main.py

import pulp
import re
import string
from collections import Counter

# -------------------------------
# 1. Define Data & Cost Factors
# -------------------------------

# Available stock: (quantity, length)
stock_list = [(9, 28), (11, 32), (9, 42), (15, 48)]
# Required pieces: (name, quantity, length)
piece_list = [('small', 64, 7.5), ('large', 32, 23.25)]

# Define cost factors (favoring smaller boards by assigning them a lower cost)
cost_factors = {28: 1.0, 32: 1.1, 42: 1.5, 48: 2.5}

# -------------------------------
# 2. Create a List of Boards
# -------------------------------
# Each board is represented as a dict with a length and cost factor.
boards = []
for qty, length in stock_list:
    boards.extend([{'length': length, 'cost': cost_factors[length]} for _ in range(qty)])
num_boards = len(boards)

# -------------------------------
# 3. Set Up the PuLP Model
# -------------------------------

model = pulp.LpProblem("CuttingStock", pulp.LpMinimize)

# Decision variables:
# y[i] is 1 if board i is used, 0 otherwise.
y = [pulp.LpVariable(f'y_{i}', cat='Binary') for i in range(num_boards)]

# n[(i, piece)] is the number of pieces of a given type cut from board i.
n = {}
for i in range(num_boards):
    for name, req, length in piece_list:
        n[(i, name)] = pulp.LpVariable(f'n_{i}_{name}', lowBound=0, cat='Integer')

# -------------------------------
# 4. Add Constraints
# -------------------------------

# (a) Board capacity: The total length of pieces assigned to board i must not exceed its length if used.
for i in range(num_boards):
    model += (
        sum(n[(i, name)] * length for name, req, length in piece_list)
        <= boards[i]['length'] * y[i],
        f"capacity_{i}"
    )

# (b) Demand: The total pieces cut must equal the required quantity for each piece type.
for name, req, length in piece_list:
    model += (
        sum(n[(i, name)] for i in range(num_boards)) == req,
        f"demand_{name}"
    )

# -------------------------------
# 5. Define the Objective
# -------------------------------
# Only count the board's length if it is used.
model += pulp.lpSum(
    boards[i]['cost'] * (boards[i]['length'] * y[i] - sum(n[(i, name)] * length for name, req, length in piece_list))
    for i in range(num_boards)
)

# -------------------------------
# 6. Solve the Model
# -------------------------------
model.solve()
print("Status:", pulp.LpStatus[model.status])

# -------------------------------
# 7. Gather and Display Board-Level Results
# -------------------------------

result_details = {}
for i in range(num_boards):
    # Only include boards that are used
    if y[i].varValue > 0.5:
        used_length = sum(n[(i, name)].varValue * length for name, req, length in piece_list)
        waste = boards[i]['length'] - used_length
        board_label = f"Board {i+1} ({boards[i]['length']}\")"
        cuts = []
        for name, req, length in piece_list:
            qty = int(n[(i, name)].varValue)
            if qty > 0:
                cuts.extend([length] * qty)
        result_details[board_label] = {"cuts": cuts, "waste": waste}

print("\nDetailed Board Assignments:")
for board, details in result_details.items():
    print(f"{board}: Cuts -> {details['cuts']} | Waste -> {details['waste']}\"")

# -------------------------------
# 8. Summarize and Label Patterns
# -------------------------------
def summarize_patterns(result_details):
    # Group boards by (stock length, sorted cuts, waste)
    pattern_counter = Counter()
    for board, details in result_details.items():
        # Extract numeric stock length from label (e.g., 'Board 1 (28")' -> 28)
        stock_length = int(re.search(r'\((\d+)"\)', board).group(1))
        cuts = tuple(sorted(details['cuts']))
        waste = details['waste']
        pattern_counter[(stock_length, cuts, waste)] += 1

    # Label patterns A, B, C, etc.
    labeled_patterns = {}
    for label, ((stock_length, cuts, waste), count) in zip(string.ascii_uppercase, pattern_counter.items()):
        labeled_patterns[label] = {
            'stock_length': stock_length,
            'cuts': list(cuts),
            'waste': waste,
            'count': count
        }
    return labeled_patterns

summary = summarize_patterns(result_details)
print("\nSummary of Patterns:")
for label, info in summary.items():
    print(
        f"Pattern {label}: Stock Length -> {info['stock_length']}\" | "
        f"Cuts -> {info['cuts']} | Waste -> {info['waste']}\" | Count -> {info['count']}"
    )