cutstock.py

Column generation is a solution process that begins with a small, manageable part of a problem (specifically, a few of the variables), solves that part, analyzes the partial solution to determine the next part of the problem (specifically, one or more variables) to add to the model, and then solves the new, enlarged model. Column generation repeats the process until a satisfactory solution to the whole problem is achieved.

# --------------------------------------------------------------------------
# Source file provided under Apache License, Version 2.0, January 2004,
# http://www.apache.org/licenses/
# (c) Copyright IBM Corp. 2015, 2016
# --------------------------------------------------------------------------

from collections import namedtuple
import json

from docplex.util.environment import get_environment
from docplex.mp.model import Model


# ----------------------------------------------------------------------------
# Initialize the problem data
# ----------------------------------------------------------------------------
DEFAULT_ROLL_WIDTH = 110
DEFAULT_ITEMS = [(1, 20, 48), (2, 45, 35), (3, 50, 24), (4, 55, 10), (5, 75, 8)]
DEFAULT_PATTERNS = [(i, 1) for i in range(1, 6)]  # (1, 1), (2, 1) etc
DEFAULT_PATTERN_ITEM_FILLED = [(p, p, 1) for p in range(1, 6)]  # pattern1 for item1, pattern2 for item2, etc.

FIRST_GENERATION_DUALS = [1, 1, 1, 1, 0]


# ----------------------------------------------------------------------------
# Build the model
# ----------------------------------------------------------------------------
class TItem(object):
    def __init__(self, item_id, item_size, demand):
        self.id = item_id
        self.size = item_size
        self.demand = demand
        self.dual_value = -1

    @classmethod
    def make(cls, args):
        arg_id = args[0]
        arg_size = args[1]
        arg_demand = args[2]
        return cls(arg_id, arg_size, arg_demand)

    def __str__(self):
        return 'item%d' % self.id


class TPattern(namedtuple("TPattern", ["id", "cost"])):
    def __str__(self):
        return 'pattern%d' % self.id

# ---


def make_cutstock_pattern_generation_model(items, roll_width, **kwargs):
    gen_model = Model(name='cutstock_generate_patterns', **kwargs)
    # store data
    gen_model.items = items
    gen_model.roll_width = roll_width
    # default values
    gen_model.duals = [1] * len(items)
    # 1. create variables: one per item
    gen_model.use_vars = gen_model.integer_var_list(keys=items, ub=999999, name='use')
    # 2 setup constraint:
    # --- sum of item usage times item sizes must be less than roll width
    gen_model.add(gen_model.dot(gen_model.use_vars, (it.size for it in items)) <= roll_width)

    # store dual expression for dynamic edition
    gen_model.use_dual_expr = 1 - gen_model.dot(gen_model.use_vars, gen_model.duals)
    # minimize
    gen_model.minimize(gen_model.use_dual_expr)

    return gen_model


def cutstock_update_duals(gmodel, new_duals):
    # update the duals array and the the duals expression...
    # edition is propagated to the objective of the model.
    gmodel.duals = new_duals
    use_vars = gmodel.use_vars
    assert len(new_duals) == len(use_vars)
    updated_used = [(use, -new_duals[u]) for u, use in enumerate(use_vars)]
    # this modification is notified to the objective.
    gmodel.use_dual_expr.set_coefficients(updated_used)
    return gmodel


def make_custstock_master_model(item_table, pattern_table, fill_table, roll_width, **kwargs):
    m = Model(name='custock_master', **kwargs)

    # store data as properties
    m.items = [TItem.make(it_row) for it_row in item_table]
    m.items_by_id = {it.id: it for it in m.items}
    m.patterns = [TPattern(*pattern_row) for pattern_row in pattern_table]
    m.patterns_by_id = {pat.id: pat for pat in m.patterns}
    m.max_pattern_id = max(pt.id for pt in m.patterns)

    # build a dictionary storing how much each pattern fills each item.
    m.pattern_item_filled = {(m.patterns_by_id[p], m.items_by_id[i]): f for (p, i, f) in fill_table}
    m.roll_width = roll_width

    # --- variables
    # one cut var per pattern...
    m.MAX_CUT = 9999
    m.cut_vars = m.continuous_var_dict(m.patterns, lb=0, ub=m.MAX_CUT, name="cut")

    # --- add fill constraints
    #
    all_patterns = m.patterns
    all_items = m.items
    m.item_fill_cts = []
    for item in all_items:
        item_fill_ct = m.sum(
            m.cut_vars[p] * m.pattern_item_filled.get((p, item), 0) for p in all_patterns) >= item.demand
        item_fill_ct.name = 'ct_fill_{0!s}'.format(item)
        m.item_fill_cts.append(item_fill_ct)
    m.add_constraints(m.item_fill_cts)

    # --- minimize total cut stock
    m.total_cutting_cost = m.sum(m.cut_vars[p] * p.cost for p in all_patterns)
    m.minimize(m.total_cutting_cost)

    return m


def add_pattern_to_master_model(master_model, item_usages):
    """ Adds a new pattern to the master model.

    This function performs the following:

    1. build a new pattern instance from item usages (taken from sub-model)
    2. add it to the master model
    3. update decision objects with this new pattern.
    """
    new_pattern_id = max(pt.id for pt in master_model.patterns) + 1
    new_pattern = TPattern(new_pattern_id, 1)
    master_model.patterns.append(new_pattern)
    for used, item in zip(item_usages, master_model.items):
        master_model.pattern_item_filled[new_pattern, item] = used

    # --- add one decision variable, linked to the new pattern.
    new_pattern_cut_var = master_model.continuous_var(lb=0, ub=master_model.MAX_CUT,
                                                      name='cut_{0}'.format(new_pattern_id))
    master_model.cut_vars[new_pattern] = new_pattern_cut_var

    # update constraints
    for item, ct in zip(master_model.items, master_model.item_fill_cts):
        # update fill constraint by changing lhs
        ctlhs = ct.lhs
        filled = master_model.pattern_item_filled[new_pattern, item]
        if filled:
            ctlhs += new_pattern_cut_var * filled

    # update objective:
    #   side-effect on  the total cutting cost expr propagates to the objective.
    cost_expr = master_model.total_cutting_cost
    cost_expr += new_pattern_cut_var * new_pattern.cost  # this performw a side effect!

    return master_model


def cutstock_print_solution(cutstock_model):
    patterns = cutstock_model.patterns
    cut_var_values = {p: cutstock_model.cut_vars[p].solution_value for p in patterns}
    pattern_item_filled = cutstock_model.pattern_item_filled
    print("| Nb of cuts | Pattern   | Pattern's detail (# of item1,item2,...) |")
    print("| {} |".format("-" * 70))
    for p in patterns:
        if cut_var_values[p] >= 1e-3:
            pattern_detail = {b.id: pattern_item_filled[a, b] for a, b in pattern_item_filled if
                              a == p}
            print(
                "| {:<10g} | {!s:9} | {!s:45} |".format(cut_var_values[p],
                                                        p,
                                                        pattern_detail))
    print("| {} |".format("-" * 70))


def cutstock_save_as_json(model, json_file):
    patterns = model.patterns
    cut_var_values = {p: model.cut_vars[p].solution_value for p in patterns}
    solution = []
    for p in patterns:
        if cut_var_values[p] >= 1e-3:
            pattern_detail = {b.id: model.pattern_item_filled[(a, b)] for (a, b) in model.pattern_item_filled if
                              a == p}
            n = {'pattern': str(p),
                 'cuts': "%g" % cut_var_values[p],
                 'details': pattern_detail}
            solution.append(n)
    json_file.write(json.dumps(solution, indent=3).encode('utf-8'))


def cutstock_solve(item_table, pattern_table, fill_table, roll_width, **kwargs):
    verbose = kwargs.pop('verbose', True)
    master_model = make_custstock_master_model(item_table, pattern_table, fill_table, roll_width, **kwargs)

    # these two fields contain named tuples
    items = master_model.items
    patterns = master_model.patterns
    gen_model = make_cutstock_pattern_generation_model(items, roll_width, **kwargs)

    rc_eps = 1e-6
    obj_eps = 1e-4
    loop_count = 0
    best = 0
    curr = 1e+20
    ms = None

    while loop_count < 100 and abs(best - curr) >= obj_eps:
        ms = master_model.solve(**kwargs)
        loop_count += 1
        best = curr
        if not ms:
            print('{}> master model fails, stop'.format(loop_count))
            break
        else:
            assert ms
            curr = master_model.objective_value
            if verbose:
                print('{}> new column generation iteration, #patterns={}, best={:g}, curr={:g}'
                      .format(loop_count, len(patterns), best, curr))
            duals = master_model.dual_values(master_model.item_fill_cts)
            if verbose:
                print('{0}> moving duals from master to sub model: {1}'
                      .format(loop_count, list(map(lambda x: float('%0.2f' % x), duals))))
            cutstock_update_duals(gen_model, duals)
            gs = gen_model.solve(**kwargs)
            if not gs:
                print('{}> slave model fails, stop'.format(loop_count))
                break

            rc_cost = gen_model.objective_value
            if rc_cost <= -rc_eps:
                if verbose:
                    print('{}> slave model runs with obj={:g}'.format(loop_count, rc_cost))
            else:
                if verbose:
                    print('{}> pattern-generator model stops, obj={:g}'.format(loop_count, rc_cost))
                break

            use_values = gen_model.solution.get_values(gen_model.use_vars)
            if verbose:
                print('{}> add new pattern to master data: {}'.format(loop_count, str(use_values)))
            # make a new pattern with use values
            if not (loop_count < 100 and abs(best - curr) >= obj_eps):
                print('* terminating: best-curr={:g}'.format(abs(best - curr)))
                break
            add_pattern_to_master_model(master_model, use_values)

    if ms:
        if verbose:
            print('\n* Cutting-stock column generation terminates, best={:g}, #loops={}'.format(curr, loop_count))
            cutstock_print_solution(master_model)
        return ms
    else:
        print("!!!!  Cutting-stock column generation fails  !!!!")
        return None


def cutstock_solve_default(**kwargs):
    return cutstock_solve(DEFAULT_ITEMS, DEFAULT_PATTERNS, DEFAULT_PATTERN_ITEM_FILLED, DEFAULT_ROLL_WIDTH,
                          **kwargs)


# -----------------------------------------------------------------------------
# Solve the model and display the result
# -----------------------------------------------------------------------------
if __name__ == '__main__':
    s = cutstock_solve_default()
    assert abs(s.objective_value - 46.25) <= 0.1
    # Save the solution as "solution.json" program output.
    with get_environment().get_output_stream("solution.json") as fp:
        cutstock_save_as_json(s.model, fp)