An Assembly Line Balancing Problem

from docplex.mp.model import Model #cplex

W = 3 #worker
P = [[], [0], [0], [2], [3], [4]]   #precedence
T = [5, 4, 2, 3, 8]      #times
M = 999999999 #big M

def mat_model(S:int,P:list,T:list):
    """ S => Worker
        P => Precedence
        T => Job Times
    """
    math_model = Model(name="SALB - Type 2")
    #math_model.parameters.workmem = 8192
    M = 99999

    #Decision Variable
    x = [[math_model.binary_var(name=f'x({i}_{s})') for s in range(S)] for i in range(len(T))]

    #Objective Function
    C = math_model.continuous_var(name="Cycle")
    math_model.set_objective('min', C)

    #Constraint 1 - Assign all jobs:
    for i in range(len(T)):
        math_model.add_constraint(math_model.sum(x[i][s] for s in range(S)) == 1)

    #Constraint 2 - Precedence Relationships:
    for j in range(len(T)):
        for i in range(len(T)):
            if i in P[j]:
                math_model.add_constraint(
                    math_model.sum(s * x[i][s] for s in range(S)) <= math_model.sum(s * x[j][s] for s in range(S)))

    #Constraint 3 - Stations/Workers Cycle:
    for s in range(S):
            math_model.add_constraint(C >= (math_model.sum(x[i][s] * T[i] for i in range(len(T)))))

    
    def solve_model():
        print("Starting to solve.. "+"SALP")
        solution = math_model.solve()
        objective_value = math_model.objective_value
        print("The solution process is completed.\n")
        print(math_model.solve_status)
        if solution:
            math_model.print_information()
            print("Obj:", math_model.objective_value)
            for i in range(len(T)):
                for s in range((S)):
                    if x[i][s].solution_value == 1:
                        print(x[i][s], T[i])

    solve_model()

mat_model(W, P, T)