import gurobipy as gp
def batch_scheduling(m, L0, L1, j, rj, pj, qj):
# Define the values of the variables
m = 2
L0 = 30
L1 = 45
j = range(10)
rj = [12, 7, 4, 9, 2, 14, 3, 0, 9, 18]
pj = [9, 14, 5, 11, 12, 6, 7, 4, 9, 8]
qj = [16, 25, 19, 11, 13, 10, 18, 22, 12, 15]
# Create the model
m = gp.Model("batch_scheduling")
# Decision variables
x = m.addVars([(j, b, m) for j in range(10) for b in range(2) for m in range(2)], vtype="binary")
y = m.addVars([(j, b) for j in range(10) for b in range(2)], vtype="binary")
t = m.addVars([b for b in range(2)], vtype="continuous")
# Objective function
m.setObjective(m.minimize(t[0] + t[1]))
# Constraints
# Each job must be assigned to exactly one batch
for j in range(10):
m.addConstr(gp.sum(x[j, b, m] for b in range(2) for m in range(2)) == 1)
# Each job must be processed in exactly one batch
for j in range(10):
m.addConstr(gp.sum(y[j, b] for b in range(2)) == 1)
# The processing time of each batch must be less than or equal to its capacity
for b in range(2):
m.addConstr(t[b] <= gp.sum(p[j] * x[j, b, m] for j in range(10) for m in range(2)))
# The start time of each job must be greater than or equal to its release time
for j in range(10):
m.addConstr(t[0] + gp.sum(p[j] * x[j, 0, m] for m in range(2)) >= r[j])
# The size of each batch must be less than or equal to the capacity of the machine it is assigned to
for j in range(10):
for m in range(2):
m.addConstr(q[j] * x[j, b, m] <= L[m])
# The variables must be binary
for j in range(10):
for b in range(2):
for m in range(2):
m.addConstr(x[j, b, m] <= 1)
m.addConstr(y[j, b] <= 1)
# Solve the model
m.optimize()
# Print the solution
if m.status == gp.OPTIMAL:
print("The optimal objective value is", m.objVal)
print("The optimal schedule is")
for j in range(10):
for b in range(2):
if x[j, b, 0].x == 1:
print("Job", j, "is assigned to batch", b, "on machine", 0)
if x[j, b, 1].x == 1:
print("Job", j, "is assigned to batch", b, "on machine", 1)
else:
print("The model is infeasible")
