Operational research — Study Path Agent

Chapter 1

OR foundations & modeling mindset

1

Problem structuring: objectives, decisions, constraints, stakeholders

2

Units, scaling, and linearization intuition (what’s reasonable to assume)

3

Feasibility vs optimality; sensitivity vs robustness (conceptual)

4

Model validation & verification (sanity checks, boundary tests)

5

Communicating OR results (assumptions, tradeoffs, story)

Chapter 2

Optimization basics (LP core)

6

Linear programming formulation (standard form, constraints, bounds)

7

Geometry of LP (polyhedra, extreme points, degeneracy intuition)

8

Duality & complementary slackness (interpretation + calculations)

9

Simplex & interior-point overview (when each is used)

Chapter 3

Discrete optimization (integer & combinatorial)

10

MILP modeling patterns (big-M, indicator constraints, SOS, piecewise linear)

11

Branch-and-bound / branch-and-cut intuition (bounds, cuts, gaps)

12

Common OR combinatorial problems (assignment, knapsack, set cover)

13

Graph modeling for OR (nodes/arcs, paths, cuts, connectivity)

14

Decomposition methods (Benders, Dantzig–Wolfe / column generation)

Chapter 4

Stochastic models & decision-making under uncertainty

15

Probability essentials for OR (random variables, expectation, conditioning)

Chapter 5

Simulation & system performance analysis

16

Discrete-event simulation building blocks (events, entities, resources)

Chapter 6

Implementation, analytics workflow & OR practice

17

Data-to-model pipeline (cleaning, feature creation, parameter estimation)

18

Deployment & monitoring (drift, re-optimization triggers, SLAs)

19

Ethics, fairness, and risk in decision support

20

Capstone: end-to-end OR case study (choose: routing, staffing, inventory, pricing)