Lectures	Date	Subjects Covered	Lecture Contents/Supplementary Materials
Lecture 34	Nov. 28	Dynamic Programming	Dynamic Programming greedy algorithm for interval scheduling problem recursive algorithm for interval scheduling problem recursive algorithm for multistage city commuters problem
Lecture 33	Nov. 26	Network Flows	Network Flows and the Network Simplex Method: spanning trees, basic solutions, phase I by adding artificial variables/arcs, finding an entering variable/arc Xij to get a unique loop, increase Xij (or decrease if Xij was at upper bound) until a basic variable (or Xij) reaches a bound (leaves the basis). Theory and EXAMPLE.
Lecture 32	Nov. 24	Network Flows	Network Flows and the Network Simplex Method (spanning trees and basic solutions)
Lecture 31	Nov. 21	Network Flows	Network Flow Models: Min Cost (Transportation and Assignment Problems); Max Flow; Shortest Path.
Lecture 30	Nov. 19	Network Flows	Network Flows
Lecture 29	Nov. 17	Solving Integer Programs Network Flows	Branch & Bound Methods (fathom using: infeasibility; bounds; feasibility) Cutting Plane Methods (Chvatal-Gomory Cuts; Gomory Cuts) Network Flows
Lecture 28	Nov. 14	Solving Integer Programs	Branch & Bound Methods (fathom using: infeasibility; bounds; feasibility) Cutting Plane Methods (Chvatal-Gomory Cuts; Gomory Cuts)
Lecture 26-7	Nov. 10-12	Integer Programming	Set Covering/Partitioning: Cutting Stock Problem and Knapsack Problem Branch and Bound for Knapsack Problem pdf file ( useful AMPL link)
Lecture 25	Nov. 5	Integer Programming	Set Covering/Partitioning: Cutting Stock Problem and Knapsack Problem Branch and Bound for Knapsack Problem pdf file
Lecture 24	Nov. 3	Integer Programming	Facility Location AMPL files considered: kilroy.mod; kilroy.dat; runkilroy; kilroy.txt.
Lecture 23	Oct. 31	Integer Programming	Logical Constraints: e.g. cardinality, exclusion, implication, fixed cost. AMPL files considered: gandhi.mod; gandhi.dat; rungandhi; gandhi.txt.
Lecture 22	Oct. 29	Robust Optimization	Decision making under uncertainty; complete the Bertsimas-Sim model; assignment problem example
Lecture 21	Oct. 27	Robust Optimization	Decision making under uncertainty; Bertsimas-Sim model
Lecture 20	Oct. 24	Robust Optimization	Decision making under uncertainty; Soyster's model; Derivation using the dual of the subproblem
Lecture 19	Oct. 22	Robust Optimization	Decision making under uncertainty; Soyster's model
Lecture 18	Oct. 20	Modelling Uncertainty	Decision making under uncertainty; the farmer's problem
Midterm	Oct. 17	Midterm exam 7-9PM	Midterm Exam Problems; Question: What is the best strategy for writing an exam? Start with easy problems? Or start with problems with high marks? Or ??? midterm marking scheme (with some solutions) Problem #4 AMPL files: cargomid.mod; cargomid.dat; runcargo
Lecture 17	Oct. 17	Modelling Uncertainty	Decision making under uncertainty; facility location 2-stage stochastic optimization with recourse
Lecture 16	Oct. 15	Modelling Uncertainty	Decision making under uncertainty; facility location deterministic example; AMPL files: facstoch.mod; facstoch.dat; runfacstoch;
Lecture 15	Oct. 10	Parametric Programming	Review of parametric programming (RHS and obj. coefficients)
Lecture 14	Oct. 8	Sensitivity Analysis	Review of sensitivity analysis (using revised simplex method), cont... MATLAB files: oct6.m, logoct6.txt,
		Simultaneous Changes in the Data	Simultaneous changes for objective costs (corresp. to basic and nonbasic variables). Simultaneous changes for RHS (resources). (See two theorems in course notes/text.) MATLAB files for example done in class: oct6.m, oct8log.txt,
		Dual Simplex Method	Motivation and review of dual simplex method; recovering optimality after an addition of an extra constraint and/or perturbation of RHS.
Lecture 13	Oct. 6	Sensitivity Analysis	Review of sensitivity analysis (using revised simplex method), cont... MATLAB files: oct6.m, logoct6.txt,
		Dual Simplex Method	Motivation and review of dual simplex method
Lecture 12	Oct. 3	Sensitivity Analysis	Review of sensitivity analysis (using revised simplex method), cont... files used from problem 2 in assignment 2: blendgas.mod, blendgas.dat.
		Sensitivity Analysis via AMPL	AMPL data file: gtc-resconst.dat. Model is resconstr.mod. Transcript of AMPL session gtc.log. A listing of sensitivity-analysis and some other useful AMPL commands: ampl-cmd.txt. See also: Some Hints for Getting More from AMPL and CPLEX, including list of all the cplex options available in AMPL; The CPLEX distribution of AMPL examples can be found.
Lecture 11	Oct. 1	Sensitivity Analysis	Review of sensitivity analysis (using revised simplex method), cont...
Lecture 10	Sept. 29	Sensitivity Analysis	Review of sensitivity analysis
Lecture 9	Sept. 26	Simplex Method cont...	Review of the simplex method (with an economic interpretation).
		Modelling with AMPL (sets before variables)	In modelling, we see that it helps to find the sets before the decision variables, e.g. for (a simplified version of) problem 3 in assignment 1: ass1p3.mod; ass1p3.dat.
Lecture 8	Sept. 24	Simplex Method	Review of the simplex method (with an economic interpretation).
Lecture 7	Sept. 22	LP Formulations (and AMPL)	Minimum Cost Flow Problem (as extension of the transportation problem, e.g. transshipment problem; production scheduling problem.) using AMPL and subsets: mincostflow.mod; mincostflow.dat; runmcf (from AMPL/CPLEX notes and a local copy)
		Simplex Method	Review of the simplex method (with an economic interpretation).
		Sensitivity Analysis via AMPL	AMPL data file: gtc-resconst.dat. Model is resconstr.mod. Transcript of AMPL session gtc.log. A listing of sensitivity-analysis and some other useful AMPL commands: ampl-cmd.txt. See also: Some Hints for Getting More from AMPL and CPLEX, including list of all the cplex options available in AMPL; The CPLEX distribution of AMPL examples can be found.
Lecture 6	Sept. 19	Duality/Shadow Prices	Duality and shadow price interpretation of dual variables.
		LP Formulations	Modeling problems with piecewise linear functions, and with absolute values, e.g. minimize \|x\|. (Section 2.5 in the notes)
Lecture 5	Sept. 17	LP Review - Duality	Derivation of the linear programming dual for different forms of LP done using a game theory approach; including an economic interpretation. (The diet problem was used to illustrate the approach.)
Lecture 4	Sept. 15	LP Formulations (and AMPL)	multiple sets again: (From AMPL-a tutorial [pdf- pgs 7-11] (multiple warehouses; multiple customers) multpaintset.mod; multpaintset.dat; With integer (0,1 - binary) constraint: integprogr1.mod; integprogr1.dat; quadratic objective function A list of some of the AMPL commands were used during lecture 4.
Lecture 3	Sept. 12	Software (AMPL/Solvers) cont...	feed blending example [pdf-2 pgs]; multsets.mod; multsets.dat; runmultsets; (Alternate blending example [html]) A list of AMPL commands used during lecture 3. A listing of sensitivity-analysis and some other useful AMPL commands: ampl-cmd.txt.
		LP Formulations (and AMPL)	multiple sets again: multpaintset.mod; multpaintset.dat; And with integer (0,1 - binary) constraint: integprogr1.mod; integprogr1.dat;
Lecture 2	Sept. 10	Software (AMPL/Solvers)	AMPL FAQ; Intro. to AMPL-a tutorial [pdf-13 pgs] paint.mod; paint2.mod; paint2.dat; paint2alt.dat; paintset.mod; paintset.dat; paintsetalt.dat; A list of AMPL commands used during the lecture. A listing of sensitivity-analysis and some other useful AMPL commands: ampl-cmd.txt.
Lecture 1	Sept. 8	Introduction/Administrivia/LP-review	Lecture 1 Slides [ppt] Nobel Lecture/75 - "best use of scarce resources" (local copy) AMPL file for assignment 1: examp1.mod AMPL links: AMPL at ILOG; AMPL FAQ.

Supplementary Material, Fall'08

This webpage contains files used during the lectures. Additional material/links are also included. Be aware that this webpage is continually being polished/changed.