Dear All,
Good day to you.

As a background, my objective of MILP case is to minimize the lead time (obj_lambda) by using docplex.mp only.
Supposing the decision variables for the minimizing the lead time are several x in X as model.integer_variables with several constraints.
Then, I also would like to sort the decision variables x in X into s in S as model.integer_list_variables for the next constraints. In short, S is X.sort(). 

Based on my manual calculation, the obj_lambda is 270 and the value of x should be different each other in range of 2 to 270, for example: 2,...,100, and 270. 

I have tried 4 scenarios by using Pycharm (all files are attached and named respectively).

File A: Running the CPLEX by defining S = np.array(np.sort(x))
             Result:
                     obj_lambda=310.000 ,
                     obj_lambda=310.000
                     x2=2.000
                     x3=103.000
                     x4=105.000
                     x5=306.000
                     x6=308.000
                     no result for S

File B: Running the CPLEX by defining S just as S[k] = mdl.integer_var(lb= 0, ub= inf, name='S' + str(k+1)) 
             Result:
             objective: 207
             obj_lambda=207
              x1=8
              x2=10
              x3=4
              x4=6
              x6=2
              S2=2
              S3=4
              S4=6
              S5=8
              S6=10

File C:  Running CPLEX by using the example from: howtowithdocplex/sortdecisionvariablesMP.py at main · AlexFleischerParis/howtowithdocplex and combine into 1 Model. (S = y_temp.reshape(Total_T,1))
               Result:
               objective: 207
               obj_lambda=207
               x1=8
               x2=10
               x3=4
               x4=6
               x6=2
               S_1=2
               S_2=4
               S_3=6
               S_4=8
               S_5=10

File D:  Running CPLEX by using the example from: howtowithdocplex/sortdecisionvariablesMP.py at main · AlexFleischerParis/howtowithdocplex and use 2 Model within the same coding. (mdl = Model(name='Scheduling') and mdl2 = Model(name='sortvariables').
             Result:
              Error: docplex.mp.utils.DOcplexException: Cannot mix objects from different models in new_binary_constraint. obj1=x_temp_0, obj2=x1

In this case,
1. is it impossible if we have two Models run within the same python coding but still with the same main objective ? (Model 1 (main objective) for minimizing and  Model 2 for sorting for the respective constraints) ?

2. Given I would like to get the minimum obj_lambda, x in X, and s in S, could anyone help me, please?

Here is the original objective function and constraints.
​​​​
#DecisionOptimization