Modelling with Gurobi-Python a Supply Chain Problem

Question

I would like to write the following simple model in GurobiPy, which is part of many terms that's belongs to the objective function, I assumed that I have three suppliers are selected and three warehouses are opened, where $QS_{swpt}$, $Q_{whpt}$ and $QU_{whpt}$.are CONTINUOUS decicison variables. $S_{st}$, $W_{wt}$, $G_{gt}$, $O_{ot}$ and $L_{lt}$ are BINARY decision variables, I have tried a toy instance by hand and on GurobiPy but, the results from the latter was wrong, I would like to know a rule of thumb to model such problems, or any resource that explain how to model similar and advanced problems.

$t$ is the time.

$s$ are the suppliers.

$w$ are the warehouses.

$p$ are the products.

$$COF= \sum_ {t}\sum_{s}FS_{st}*S_st+\sum_ {t}\sum_{w}FW_{wt}*W_{wt}+\sum_ {t}\sum_{g}FG_{gt}*G_{gt}$$ $$+\sum_ {t}\sum_{o}FO_{ot}*O_{ot}+\sum_ {t}\sum_{l}FL_{lt}*L_{lt}$$ $$ OCS= \sum_{t}\sum_{s}\sum_{w}\sum_{p}QS_{swpt}(MC_{spt}+TS_{swpt}) $$ $$PCS=\sum_{t}\sum_{s}\sum_{w}\sum_{p}KW_{wpt}*Y_{wt}+QS_{swpt}*c_{spt}$$ $$CIW=\sum_{t}\sum_{s}\sum_{w}\sum_{p}QW_{whpt}*[I_{wt}+HCW_{wt}+TW_{wpht}*(\boldsymbol{1-\bar{p}})]$$ $$SCH=\sum_{t}\sum_{w}\sum_{h}\sum_{p}QU_{whpt}*p_{ht}$$
$Minimize\; Z = COF+OCS+PCS+CIW+SCH$

#Contiuous Decision Variables
    QS_swpt= m.addVar(vtype=GRB.CONTINUOUS, name="QS_swpt", lb=0)
    QW_whpt= m.addVar(vtype=GRB.CONTINUOUS, name="QW_whpt", lb=0 )
    QW_gpt= m.addVar(vtype=GRB.CONTINUOUS, name= "QW_gpt", lb=0)
    QU_whpt=m.addVar(vtype=GRB.CONTINUOUS, name= "QU_whpt", lb=0)
#Binary Decision Variables
    Y_wt= m.addVar(vtype=GRB.BINARY, name="Y_wt")
    S_st=m.addVar(vtype=GRB.BINARY, name="S_st")
    W_wt= m.addVar(vtype=GRB.BINARY, name="W_wt")
    G_gt=m.addVar(vtype=GRB.BINARY, name="G_gt")
    O_ot=m.addVar(vtype=GRB.BINARY, name="O_ot")
    L_lt=m.addVar(vtype=GRB.BINARY, name="L_lt")
#Modelling the objective Function.
    COF=  quicksum(FS_st[s]*S_st for s in FS_st for sp in S for t in Time)\
            + quicksum(FW_wt[w]*W_wt for w in FW_wt for wr in W for t in Time)\
            + quicksum(FG_gt[g]*G_gt for g in FG_gt for gs in G  for t in Time)\
            + quicksum(FO_ot[o]*O_ot for o in FO_ot for om in O for t in Time)\
            + quicksum(FL_lt[l]*L_lt for l in FL_lt for lf in L for t in Time)
    OCS= quicksum(QS_swpt*(MC_spt[p]) for p in MC_spt for w in W for t in Time )\
            + quicksum(QS_swpt*(TS_swt[s]) for s in TS_swt for w in W for t in Time )
    PCS = quicksum(KW_wpt[k]* Y_wt for k in KW_wpt for w in W for t in Time)\
              + quicksum(c_st[c] for c in c_st for w in W for t in Time)
    CIW =  quicksum(QW_swpt[qs]*(I_wt[i]) for i in I_wt for s in S for qs in QW_swpt for t in Time)\
              + quicksum((QW_whpt[qs]*HCW_wt[hc]) for hc in HCW_wt for s in S for qs in QW_whpt for t in Time )\
              + quicksum(QW_whpt[qw]*(TW_whpt[ts]*(p_bc)) for ts in TW_whpt for w in W for qw in QW_whpt for t in Time)
    SCH= quicksum(QU_whpt[qu]*p_ht[ph] for ph in p_ht for u in W for qu in QU_whpt for t in Time)

Answer 1

One possible way is by defining each part of the objective function separately and finally collecting them in an objective method. For example, suppose there are two different terms in the object as $\sum_{i} P_{i}x_{i}$ and $\sum_{i} \sum_{j} C_{i,j}y_{i,j}$ , then a simple template would be:

I = 10
J = 10
P = np.random.rand(I)
C = np.random.rand(I,J)

m = gp.Model()

x = m.addVars(I)
y = m.addVars(I,J)

part_1= gp.quicksum(P[i] * x[i] for i in range(I))   
part_2= gp.quicksum(C[i, j] * y[i, j] for i in range(I) for j in range(J))
objective= part_1 - part_2
m.setObjective(objective, GRB.MINIMIZE)

Answer 2

Sample variable declaration and use in expressions or constraints\

    QS_swpt =model addVars((S,W,P,T))# lb=o, vtype='c' is by default
    #similary for binary
    Y_wt= model.addVars((W,T),vtype='b') # S is set/list of suppliers,\
# T is list of time periods, W is list of warehouses. You can also make combinations like SWPT a list/set of tuples or tuplelist like [(s,w,p,t) for s in S for p in P for w in W]. In that case your variable declaration will be like mode.addVars(SWPT)
    
    # then expressions like OCS
    OCS= gp.quicksum(QS_swpt[s,w,p,t](MC_[s,p,t]+TS_swpt[s,w,p,t]) for p in products for w in warehouses for s in supplier for t in time)