How to compare a expression with 0, Invalid data in vars array

Answered

伟星 郭

• March 12, 2023 11:47

This is my obj : to minimize $\sum^{-1}_{t=-T_H}(a_t*q_t*p*K + h*y_t+b*z_t)$

A constraint is ​$y_t = max(0, y_{t-1} + \sum_{i∈{j:j+l_j=t}}q_i * p - d_t)$

And all I want to do is to get max(expression, 0). What should I do?

np.random.seed(4)

T_H = [i for i in range(10)]
T = len(T_H)
# transport_cost
K = 50
# holding cost
h = 1
# stock-out cost
b = 100
# The number of boxes contained in a tray
p = 40
# VLT
l = [2 for i in range(10)]
# demand
d = [np.random.randint(100) for i in range(10)]
# initial inventory level
I = 109

# var
q = model.addVars(10, vtype=gp.GRB.INTEGER, name='q')
y = model.addVars(10, vtype=gp.GRB.INTEGER, name='y')
z = model.addVars(10, vtype=gp.GRB.INTEGER, name='z')
a = model.addVars(10, vtype=gp.GRB.BINARY, name='a')

# obj
obj = gp.quicksum((a[t] * q[t] * p * K + h * y[t] + b * z[t]) for t in range(T))
model.setObjective(obj, gp.GRB.MINIMIZE)

# cons
for t in range(T):
    if t == 0:
        model.addConstr(y[0] == I)
        model.addConstr(z[0] == 0)
    else:
        # model.addConstr(temp == y[t - 1] - d[t] + gp.quicksum(q[i] * p for i in range(t) if i + l[i] == t))
        # model.addConstr(temp1 == 0)
        model.addConstr(y[t] == gp.max_(y[t - 1] - d[t] + gp.quicksum(q[i] * p for i in range(t) if i + l[i] == t), 0))
        # model.addGenConstrMin(y[t], [temp, temp1])

        # model.addConstr(z[t] == (z[t-1] - d[t] + gp.quicksum(q[i] * p for i in range(t) if i + l[i] == t)))
        model.addConstr(y[t] >= 0)
        model.addConstr(z[t] >= 0)
        model.addConstr(q[t] >= 0)

• 

Related to

• Python
• General Constraints

1

• 

  伟星 郭

  • March 12, 2023 11:57

  

  

  

  In another word, Max of value and if negative, return 0. 

  

  These are my two main constraints, y_t means the inventory level while z_t means the stock-out inventory level in time t.

  0
• 

  伟星 郭

  • March 12, 2023 12:16

  

  

  

  Oh,sorry, z_t shoule be like this,

  0
• 

  Mario Ruthmair

  Gurobi Staff

  • March 13, 2023 10:37

  Hi,

  The issue here is that gp.max_() requires a list of variables (and an optional constant).
  You need to introduce additional helper variables that are set equal to the term in your max-function. Then you can use these variables in the max_() function.

  Alternatively, you do not necessarily need the max_() function here. You could just set a lower bound of 0 for the y- and z-variables, and add

  y_t >= y_{t-1} + sum ...

  to push y_t up if the right-hand side is positive (similar for z_t).
  Due to the minimization objective, the y_t and z_t variables should then always be equal to the max of 0 and the term in an optimal solution.

  Best regards,
  Mario

  0

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