])
    M.update()
    
"constraint inventory"
    for k in range (T):
        if k == 0:
            M.addConstr((I[k] == initial_inventory - d[k] + gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n))),name="inventory 1")
        else:
            M.addConstr((I[k] == I[k-1] - d[k] + gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n))), name= "inventory 2")
    M.update()

We get this error code:

---------------------------------------------------------------------------
KeyError                                  Traceback (most recent call last)
<ipython-input-22-440a50de8d8b> in <module>
      1 decisionVariables(M, gb, m, n, t, e, I, y, z, s)  # add decision variables to model
      2 objectiveFunction(M, gb, z, n, m, t, grid) # add objective function to model
----> 3 Constraints(M, gb, e, I, y, z, s, m, n, t, et, lt, sd, grid, bigM, d, P, initial_inventory, ss, df_V, tao) # add constraints to model
      4 
      5 # M.computeIIS()

<ipython-input-18-1ab10697b5ae> in Constraints(M, gb, e, I, y, z, s, m, n, t, et, lt, sd, grid, bigM, d, P, initial_inventory, ss, df_V, tao)
     83             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - initial_inventory) #apakah ga masalah d[k] aja?
     84         if k <= t:
---> 85             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - I[k]) #not really sure penggunaannya
     86     M.update()
     87 

src\gurobipy\gurobi.pxi in gurobipy.gurobipy.quicksum()

<ipython-input-18-1ab10697b5ae> in <genexpr>(.0)
     83             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - initial_inventory) #apakah ga masalah d[k] aja?
     84         if k <= t:
---> 85             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - I[k]) #not really sure penggunaannya
     86     M.update()
     87 

src\gurobipy\gurobi.pxi in gurobipy.gurobipy.quicksum()

<ipython-input-18-1ab10697b5ae> in <genexpr>(.0)
     83             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - initial_inventory) #apakah ga masalah d[k] aja?
     84         if k <= t:
---> 85             M.addConstr(gb.quicksum(gb.quicksum(e[i, j, k] for i in range (m)) for j in range (n)) >= d[k+1] + ss - I[k]) #not really sure penggunaannya
     86     M.update()
     87 

KeyError: (0, 0, 2)

Can you help to check where the possible error comes from?

Thank you very much. I hope it's quite clear.