Optimization Methods · interactive study notes

Optimization
Methods

Linear programming, worked through from end to end. How to turn a problem stated in words into a model, how to solve it by hand in two dimensions and by algorithm in any number, and how to read out of the answer what each scarce resource is really worth.

01Operations Research and the Modelling Approach
What a model is, what it is for, and the three parts every optimisation problem has.
02Introduction to Linear Programming and Formulation
The four assumptions, the standard forms, and the six rules that convert any linear programme into one shape.
03The Graphical Method
Draw the region, find the corners, slide the profit line. Every later idea is visible in this picture.
04The Simplex Method I: Theory
What a corner is algebraically, and why checking neighbours is enough to certify a global optimum.
05The Simplex Method II: The Tableau Algorithm
Pivoting in full, and how to read shadow prices and alternate optima straight off the final tableau.
06Big-M, Two-Phase Methods and Special Cases
What to do when there is no obvious starting point, and how to diagnose an infeasible or unbounded model.
07Duality and Sensitivity Analysis
The same problem seen from the other side: what the resources are worth, and how far the answer can be trusted.

How each page is laid out

Every page follows the same shape, so you always know where you are.

Start here — what the idea actually is, before any notation.

The theory — definitions in boxes, results with their proofs, and a diagram wherever a picture beats a paragraph.

Solved problems — every one worked step by step, with the answer boxed.

Applications, common mistakes, practice problems and a summary — in that order, every time.

The diagrams are live Sliders, buttons and steppers change the mathematics in front of you. Nothing needs installing and nothing is fetched from a network: every diagram is drawn in your browser.

One example, all the way through

A furniture workshop makes tables and chairs. A table needs 5 hours of carpentry and 2 of finishing; a chair needs 3 and 4. There are 120 carpentry hours and 90 finishing hours a week, and the profits are ₹450 and ₹300.

That one problem is formulated in the first lesson, solved graphically in the third, solved again by simplex in the fifth, and finally priced in the seventh, where the tableau reveals that a carpentry hour is worth ₹85.71 at the margin and a finishing hour only ₹10.71. Watching a single problem acquire more meaning at each stage is the point of the whole sequence.

The answer, for referenceMake 15 tables and 15 chairs for a weekly profit of ₹11,250, with both resources fully consumed — and the plan survives any table profit between ₹150 and ₹500.

Present it

The whole set is also a 252-slide deck you can run straight in the browser, full screen, with no download and nothing to install. It is built from the same source as these pages, so the two cannot disagree.

Open the slides ▶

Arrow keys or space to move, N for the explanation panel, O for a thumbnail overview, F for full screen. Every lesson is reachable from the picker at the top.

Every slide is explained

Under each slide sits a written note saying what the slide claims, why it is true and where it fails, so the deck can be read on its own rather than only presented. It is on by default; press N to hide it.

Two PowerPoint copies

The study deck carries the written explanation on the slide itself, so it reads on its own. The presenter deck is the same lessons with those explanations moved into the speaker notes, which is a shorter deck to stand in front of.

OptimizationMethods