pycsp3-scheduling 0.1.1

Scheduling extension for pycsp3 with interval variables, sequence variables, and scheduling constraints

pycsp3-scheduling

Scheduling extension for pycsp3 with interval variables, sequence variables, and scheduling constraints.

Features

• Interval Variables: Represent tasks/activities with start, end, size, and optional presence
• Sequence Variables: Ordered sequences of intervals on disjunctive resources
• Precedence Constraints: end_before_start, start_at_start, etc.
• Grouping Constraints: span, alternative, synchronize
• Cumulative Functions: pulse, step_at_start, step_at_end for resource modeling
• State Functions: Model resource states with transitions
• XCSP3 Extension: Output scheduling models in extended XCSP3 format

Installation

pip install pycsp3-scheduling

For development:

git clone https://github.com/sohaibafifi/pycsp3-scheduling.git
cd pycsp3-scheduling
pip install -e ".[dev]"

Quick Start

from pycsp3 import *
from pycsp3_scheduling import *

# Create interval variables for tasks
task1 = IntervalVar(size=10, name="task1")
task2 = IntervalVar(size=15, name="task2")
task3 = IntervalVar(size=8, name="task3")

# Precedence: task1 must finish before task2 starts
satisfy(end_before_start(task1, task2))

# No overlap: task2 and task3 cannot overlap
satisfy(SeqNoOverlap([task2, task3]))

# Minimize makespan
minimize(max(end_time(task1), end_time(task2), end_time(task3)))

Example: Job Shop Scheduling

from pycsp3 import *
from pycsp3_scheduling import *

# Data
n_jobs, n_machines = 3, 3
durations = [[3, 2, 2], [2, 1, 4], [4, 3, 3]]
machines = [[0, 1, 2], [0, 2, 1], [1, 0, 2]]

# Create interval variables for each operation
ops = [[IntervalVar(size=durations[j][o], name=f"op_{j}_{o}")
        for o in range(n_machines)] for j in range(n_jobs)]

# Sequences for each machine
sequences = [SequenceVar(
    intervals=[ops[j][o] for j in range(n_jobs)
               for o in range(n_machines) if machines[j][o] == m],
    name=f"machine_{m}"
) for m in range(n_machines)]

# Precedence within jobs
satisfy(
    end_before_start(ops[j][o], ops[j][o+1])
    for j in range(n_jobs) for o in range(n_machines-1)
)

# No overlap on machines
satisfy(SeqNoOverlap(seq) for seq in sequences)

# Minimize makespan
minimize(Maximum(end_time(ops[j][-1]) for j in range(n_jobs)))

Example: RCPSP (Resource-Constrained Project Scheduling)

from pycsp3 import *
from pycsp3_scheduling import *

# Data
durations = [3, 2, 5, 4, 2]
demands = [[2, 1], [1, 2], [3, 0], [2, 1], [1, 3]]
capacities = [4, 3]
precedences = [(0, 2), (1, 3), (2, 4)]

# Interval variables
tasks = [IntervalVar(size=durations[i], name=f"task_{i}")
         for i in range(len(durations))]

# Precedence constraints
satisfy(end_before_start(tasks[p], tasks[s]) for p, s in precedences)

# Cumulative resource constraints
for r in range(len(capacities)):
    resource = sum(pulse(tasks[i], demands[i][r])
                   for i in range(len(tasks)) if demands[i][r] > 0)
    satisfy(resource <= capacities[r])

# Minimize makespan
minimize(Maximum(end_time(t) for t in tasks))

API Reference

Variables

Function	Description
IntervalVar(size, start, end, optional, name)	Create an interval variable
IntervalVarArray(size, ...)	Create array of interval variables
SequenceVar(intervals, types, name)	Create a sequence variable

Expressions

Function	Description
start_of(interval, absent_value=0)	Start time of interval
end_of(interval, absent_value=0)	End time of interval
size_of(interval, absent_value=0)	Size/duration of interval
length_of(interval, absent_value=0)	Length of interval
presence_of(interval)	Boolean presence status

Interop Helpers

Function	Description
start_time(interval)	pycsp3 variable for start time
end_time(interval)	pycsp3 expression for end time

Precedence Constraints

Constraint	Semantics (when both present)
start_before_start(a, b, delay)	start(b) >= start(a) + delay
start_before_end(a, b, delay)	end(b) >= start(a) + delay
end_before_start(a, b, delay)	start(b) >= end(a) + delay
end_before_end(a, b, delay)	end(b) >= end(a) + delay
start_at_start(a, b, delay)	start(b) == start(a) + delay
start_at_end(a, b, delay)	start(b) == end(a) + delay
end_at_start(a, b, delay)	end(a) == start(b) + delay
end_at_end(a, b, delay)	end(b) == end(a) + delay

Grouping Constraints

Constraint	Description
span(main, subtasks)	Main interval spans all present subtasks
alternative(main, alts, card=1)	Select card alternatives matching main
synchronize(main, intervals)	All present intervals sync with main

Cumulative Functions

Function	Description
pulse(interval, height)	Constant consumption during interval
step_at(time, height)	Step at fixed time point
step_at_start(interval, height)	Step at interval start
step_at_end(interval, height)	Step at interval end
cumul_range(cumul, min, max)	Constrain cumul to [min, max]

State Functions

Function	Description
StateFunction(transition_matrix)	Create state function
always_in(func, interval, min, max)	State in range during interval
always_equal(func, interval, value)	State equals value during interval
always_constant(func, interval)	State constant during interval

Requirements

• Python >= 3.9
• pycsp3 >= 2.5
• lxml >= 4.9

License

MIT License - see LICENSE file.

References

• PyCSP3 Documentation
• XCSP3 Specification