Operations Research Mathematical Framework

Comprehensive mapping of mathematical domains to real-world OR applications

Every complex business problem can be broken down into mathematical foundations. This framework shows how I approach data challenges using proven mathematical principles from operations research.

1. Linear Algebra
Vector spaces, matrices, eigenvalues, decomposition
▸Core Applications
  • •Portfolio optimization (covariance matrices)
  • •Network flows (adjacency, incidence matrices)
  • •Recommendation systems (matrix factorization, SVD)
  • •PCA for dimensionality reduction
▸Advanced Uses
  • •Markov chains (transition matrices)
  • •Graph algorithms (shortest path)
  • •Power grid optimization (load flow)
  • •Image processing in quality control

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Profit ClarityData Mirror (OR)Algorithm Auditor
2. Optimization Theory
Calculus, gradients, KKT conditions, duality
▸Linear Programming (LP)
  • •Production scheduling
  • •Resource allocation
  • •Transportation problems
  • •Diet and blending problems
▸Integer Programming (IP/MIP)
  • •Facility location (warehouses, stores)
  • •Scheduling (staff, production, OR)
  • •Network design (telecom)
  • •Vehicle routing
▸Nonlinear/Convex
  • •Portfolio optimization (quadratic)
  • •Revenue management pricing
  • •ML model training
  • •Control systems

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System OptimizerProfit Clarity
3. Stochastic Processes
Random variables, distributions, expectation, conditional probability
▸Queuing Theory
  • •Hospital bed allocation
  • •Call center staffing
  • •Service desk optimization
  • •Traffic flow analysis
▸Markov Processes
  • •Customer behavior modeling
  • •Inventory with uncertain demand
  • •Maintenance scheduling
  • •Epidemic modeling
▸Monte Carlo
  • •Risk assessment in finance
  • •Project management (PERT)
  • •Complex system simulation
  • •Demand forecasting validation

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Predictive EngineSystem Optimizer
4. Graph Theory
Graphs, trees, connectivity, flows
▸Path Problems
  • •Route optimization / GPS navigation
  • •Network routing (telecom)
  • •TSP (delivery routes, circuit boards)
▸Flow Problems
  • •Maximum flow / minimum cut
  • •Supply chain network capacity
  • •Pipeline optimization
  • •Bandwidth allocation
▸Network Design
  • •Minimum spanning tree (utilities)
  • •Transportation logistics
  • •Assignment problems

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System Optimizer
5. Game Theory
Strategic decision-making, Nash equilibrium, utility theory
▸Applications
  • •Pricing strategies (competitive markets)
  • •Auction design (spectrum allocation)
  • •Contract negotiation (supply chain)
  • •Resource allocation (competition)
  • •Security games (patrol scheduling)

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System Optimizer
6. Dynamic Programming
Bellman equations, optimal control, recursion
▸Time-Based Optimization
  • •Inventory management (multi-period)
  • •Production planning over time
  • •Revenue management (dynamic pricing)
  • •Maintenance scheduling
▸Algorithms
  • •Resource allocation over time
  • •Shortest path (Dijkstra, Bellman-Ford)

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System OptimizerPredictive Engine
7. Real and Functional Analysis
Continuity, convergence, optimization on function spaces
▸Applications
  • •Continuous optimization problems
  • •Calculus of variations (optimal paths)
  • •Infinite-dimensional optimization
  • •Convergence analysis of algorithms
  • •Approximation theory for models

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Algorithm Auditor
8. Discrete Mathematics
Counting, permutations, combinations, set theory
▸Scheduling
  • •Staff rostering
  • •Production scheduling
  • •Timetabling (courses, exams)
▸Combinatorial Problems
  • •Assignment problems
  • •Bin packing (container loading)
  • •Set covering (crew scheduling)
  • •Combinatorial auctions

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System Optimizer
9. Numerical Analysis
Approximation methods, iterative algorithms, error analysis
▸Computational Methods
  • •Solving large linear systems (sparse)
  • •Gradient descent methods
  • •Newton's method (nonlinear opt)
  • •Numerical integration in simulation
  • •Finite element methods

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Predictive EngineSystem Optimizer
10. Statistical Analysis
Estimation, hypothesis testing, regression
▸Forecasting
  • •Demand forecasting (ARIMA)
  • •Time series analysis
  • •Regression models
▸Quality and Testing
  • •Statistical process control (SPC)
  • •Six Sigma methodologies
  • •A/B testing (pricing, products)
  • •Reliability analysis
  • •Survival analysis (churn, failure)
  • •Experimental design

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Predictive EngineProfit Clarity
11. Information Theory
Entropy, mutual information, coding theory
▸Applications
  • •Network capacity planning (Shannon)
  • •Data compression for logistics
  • •Communication system optimization
  • •Feature selection in ML

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Algorithm Auditor
12. Topology and Diff. Geometry
Continuous spaces, manifolds
▸Applications
  • •Robot path planning (config spaces)
  • •Network topology optimization
  • •Manifold learning (dimension reduction)

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System Optimizer

Cross-Cutting Real-World Examples

Supply Chain Optimization

  • ○Linear algebra: Network flow matrices
  • ○Stochastic processes: Demand uncertainty
  • ○Graph theory: Transportation networks
  • ○Optimization: Cost minimization
  • ○Statistics: Demand forecasting

Portfolio Optimization

  • ○Linear algebra: Covariance matrices
  • ○Stochastic processes: Asset price modeling
  • ○Optimization: Efficient frontier
  • ○Statistics: Parameter estimation
  • ○Numerical analysis: Solving systems

Hospital Scheduling

  • ○Stochastic: Queuing (patient arrivals)
  • ○Discrete math: Staff scheduling
  • ○Optimization: Resource allocation
  • ○Statistics: Demand patterns
  • ○Dynamic programming: Multi-period

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