msci555.py

# -*- coding: utf-8 -*-
"""MSCI555.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/1lr7r9t6_LT4on65U6SwCNN-5Jd2mEhPn
"""

pip install pulp

import pulp
import random

# Constants
num_full_time_nurses = 34
num_part_time_nurses = 20
num_nurses = num_full_time_nurses + num_part_time_nurses
num_days = 42
num_shifts = num_days * 2  # Day and night shifts for each day
max_consecutive_days = 3
max_consecutive_shifts = 5

# Generate cost matrix
# Full-time nurses have 1.5 times higher cost than part-time nurses
cost_matrix = [
    [random.randint(50, 100) * (1.5 if i < num_full_time_nurses else 1) for j in range(num_shifts)] for i in range(num_nurses)
]

print(cost_matrix)

# Decision Variables
x = pulp.LpVariable.dicts("x", (range(num_nurses), range(num_shifts)), cat="Binary")

# Create Model
model = pulp.LpProblem("Nurse Scheduling", pulp.LpMinimize)

# Objective Function
model += pulp.lpSum([cost_matrix[i][j] * x[i][j] for i in range(num_nurses) for j in range(num_shifts)])

# Constraints for maximum consecutive shifts
for i in range(num_nurses):
    for j in range(0, num_shifts - max_consecutive_shifts + 1):
        model += pulp.lpSum([x[i][j+k] for k in range(max_consecutive_shifts + 1)]) <= max_consecutive_shifts

# Constraints for minimum nurses per shift
for j in range(0, num_shifts, 2):
    model += pulp.lpSum([x[i][j] for i in range(num_nurses)]) >= 12  # At least 12 nurses for day shifts (even shifts)

for j in range(1, num_shifts, 2):
    model += pulp.lpSum([x[i][j] for i in range(num_nurses)]) >= 8  # At least 8 nurses for night shifts (odd shifts)

# Constraints for maximum consecutive days
for i in range(num_nurses):
    for j in range(0, num_shifts - max_consecutive_days * 2 + 1, 2):
        model += pulp.lpSum([x[i][j+k] + x[i][j+k+1] for k in range(0, (max_consecutive_days + 1) * 2, 2)]) <= 2 * max_consecutive_days

# Constraints for minimum and maximum shifts per 42 days
min_shifts = 9
max_shifts = 30
for i in range(num_nurses):
    model += pulp.lpSum([x[i][j] for j in range(num_shifts)]) >= min_shifts
    model += pulp.lpSum([x[i][j] for j in range(num_shifts)]) <= max_shifts

# Solve Model
model.solve()
print("Status:", pulp.LpStatus[model.status])
print("Solver used:", model.solver)  # Print the solver used

# Print Solution
for i in range(num_nurses):
    assigned_shifts = [j for j in range(num_shifts) if x[i][j].varValue == 1]
    nurse_type = "Full-time" if i < num_full_time_nurses else "Part-time"
    print(f"{nurse_type} Nurse {i+1}: {', '.join(map(str, assigned_shifts))}")

import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

# Prepare data for the heatmap
heatmap_data = np.zeros((num_nurses, num_days * 2))
for i in range(num_nurses):
    for j in range(num_shifts):
        if x[i][j].varValue == 1:
            heatmap_data[i, j] = 2 if i < num_full_time_nurses else 1

# Create a custom colormap to differentiate between full-time and part-time nurses
from matplotlib.colors import ListedColormap
custom_cmap = ListedColormap(['white', 'orange', 'blue'])

# Create a heatmap
plt.figure(figsize=(15, 5))
ax = sns.heatmap(heatmap_data, cmap=custom_cmap, cbar=False, linewidths=0.5, linecolor='black')

# Set labels and title
ax.set_xlabel('Shifts')
ax.set_ylabel('Nurses')
ax.set_title('Nurse Scheduling Heatmap')

# Customize tick labels
shift_labels = ['D' + str(j//2 + 1) if j % 2 == 0 else 'N' + str(j//2 + 1) for j in range(num_shifts)]
ax.set_xticks(np.arange(num_shifts))  # Add this line to set tick locations explicitly
ax.set_xticklabels(shift_labels, rotation=90)
ax.set_yticks(np.arange(num_nurses) + 0.5)
ax.set_yticklabels(range(1, num_nurses + 1))

plt.show()