Single-Reactor Pharmaceutical Batch Scheduling Under Uncertainty

Research companion repository for the paper:

Rababah, A. (2025). Heuristic Scheduling Strategies for Single-Reactor Pharmaceutical Batch Production Under Uncertainty: A Comparative Statistical and Machine Learning Analysis. ChemRxiv. https://doi.org/10.26434/chemrxiv-2025-wq0tr

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📋 Abstract

Pharmaceutical batch production faces significant scheduling challenges due to operational uncertainties including equipment failures, yield variability, and demand fluctuations. This study evaluates three scheduling heuristics (FIFO, SPT, LPT) for single-reactor configurations across varying uncertainty levels using a discrete-event simulation model of a 10,000L bioreactor producing three antibiotic products.

Key Findings:

• Campaign-based strategies (SPT, LPT) outperform round-robin FIFO by 16.5% in makespan reduction
• SPT and LPT are statistically equivalent (Cohen's d = 0.12), providing operational flexibility
• No heuristic × uncertainty interaction—benefits remain consistent across all uncertainty levels
• Machine learning models achieve 90-97% accuracy in predicting schedule robustness
• Polynomial SVM achieves best performance (96.7% accuracy, AUC = 0.972)

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🔬 Study Design

Experimental Configuration

Parameter	Value
Reactor Configuration	Single 10,000L bioreactor
Products	3 antibiotics (A: 48h, B: 72h, C: 120h fermentation)
Scheduling Heuristics	FIFO, SPT, LPT
Uncertainty Levels	Low, Medium, High
Total Observations	450 (3 × 3 × 50 scenarios)

Uncertainty Parameters

Parameter	Low	Medium	High
Equipment Failure Probability	2%	5%	8%
Yield Variability (CV)	±5%	±10%	±15%
Processing Time Deviation	±5%	±10%	±15%

Scheduling Heuristics Evaluated

• FIFO (First-In-First-Out): Round-robin cycling through products A→B→C
• SPT (Shortest Processing Time): Campaign-based, shortest products first (A→B→C)
• LPT (Longest Processing Time): Campaign-based, longest products first (C→B→A)

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📊 Key Results

Statistical Analysis (Two-Way ANOVA)

Source	F	p	η²	Interpretation
Uncertainty Level	346.69	<.001	0.437	Large effect
Heuristic	225.71	<.001	0.285	Large effect
Interaction	0.103	.981	<0.001	No interaction

Model explains ~72% of variance in makespan (η² combined = 0.722)

Mean Makespan by Condition (Hours)

Uncertainty	SPT	LPT	FIFO
Low	1,762 (CV=2.6%)	1,778 (CV=2.5%)	2,157 (CV=3.0%)
Medium	1,914 (CV=6.1%)	1,942 (CV=6.1%)	2,322 (CV=6.5%)
High	2,300 (CV=11.0%)	2,323 (CV=11.7%)	2,680 (CV=11.6%)
Marginal Mean	1,992	2,014	2,387

Machine Learning Classification Performance

Model	Test Accuracy	AUC	F1	MCC
Polynomial SVM	96.7%	0.972	0.967	0.934
Random Forest	94.4%	0.985	0.944	0.890
RBF SVM	94.4%	0.946	0.945	0.891
Decision Tree	94.4%	0.944	0.945	0.884
Gradient Boosting	93.3%	0.997	0.933	0.869
Linear SVM	92.2%	0.920	0.922	0.845
Logistic Regression	90.0%	0.900	0.900	0.799

Feature Importance (Averaged Across Models)

Feature	Relative Importance
Heuristic Type	33%
Uncertainty Level	30%
Total Demand	18%
Average Yield	8%
Downtime Hours	6%
Equipment Failure	5%

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📁 Repository Structure

single-reactor-scheduling/
├── README.md                    # This file
├── LICENSE                      # MIT License
├── DATA_DICTIONARY.md           # Variable definitions
├── CITATION.cff                 # Citation metadata
│
├── data/
│   ├── optimized_dataset.csv            # Base simulation output (450 obs)
│   └── optimized_dataset_ML.csv         # ML-ready with target variables
│
├── scripts/
│   ├── create_ml_dataset.py             # Adds ML target variables
│   └── visualization_script.py          # Generates all 8 figures
│
├── jasp/
│   ├── statistical_analysis.jasp        # ANOVA, regression, post-hoc
│   └── ml_classification.jasp           # All ML models
│
├── figures/
│   ├── Figure1_Main_Results.png         # Makespan by heuristic & interaction
│   ├── Figure2_Mechanism_Analysis.png   # Changeover & learning effects
│   ├── Figure3_Uncertainty_Effects.png  # Distribution & SPT advantage
│   ├── FigureS1_Data_Quality.png        # Data quality dashboard
│   ├── FigureS2_Statistical_Diagnostics.png  # ANOVA assumptions
│   └── FigureS3_Detailed_Comparison.png # Violin plots by condition
│
└── paper/
    └── Rababah_2025_Single_Reactor_Scheduling.pdf

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🛠️ Analysis Workflow

Software Requirements

Software	Version	Purpose
Python	3.8+	Data preparation & visualization
JASP	0.18+	All statistical & ML analysis
pandas	1.5+	Data manipulation
numpy	1.21+	Numerical operations
matplotlib	3.5+	Figure generation
seaborn	0.12+	Statistical visualization
scipy	1.9+	Statistical functions

Division of Labor

Task	Tool	Script/File
Dataset preparation	Python	create_ml_dataset.py
Figure generation	Python	visualization_script.py
Descriptive statistics	JASP	statistical_analysis.jasp
Two-Way ANOVA	JASP	statistical_analysis.jasp
Kruskal-Wallis tests	JASP	statistical_analysis.jasp
Post-hoc comparisons	JASP	statistical_analysis.jasp
Multiple regression	JASP	statistical_analysis.jasp
ML Classification	JASP	ml_classification.jasp

Reproduction Steps

Step 1: Prepare ML Dataset

cd scripts/
python create_ml_dataset.py

This creates optimized_dataset_ML.csv with three target variables:

• schedule_robust: Binary (0=Vulnerable, 1=Robust)
• performance_class: 3-class (Excellent/Acceptable/Poor)
• performance_numeric: Ordinal encoding (0/1/2)

Step 2: Generate Figures

cd scripts/
python visualization_script.py

This generates all 8 publication-quality figures:

Main Paper Figures:

Figure	Description	Output Files
Figure 1	Main results: boxplots & interaction plot	Figure1_Main_Results.png/pdf
Figure 2	Mechanism: changeover time, learning savings, changeover count	Figure2_Mechanism_Analysis.png/pdf
Figure 3	Uncertainty effects: distributions & SPT advantage	Figure3_Uncertainty_Effects.png/pdf

Supplementary Figures:

Figure	Description	Output Files
Figure S1	Data quality dashboard (6 panels)	FigureS1_Data_Quality.png/pdf
Figure S2	ANOVA diagnostics: Q-Q, residuals, homogeneity	FigureS2_Statistical_Diagnostics.png/pdf
Figure S3	Violin plots by heuristic × uncertainty	FigureS3_Detailed_Comparison.png/pdf

Summary Tables:

• Table1_PanelA_Heuristic_Stats.csv
• Table1_PanelB_Uncertainty_Stats.csv
• Table1_PanelC_CrossTab.csv

Step 3: Run Statistical Analysis in JASP

1. Open jasp/statistical_analysis.jasp
2. Analyses included:
   • Descriptive Statistics
   • Two-Way Factorial ANOVA
   • Kruskal-Wallis Tests (non-parametric confirmation)
   • Post-Hoc Comparisons (Tukey HSD, Dunn's test)
   • Multiple Linear Regression
   • Assumption Diagnostics

Step 4: Run ML Classification in JASP

1. Open jasp/ml_classification.jasp
2. Set variable types:
   • schedule_robust → Nominal (target)
   • performance_class → Nominal (multi-class target)
3. ML models configured:
   • Random Forest (100 trees)
   • Gradient Boosting (100 iterations)
   • SVM (Linear, RBF, Polynomial kernels)
   • Decision Tree (max depth = 30)
   • Logistic Regression

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📖 Data Dictionary

See DATA_DICTIONARY.md for complete variable definitions.

Quick Reference

Variable	Type	Description
scenario_id	Integer	Unique identifier (1-450)
heuristic	Categorical	FIFO, SPT, or LPT
uncertainty_level	Ordinal	Low, Medium, or High
makespan	Continuous	Total production time (hours)
utilization	Continuous	Equipment utilization (0-1)
total_changeover_time	Continuous	Sum of changeover durations
total_learning_savings	Continuous	Time saved via learning curves
schedule_robust	Binary	ML target (0/1)
performance_class	Categorical	ML target (3-class)

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📈 Practical Implications

For Production Planning

• ✅ Use campaign-based scheduling (SPT or LPT) as the default strategy
• ❌ Avoid FIFO/round-robin except when explicitly required
• 📊 Expected savings: ~395 hours (~16.5%) per production cycle

For Risk Management

• 🎯 Deploy ML-based prediction tools to flag high-risk schedules
• 📈 Increase buffer time allocation under high uncertainty
• 📉 Monitor CV of schedule outcomes as reliability metric

Decision Rules from ML Models

IF heuristic = FIFO:
    → VULNERABLE schedule (94-101 of 150 cases)
    
IF heuristic = SPT or LPT:
    IF uncertainty = Low or Medium:
        → ROBUST schedule (116-118 of 200 cases)
    IF uncertainty = High:
        → Check demand level for final classification

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📚 Citation

If you use this dataset or methodology, please cite:

@article{rababah2025single,
  title={Heuristic Scheduling Strategies for Single-Reactor Pharmaceutical 
         Batch Production Under Uncertainty: A Comparative Statistical 
         and Machine Learning Analysis},
  author={Rababah, Anfal},
  journal={ChemRxiv},
  year={2025},
  doi={10.26434/chemrxiv-2025-wq0tr}
}

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🔗 Related Work

This study complements multi-reactor scheduling research. For facilities with parallel processing capacity, different scheduling considerations apply.

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📬 Contact

Anfal Rababah

• Email: Anfal0Rababah@gmail.com
• ORCID: 0009-0003-7450-8907

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📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

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🙏 Acknowledgments

• JASP Team for open-source statistical software
• Python scientific computing community (NumPy, pandas, Matplotlib, Seaborn, SciPy)
• Anthropic's Claude AI for technical writing assistance