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157 | # --------------------------------------------------------------------------
# Source file provided under Apache License, Version 2.0, January 2004,
# http://www.apache.org/licenses/
# (c) Copyright IBM Corp. 2015, 2022
# --------------------------------------------------------------------------
"""
This example solves a scheduling problem on two alternative heterogeneous machines.
A set of tasks {a_1,...,a_n} has to be executed on either one of the two machines.
Different types of tasks are distinguished, the type of task a_i is denoted tp_i.
A machine m needs a sequence dependent setup time setup(tp,tp') to switch from a
task of type tp to the next task of type tp'.
Furthermore some transitions tp->tp' are forbidden.
The two machines are different: they process tasks with different speed and have
different setup times and forbidden transitions.
The objective is to minimize the makespan.
The model uses transition distances and no_overlap constraints to model machines
setup times.
The no_overlap constraint is specified to enforce transition distance between
immediate successors on the sequence.
Forbidden transitions are modeled with a very large transition distance.
Please refer to documentation for appropriate setup of solving configuration.
"""
from docplex.cp.model import *
#-----------------------------------------------------------------------------
# Initialize the problem data
#-----------------------------------------------------------------------------
# Number of types
NB_TYPES = 5
# Setup times of machine M1. -1 means forbidden transition
SETUP_M1 = [[0, 26, 8, 3, -1],
[22, 0, -1, 4, 22],
[28, 0, 0, 23, 9],
[29, -1, -1, 0, 8],
[26, 17, 11, 7, 0]]
# Setup times of machine M2. -1 means forbidden transition
SETUP_M2 = [[0, 5, 28, -1, 2],
[-1, 0, -1, 7, 10],
[19, 22, 0, 28, 17],
[7, 26, 13, 0, -1],
[13, 17, 26, 20, 0]]
# Task types
TASK_TYPE = [3, 3, 1, 1, 1, 1, 2, 0, 0, 2,
4, 4, 3, 3, 2, 3, 1, 4, 4, 2,
2, 1, 4, 2, 2, 0, 3, 3, 2, 1,
2, 1, 4, 3, 3, 0, 2, 0, 0, 3,
2, 0, 3, 2, 2, 4, 1, 2, 4, 3]
# Number of tasks
NB_TASKS = len(TASK_TYPE)
# Task duration if executed on machine M1
TASK_DUR_M1 = [ 4, 17, 4, 7, 17, 14, 2, 14, 2, 8,
11, 14, 4, 18, 3, 2, 9, 2, 9, 17,
18, 19, 5, 8, 19, 12, 17, 11, 6, 3,
13, 6, 19, 7, 1, 3, 13, 5, 3, 6,
11, 16, 12, 14, 12, 17, 8, 8, 6, 6]
# Task duration if executed on machine M2
TASK_DUR_M2 = [12, 3, 12, 15, 4, 9, 14, 2, 5, 9,
10, 14, 7, 1, 11, 3, 15, 19, 8, 2,
18, 17, 19, 18, 15, 14, 6, 6, 1, 2,
3, 19, 18, 2, 7, 16, 1, 18, 10, 14,
2, 3, 14, 1, 1, 6, 19, 5, 17, 4]
#-----------------------------------------------------------------------------
# Prepare the data for modeling
#-----------------------------------------------------------------------------
# Put max value for forbidden transitions in setup times
for i in range(NB_TYPES):
for j in range(NB_TYPES):
if SETUP_M1[i][j] < 0:
SETUP_M1[i][j] = INTERVAL_MAX;
if SETUP_M2[i][j] < 0:
SETUP_M2[i][j] = INTERVAL_MAX;
#-----------------------------------------------------------------------------
# Build the model
#-----------------------------------------------------------------------------
# Create model
mdl = CpoModel()
# Build tasks for machine M1 and M2
tasks_m1 = [interval_var(name='A{}_M1_TP{}'.format(i, TASK_TYPE[i]), optional=True, size=TASK_DUR_M1[i]) for i in range(NB_TASKS)]
tasks_m2 = [interval_var(name='A{}_M2_TP{}'.format(i, TASK_TYPE[i]), optional=True, size=TASK_DUR_M1[i]) for i in range(NB_TASKS)]
# Build actual tasks as an alternative between machines
tasks = [interval_var(name='A{}_TP{}'.format(i, TASK_TYPE[i])) for i in range(NB_TASKS)]
mdl.add(alternative(tasks[i], [tasks_m1[i], tasks_m2[i]]) for i in range(NB_TASKS))
# Build a map to retrieve task id from variable name (for display purpose)
task_id = dict()
for i in range(NB_TASKS):
task_id[tasks_m1[i].get_name()] = i
task_id[tasks_m2[i].get_name()] = i
# Constrain tasks to no overlap on each machine
s1 = sequence_var(tasks_m1, types=TASK_TYPE, name='M1')
s2 = sequence_var(tasks_m2, types=TASK_TYPE, name='M2')
mdl.add(no_overlap(s1, SETUP_M1, 1))
mdl.add(no_overlap(s2, SETUP_M2, 1))
# Minimize the makespan
mdl.add(minimize(max([end_of(tasks[i]) for i in range(NB_TASKS)])))
#-----------------------------------------------------------------------------
# Solve the model and display the result
#-----------------------------------------------------------------------------
def compact(name):
# Example: A31_M1_TP1 -> 31
task, foo = name.split('_', 1)
return task[1:]
import docplex.cp.utils_visu as visu
def showsequence(s, setup):
seq = res.get_var_solution(s)
visu.sequence(name=s.get_name())
vs = seq.get_value()
for v in vs:
nm = v.get_name()
visu.interval(v, TASK_TYPE[task_id[nm]], compact(nm))
for i in range(len(vs) - 1):
end = vs[i].get_end()
tp1 = TASK_TYPE[task_id[vs[i].get_name()]]
tp2 = TASK_TYPE[task_id[vs[i + 1].get_name()]]
visu.transition(end, end + setup[tp1][tp2])
# Solve model
print('Solving model...')
res = mdl.solve(FailLimit=100000, TimeLimit=10)
print('Solution: ')
res.print_solution()
if res and visu.is_visu_enabled():
visu.timeline('Solution for SchedSetup')
showsequence(s1, SETUP_M1)
showsequence(s2, SETUP_M2)
visu.show()
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