237 lines
9.1 KiB
Python
237 lines
9.1 KiB
Python
# -*- coding: utf-8 -*-
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"""Scheduling problem with transition time between tasks and transitions costs.
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@author: CSLiu2
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"""
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from __future__ import print_function
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from __future__ import absolute_import
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from __future__ import division
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import collections
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from ortools.sat.python import cp_model
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def main():
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"""Solves the scheduling with transitions problem."""
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#------------------------------------------------------------------------------
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# Intermediate solution printer
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class SolutionPrinter(cp_model.CpSolverSolutionCallback):
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"""Print intermediate solutions."""
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def __init__(self):
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cp_model.CpSolverSolutionCallback.__init__(self)
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self.__solution_count = 0
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def OnSolutionCallback(self):
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print('Solution %i, time = %f s, objective = %i, makespan = %i' %
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(self.__solution_count, self.WallTime(), self.ObjectiveValue(),
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self.Value(makespan)))
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self.__solution_count += 1
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#------------------------------------------------------------------------------
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jobs = [[[(100, 0, 'R6'), (2, 1, 'R6')]], [[(2, 0, 'R3'), (100, 1, 'R3')]],
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[[(100, 0, 'R1'), (16, 1, 'R1')]], [[(1, 0, 'R1'), (38, 1, 'R1')]],
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[[(14, 0, 'R1'), (10, 1, 'R1')]], [[(16, 0, 'R3'), (17, 1, 'R3')]],
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[[(14, 0, 'R3'), (14, 1, 'R3')]], [[(14, 0, 'R3'), (15, 1, 'R3')]],
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[[(14, 0, 'R3'), (13, 1, 'R3')]], [[(100, 0, 'R1'), (38, 1, 'R1')]]]
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#------------------------------------------------------------------------------
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# Helper data
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num_jobs = len(jobs)
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all_jobs = range(num_jobs)
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num_machines = 2
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all_machines = range(num_machines)
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#------------------------------------------------------------------------------
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# Model
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model = cp_model.CpModel()
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#------------------------------------------------------------------------------
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# Sum each lot longest process time for max makespan
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horizon = 0
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for job in jobs:
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for task in job:
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max_task_duration = 0
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for alternative in task:
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max_task_duration = max(max_task_duration, alternative[0])
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horizon += max_task_duration
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print('Horizon = %i' % horizon)
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#------------------------------------------------------------------------------
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# Scan the jobs and create the relevant variables and intervals.
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intervals_per_machines = collections.defaultdict(list)
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presences_per_machines = collections.defaultdict(list)
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starts_per_machines = collections.defaultdict(list)
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ends_per_machines = collections.defaultdict(list)
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resources_per_machines = collections.defaultdict(list)
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job_starts = {} # indexed by (job_id, task_id).
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job_presences = {} # indexed by (job_id, task_id, alt_id).
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job_ends = []
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for job_id in all_jobs:
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job = jobs[job_id]
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num_tasks = len(job)
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previous_end = None
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for task_id in range(num_tasks):
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task = job[task_id]
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min_duration = task[0][0]
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max_duration = task[0][0]
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num_alternatives = len(task)
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all_alternatives = range(num_alternatives)
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for alt_id in range(1, num_alternatives):
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alt_duration = task[alt_id][0]
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min_duration = min(min_duration, alt_duration)
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max_duration = max(max_duration, alt_duration)
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# Create main interval for the task
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suffix_name = '_j%i_t%i' % (job_id, task_id)
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start = model.NewIntVar(0, horizon, 'start' + suffix_name)
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duration = model.NewIntVar(min_duration, max_duration,
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'duration' + suffix_name)
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end = model.NewIntVar(0, horizon, 'end' + suffix_name)
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interval = model.NewIntervalVar(start, duration, end,
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'interval' + suffix_name)
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# Store the start for the solution
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job_starts[(job_id, task_id)] = start
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# Add precedence with previous task in the same job
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if previous_end:
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model.Add(start >= previous_end)
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previous_end = end
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# Create alternative intervals
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if num_alternatives > 1:
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l_presences = []
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for alt_id in all_alternatives:
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### add to link interval with eqp constraint
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### process time = -1 cannot be processed at this machine
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if jobs[job_id][task_id][alt_id][0] == -1:
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continue
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alt_suffix = '_j%i_t%i_a%i' % (job_id, task_id, alt_id)
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l_presence = model.NewBoolVar('presence' + alt_suffix)
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l_start = model.NewIntVar(0, horizon, 'start' + alt_suffix)
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l_duration = task[alt_id][0]
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l_end = model.NewIntVar(0, horizon, 'end' + alt_suffix)
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l_interval = model.NewOptionalIntervalVar(
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l_start, l_duration, l_end, l_presence, 'interval' + alt_suffix)
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l_presences.append(l_presence)
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l_machine = task[alt_id][1]
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l_type = task[alt_id][2]
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# Link the master variables with the local ones
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model.Add(start == l_start).OnlyEnforceIf(l_presence)
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model.Add(duration == l_duration).OnlyEnforceIf(l_presence)
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model.Add(end == l_end).OnlyEnforceIf(l_presence)
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# Add the local variables to the right machine
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intervals_per_machines[l_machine].append(l_interval)
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starts_per_machines[l_machine].append(l_start)
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ends_per_machines[l_machine].append(l_end)
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presences_per_machines[l_machine].append(l_presence)
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resources_per_machines[l_machine].append(l_type)
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# Store the presences for the solution.
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job_presences[(job_id, task_id, alt_id)] = l_presence
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# Only one machine can process each lot
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model.Add(sum(l_presences) == 1)
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else:
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intervals_per_machines[task[0][1]].append(interval)
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job_presences[(job_id, task_id, 0)] = model.NewIntVar(1, 1, '')
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job_ends.append(previous_end)
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#--------------------------------------------------------------------------------------------
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# Create machines constraints nonoverlap process
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for machine_id in all_machines:
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intervals = intervals_per_machines[machine_id]
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if len(intervals) > 1:
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model.AddNoOverlap(intervals)
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#--------------------------------------------------------------------------------------------
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# Transition times and transition costs using a circuit constraints.
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switch_literals = []
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for machine_id in all_machines:
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machine_starts = starts_per_machines[machine_id]
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machine_ends = ends_per_machines[machine_id]
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machine_presences = presences_per_machines[machine_id]
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machine_resources = resources_per_machines[machine_id]
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intervals = intervals_per_machines[machine_id]
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arcs = []
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num_machine_tasks = len(machine_starts)
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all_machine_tasks = range(num_machine_tasks)
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for i in all_machine_tasks:
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arcs.append([0, i + 1, model.NewBoolVar('')])
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arcs.append([i + 1, 0, model.NewBoolVar('')])
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arcs.append([i + 1, i + 1, machine_presences[i].Not()]) # Self arc.
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for j in all_machine_tasks:
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lit = model.NewBoolVar('%i follows %i' % (j, i))
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if i == j:
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model.Add(lit == 0)
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else:
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arcs.append([i + 1, j + 1, lit])
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model.AddImplication(lit, machine_presences[i])
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model.AddImplication(lit, machine_presences[j])
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# Compute the transition time if task j is the successor of task i.
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if machine_resources[i] != machine_resources[j]:
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transition_time = 3
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switch_literals.append(lit)
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else:
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transition_time = 0
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# We add the reified transition to link the literals with the times of the tasks.
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model.Add(machine_starts[j] >= machine_ends[i] +
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transition_time).OnlyEnforceIf(lit)
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model.AddCircuit(arcs)
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#--------------------------------------------------------------------------------------------
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# Objective
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makespan = model.NewIntVar(0, horizon, 'makespan')
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model.AddMaxEquality(makespan, job_ends)
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makespan_weight = 1
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transition_weight = 5
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model.Minimize(makespan * makespan_weight +
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sum(switch_literals) * transition_weight)
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#--------------------------------------------------------------------------------------------
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# Solve
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solver = cp_model.CpSolver()
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solver.parameters.max_time_in_seconds = 60 * 60 * 2
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solution_printer = SolutionPrinter()
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status = solver.SolveWithSolutionCallback(model, solution_printer)
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#--------------------------------------------------------------------------------------------
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# Print solution
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if status == cp_model.FEASIBLE or status == cp_model.OPTIMAL:
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for job_id in all_jobs:
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for task_id in range(len(jobs[job_id])):
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start_value = solver.Value(job_starts[(job_id, task_id)])
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machine = 0
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duration = 0
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select = 0
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for alt_id in range(len(jobs[job_id][task_id])):
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if solver.BooleanValue(job_presences[(job_id, task_id, alt_id)]):
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duration = jobs[job_id][task_id][alt_id][0]
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machine = jobs[job_id][task_id][alt_id][1]
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select = alt_id
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print(' Job %i starts at %i (alt %i, machine %i, duration %i)' %
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(job_id, start_value, select, machine, duration))
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print('Solve status: %s' % solver.StatusName(status))
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print('Objective value: %i' % solver.ObjectiveValue())
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print('Makespan: %i' % solver.Value(makespan))
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if __name__ == '__main__':
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main()
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