This repository stores the assignments and project of the Operation Research Application course. The topics of each assignment are organized roughly as follows, while the directory of each describes the assignment, OR model, and programming in details (see .pdf and .html files in each directory).

• Linear Programming (LP)
  • LP model with objective function and constraints.
  • Solve the model by the Python+Pulp solver.
• Markov chain (MC)
  • Description of Markovian property.
  • Steady-state probabilities of the state of the Markov chain.

• Stochastic Programming
  • Scenario Analysis and the EV solution calculations.
  • Deterministic Equivalent Problem (DEP) formulation of two-stage recourse problem (RP).
  • Expected Value of Perfect Information (EVPI) and value of the stochastic solution (VSS).
  • Monte Carlo sampling average approximation (SAA) in continuous scenarios.
• Decision Analysis and Value of Information
  • Decision tree forming: decision nodes, chance nodes, and the best production strategy.
  • Probabilities calculating: joint probabilities, marginal probabilities, and posterior probabilities.
  • EVPI and EVE calculation.

• Multi-facility location problem
  • Nonlinear programming (NLP) model solved by Python + Gurobi solver.
  • Graphic result of the solutions.
• Facility Location proofing
  • SFMS with rectilinear distances. A “short-cut” is introduced to observe that the slope at point x is equal to the sum of the weights to the left of x, minus the sum of the weights to the right of x. Prove and show why this is generally true?
  • SFMS with rectilinear distances. Given what you have shown in above question, prove that the median property gives an optimal solution to the problem.
• Cutting-stock problem
  • LP model formulation with piecewise linearization technique, solved by Python + Gurobi solver.
  • Graphic result of the solutions.

• Multi-Objective Decision Analysis (MODA)
  • Concept of Dominance.
  • Weighting method.
  • 𝜀 −Constraint Method.
  • Efficient Set.
• Data Envelopment Analysis (DEA)
  • Input-oriented DEA formulation.
  • Efficiency calculation: overall efficiency, technical efficiency, and scale efficiency.
  • Suggestion for decision making units.

• Use dummy process to deal with complicated network system, to handle arithmetic problem in network-DEA VRS model
• Update network framework in insurance industry.
• Update insurance data sets from 2002 to 2019.