Optimizing Nurse Deployment in Healthcare: A Prescriptive Machine Learning Approach

This repository contains the code and data used for the paper "Optimizing Nurse Deployment in Healthcare: A Prescriptive Machine Learning Approach". The paper introduces a novel approach to optimizing nurse deployment using machine learning models, specifically focusing on neural networks and graph neural networks, combined with mixed-integer programming solvers. The goal is to enhance decision-making in healthcare settings by providing optimized deployment strategies.

Table of Contents

• Setup Environment
• Data Generation
  • Ex post Dataset
  • Ex ante Dataset
• Training & Evaluation
  • Ex post Training
    • Stage One
    • Stage Two
  • Ex ante Training
    • Stage One
    • Stage Two
• Conclusion
• Contact

Setup Environment

To begin, ensure that you have the necessary dependencies installed. You can do this by navigating to the scheduling directory and installing the required packages listed in the requirements.txt file:

cd scheduling
pip install -r requirements.txt

Please note that this project requires access to COPT and Gurobi solvers for data generation and optimization tasks. Ensure that these solvers are installed and properly configured on your system.

Data Generation

Data generation is a critical step in our approach. We provide scripts to generate both Ex post and Ex ante datasets using the solvers mentioned above. The datasets are used to train and evaluate the neural network models described in the paper.

Ex post Dataset

To generate the Ex post dataset, run the following script:

python data_generator.py \
    --num_location 8 \
    --num_samples 10240 \
    --saving_path "./data" \
    --zero_threshold 1e-5 \
    --loss_type "quadratic" \
    --Kxi_bound "10" "200" \
    --D_bound "0" "2" \
    --with_quard_farc \
    --with_int_solution

This script generates a dataset with:

• 8 locations
• A quadratic objective function (ax^2 + bx + c)
• Location demands bounded between 10 and 200
• Transfer costs (D) bounded between 0 and 2
• Both floating-point and integer solutions provided by the solver

Ex ante Dataset

For generating the Ex ante dataset, use the following command:

python data_generator.py \
    --num_location 8 \
    --num_samples 10240 \
    --saving_path "./data" \
    --zero_threshold 1e-5 \
    --loss_type "quadratic" \
    --Kxi_bound "10" "200" \
    --D_bound "0" "2" \
    --exnt_sample_amount 100 \
    --with_int_solution \
    --exnt

This script generates an Ex ante dataset with similar parameters as the Ex post dataset. However, it includes a step where 100 samples are drawn to approximate the normal distribution of each location's demands.

Training & Evaluation

The training and evaluation process is divided into two stages: Stage One for initial model training and Stage Two for refining the model output.

Ex post Training

Stage One

To train a neural network (ANN or GNN) on the Ex post dataset, use the following script:

export CUDA_VISIBLE_DEVICES=0
python train.py \
    --model_type "NN" \
    --checkpoint_path "./checkpoint" \
    --data_filename "10240_L8_quadratic_kxi['10', '200']_D['0', '2']_zerosFalse_intsolutionTrue_qfracTrue.pkl" \
    --learning_rate 5e-3 \
    --g_type "quadratic" \
    --batch_size 768 \
    --train_bystep \
    --train_step 2000 \
    --eval_step 400 \
    --inference \
    --d_model 768 \
    --mid_layer 5 \
    --loss_combo "100010" \
    --loss_lambda "1" "1" "1" "1" "1" "1" \
    --model_selection_strategy "eval_loss" "f1" "infesibility" "cost_obj" \
    --save_name_suffix "" \
    --optimizer "adam" \
    --inference_step 100
    # --inference_only 

Explanation of Parameters:

• --model_type "NN": Specifies the use of a Neural Network. Replace with "GNN" for Graph Neural Network training.
• --checkpoint_path "./checkpoint": Directory to save model checkpoints.
• --data_filename "... .pkl": Path to the dataset file.
• --learning_rate 5e-3: Learning rate for the optimizer.
• --batch_size 768: Number of samples per batch.
• --train_bystep: Enables training by steps.
• --train_step 2000: Total number of training steps.
• --eval_step 400: Evaluation occurs every 400 steps.
• --inference: Enables inference during evaluation.
• --d_model 768: Dimensionality of the model.
• --mid_layer 5: Number of middle layers in the network.
• --loss_combo "100010": Specifies the combination of losses to use. Refer to hybrid_loss in Utils.py for details.
• --loss_lambda "1" "1" "1" "1" "1" "1": Weights for each loss component.
• --model_selection_strategy "eval_loss" "f1" "infesibility" "cost_obj": Metrics for selecting the best model.
• --inference_step 100: Number of inference steps during evaluation.
• # --inference_only: Uncomment to skip training and perform inference only.

Stage Two

After Stage One, the output can be refined in Stage Two:

export CUDA_VISIBLE_DEVICES=0
python train.py \
    --model_type "stage2_NN" \
    --g_type "quadratic" \
    --checkpoint_path "./checkpoint/qfrac" \
    --data_filename "10240_L8_quadratic_kxi['10', '200']_D['0', '2']_zerosFalse_intsolutionTrue_qfracTrue.pkl" \
    --stage1_model_path "./checkpoint/{your_checkpoint}.pth" \
    --batch_size 768 \
    --round_threshold 0.5 \
    --train_bystep \
    --train_step 2000 \
    --eval_step 400 \
    --inference \
    --d_model 768 \
    --mid_layer 5 \
    --model_selection_strategy "eval_loss" "f1" "infesibility" "cost_obj" \
    --inference_step 500
    # --inference_only

Key Points:

• --model_type "stage2_NN": Specifies Stage Two Neural Network training.
• --stage1_model_path "./checkpoint/{your_checkpoint}.pth": Path to the Stage One model checkpoint.
• --round_threshold 0.5: Threshold for rounding during post-processing.
• Ensure the dataset contains integer solutions for effective refinement.

Ex ante Training

Stage One

For Ex ante training, use the following script:

export CUDA_VISIBLE_DEVICES=0
python train.py \
    --model_type "NN" \
    --checkpoint_path "./checkpoint/exnt_real_calculated_obj" \
    --data_filename "EXNT_10240_L8_quadratic_D['0', '2']_zerosFalse_intsolutionTrue_m100.pkl" \
    --learning_rate 5e-3 \
    --g_type "quadratic" \
    --round_threshold 0.5 \
    --batch_size 768 \
    --train_bystep \
    --train_step 2000 \
    --eval_step 400 \
    --inference \
    --d_model 768 \
    --mid_layer 5 \
    --model_selection_strategy "eval_loss" "f1" "infesibility" "cost_obj" \
    --save_name_suffix "" \
    --optimizer "adam" \
    --inference_step 500 \
    --exnt \
    --calculated_obj
    # --inference_only

Additional Flags:

• --exnt: Indicates that the dataset is Ex ante.
• --calculated_obj: Uses a known formula to calculate objective values. If omitted, objective values provided by the solver are used.

Stage Two

Finally, refine the Ex ante model in Stage Two:

export CUDA_VISIBLE_DEVICES=4
python train.py \
    --model_type "stage2_NN" \
    --g_type "quadratic" \
    --checkpoint_path "./checkpoint/exnt_real_calculated_obj" \
    --data_filename "EXNT_10240_L8_quadratic_D['0', '2']_zerosFalse_intsolutionTrue_m100.pkl" \
    --stage1_model_path "./checkpoint/{your_checkpoint}.pth" \
    --batch_size 768 \
    --train_bystep \
    --train

_step 2000 \
    --eval_step 400 \
    --inference \
    --d_model 768 \
    --mid_layer 5 \
    --model_selection_strategy "eval_loss" "f1" "infesibility" "cost_obj" \
    --inference_step 500 \
    --exnt
    # --inference_only

Ensure to set the correct --stage1_model_path and include the --exnt flag to indicate the use of Ex ante datasets.

Conclusion

This repository provides all necessary scripts and instructions to reproduce the results presented in our paper. By following the steps outlined above, you should be able to generate data, train models, and evaluate their performance. Please ensure you have the required solvers (COPT and Gurobi) installed to avoid any issues during data generation or optimization tasks.

We hope this repository helps you explore the potential of prescriptive machine learning in healthcare settings, specifically in optimizing nurse deployment strategies.

Contact

For any questions, issues, or contributions, please feel free to open an issue or contact us directly.