This section presents selected case studies in mathematical optimization, algorithm design, and decision-support systems. Each case follows the problem from formulation through solution design, implementation, and computational evaluation. The focus is on translating operational requirements into rigorous models, scalable algorithms, and practical software solutions.
Mixed-Integer Linear Programming · Lagrangian Relaxation · Parallel Optimization
An integrated pricing-and-replenishment planning problem is formulated across products, suppliers, distribution centers, price options, and planning periods. The model jointly determines price selection, sales, supplier purchasing, inbound timing, and inventory while enforcing supplier availability and distribution-center receiving and storage capacities.
The solution framework combines an exact MILP benchmark with sequential and parallel SKU-decomposed Lagrangian relaxation. A bounded capacity-repair procedure converts relaxed solutions into feasible operating plans. Computational experiments demonstrate scalability from small benchmark cases to a 20,000-SKU instance with 43.2 million variables and approximately 25.0 million constraints.
Mixed-Integer Linear Programming · Genetic Algorithm · Dynamic Programming
A complete coverage-routing problem is formulated for an agricultural vehicle operating in a field with obstacles. The solution architecture combines an exact MILP model for optimal benchmarking with a scalable hybrid GA–DP method for larger instances. The case study covers problem formulation, algorithm design, implementation structure, and comparison of solution quality, runtime, and heuristic convergence.
Exploratory Data Analysis · Feature Engineering · Baseline Models · XGBoost · SHAP Analysis
A complete machine-learning workflow is developed to generate probabilistic supplier lead-time forecasts across a large wholesale product catalog using conditional quantile prediction. The case study covers exploratory analysis, data cleaning, feature engineering, dataset construction, baseline benchmarking, XGBoost quantile models, validation, and SHAP analysis. Predicted lead-time quantiles support service-level-based safety stock, reorder-point, and inventory-planning decisions.