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Proof-of-concept OR
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def job_shop(): | |
machines = [ | |
Machine(cmm_id="1"), | |
Machine(cmm_id="2"), | |
] | |
jobs = [ | |
Job(job_id="431", instances=3, duration_min=20), | |
Job(job_id="459", instances=1, duration_min=100), # ??? | |
Job(job_id="449", instances=10, duration_min=40), | |
Job(job_id="461", instances=1, duration_min=100), # ??? | |
Job(job_id="457", instances=1, duration_min=100), # ??? | |
Job(job_id="426", instances=5, duration_min=95), | |
Job(job_id="419", instances=11, duration_min=50), | |
Job(job_id="458", instances=3, duration_min=90), | |
Job(job_id="467", instances=108, duration_min=15), | |
] | |
deadline = hours(11) | |
model = cp_model.CpModel() | |
############################################################################ | |
# Decision Variables | |
############################################################################ | |
makespan = model.NewIntVar(0, deadline, "makespan") | |
machine_intervals = defaultdict(list) | |
running = {} | |
matrix = {} | |
for j, m in itertools.product(jobs, machines): | |
beg = model.NewIntVar(0, deadline, f"beg_{j.job_id}_{m.cmm_id}") | |
end = model.NewIntVar(0, deadline, f"end_{j.job_id}_{m.cmm_id}") | |
interval = model.NewIntervalVar(beg, j.duration_min, end, f"interval_{j.job_id}") | |
matrix[(j.job_id, m.cmm_id)] = { | |
"beg": beg, | |
"end": end, | |
"interval": interval, | |
} | |
machine_intervals[m.cmm_id].append(interval) | |
running[(j.job_id, m.cmm_id)] = model.NewBoolVar(f"running_{j.job_id}_{m.cmm_id}") | |
############################################################################ | |
# Constraints | |
############################################################################ | |
# Sensible makespan | |
for k, v in matrix.items(): | |
model.Add(makespan >= v["end"]) | |
# No overlapping intervals *per machine* | |
for _, xs in machine_intervals.items(): | |
model.AddNoOverlap(xs) | |
# Run each job exactly once | |
for j in jobs: | |
model.Add( | |
sum( | |
v | |
for k, v in running.items() | |
if k[0] == j.job_id | |
) == 1 | |
) | |
# Ensure four jobs get assigned to M1 (just to illustrate the lack of parallelization) | |
for j in jobs: | |
model.Add( | |
sum( | |
v | |
for k, v in running.items() | |
if k[1] == "1" | |
) == 4 | |
) | |
############################################################################ | |
# Objective | |
############################################################################ | |
model.Minimize(makespan) | |
# solve | |
solver = cp_model.CpSolver() | |
status = solver.Solve(model) | |
if status not in {cp_model.OPTIMAL}: | |
print("No solution found") | |
else: | |
results = [] | |
for k, v in matrix.items(): | |
beg, end = solver.Value(v["beg"]), solver.Value(v["end"]) | |
is_run = solver.Value(running[k]) | |
if is_run: | |
results.append((k[0], k[1], beg, end)) | |
results = sorted(results, key=lambda x: (x[1], x[2])) | |
print( | |
tui_gantt( | |
[(x[0], x[1], x[2], x[3]) for x in results], | |
scale=0.1, | |
) | |
) |
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