POM Homepage - Teaching

Tentative Schedule

(check for regularly for updates!)

Lesson 1	Introduction to Linear Programming & Simplex Algorithm
Date	March 5, 2009
Topics	outline general procedure (grading policy, topics to be covered, etc.) make sure everyone fulfills requirements introduction to linear programming motivation basic resource allocation problem keywords model types assumptions model formulation special cases types of lp's simplex algorithm setting up the initial tableau improving the solution calculate next tableau how to identify special cases
required readings	Chapter 3 [Introduction to Linear Programming] Chapter 4 [Solving Linear Programming Problems: The Simplex Method] in Introduction to Operations Research, by Frederick S. Hillier & Gerald J. Liebermann [you'll find this book in the library: english version, german version]
recommended readings	Chapter 2 [An Introduction to Linear Programming] Chapter 5 [Linear Programming: The Simplex Method] in An Introduction to Management Science by Anderson, Sweeney & Williams [you'll find this book in the library: english version]
Slides	[0 Vorbesprechung] [1 Introduction to Linear Programming] [2 Simplex Algorithm]
Assignment	[Assignment 1]
Solution	[Assignment 1 (hints)]
Links	rent a notebook (just fill out the form and I'll sign it for you) download Xpress (enter a valid email-adress - you can download it immediately - they'll send you the password required for installation by email) how to use Excel Solver for optimization (example)

Lesson 2	Introduction to Xpress-MP
Date	March 19, 2009
Topics	basic steps flow control structs indices and ranges selections loops input data from files dynamic arrays create & finalize
required readings	Chapter 1 [Getting started with Mosel] Chapter 2 [Some illustrative examples] Appendix A [Good modeling practice with Mosel] in Xpress Mosel User Guide
Slides	[3 Introduction to Xpress-MP] example1.mos example2.mos example3.mos example4.mos example4.dat (reading sets explicitely) example4b.mos example4b.dat (reading sets implicitely)
InClass Examples	InClass3_ex1.mos InClass3_ex2.mos InClass3_ex3.mos InClass3_ex4.mos InClass3_ex4.dat (reading sets explicitely) InClass3_ex4b.mos InClass3_ex4b.dat (reading sets implicitely)
Assignment	[Assignment 2]
Solution	ass2_1_mines.mos ass2_1_mines.dat ass2_1_mines_dynamic.mos ass2_1_mines_dynamic.dat ass2_2_coco.mos ass2_2_coco .dat ass2_2_coco_dynamic.mos ass2_2_coco_dynamic .dat

Lesson 3	Modeling techniques & some Applications
Date	March 26, 2009
Topics	typical constraints upper/lower bounds flow constraints material balance constraints (BOM & multi-period) quality requirements blending constraints etc. Xpress Advanced building models (reviewed) debugging sparsity sets status of solution functions & procedures Applications Transportation Problem Assignment Problem
required readings	Chapter 8 [The Transportation and Assignment Problems] in Introduction to Operations Research, by Frederick S. Hillier & Gerald J. Liebermann [you'll find this book in the library: english version, german version] Chapter 2 [Typical LP model constructs] in Applications of optimization with Xpress, by Christelle Gueret, Christian Prins & Marc Sevaux Chapter 3 [More advanced modeling features] Chapter 6 [Correcting syntax errors in Mosel] Chapter 8 [Sets] Chapter 9 [Functions and procedures] in Xpress Mosel User Guide
recommended readings	Chapter 7.1 & 7.2 [Transportation and Assignment Problems] in An Introduction to Management Science by Anderson, Sweeney & Williams [you'll find this book in the library: english version]
Slides	[4 Modeling Techniques] [5 Xpress Advanced] [A1 Transportation] [A2 Assignment Problem]
InClass Examples	(use the provided data files - do NOT change them!) A1 Transportation_1.dat A1 Transportation_2.dat (choose the one you like best) A2 Assignment_1.dat A2 Assignment_2.dat (choose the one you like best) A1 Transportation readDataFromFile.mos A1 Transportation dynamicArrays.mos A2 Assignment readDataFromFile.mos A2 Assignment dynamicArrays.mos
Assignment	[Assignment 3] (use the provided data files - do NOT change them!) ass3 - Transportation.dat ass3 - cocoMultiPeriod.dat ass3_sudoku6x6.dat ass3_sudoku9x9.dat
Solution	ass3_transportation.mos ass3_cocoMultiPeriod.mos

Lesson 4	Advanced Modeling Techniques
Date	April 2, 2009
Topics	special kinds of objective functions minimax modeling with binary variables do/don't do decisions choice among serveral possibilities simple implications general implications dichotomies: either/or-constraints Non-Linearities: Absolute Values optimize sum of absolute deviations optimize largest absolute deviation Non-Linearities (cont.): piecewise linear objective functions fixed setup costs price breaks economies of scale
required readings	Chapter 12.1 - 12.4 [Integer Programming] in Introduction to Operations Research, by Frederick S. Hillier & Gerald J. Liebermann [you'll find this book in the library: english version, german version] Chapter 3 [Integer Programming Models] in Applications of optimization with Xpress, by Christelle Gueret, Christian Prins & Marc Sevaux
Slides	[6 Advanced Modeling] [A3 Transshipment]
InClass	templates A3 Transshipment simple_template.mos data files A3 Transshipment simple.dat solution A3 Transshipment simple.mos
Assignment	[Assignment 4] (use the provided data files - do NOT change them!) templates ass4_cocoMultiPeriodTempClosure_template.mos ass4_pork_template.mos ass4_allUnitDiscount_template.mos data files ass4_cocoMultiPeriod.dat ass4_PorkProduction.dat solution ass4_cocoMultiPeriodTempClosure.mos ass4_pork.mos ass4_allUnitDiscount.mos

Lesson 5	Duality and Sensitivity Analysis
Date	April 23, 2009
Topics	Theoretical Background dual problems primal-dual relationships complementary slackness price theorem Interpretation & Sensitivity Analysis shadow prices reduced costs economic interpretations to solve - or not to solve - dual problems graphically Simplex Microsoft Excel's Solver Xpress
required readings	required readings Chapter 6 [Duality Theory and Sensitivity Analysis] in Introduction to Operations Research, by Frederick S. Hillier & Gerald J. Liebermann [you'll find this book in the library: english version, german version]
recommended readings	Chapter 3 [Sensitivity Analysis and Interpretation of Solution] Chapter 6 [Simplex-Based Sensitivity Analysis and Duality] in An Introduction to Management Science by Anderson, Sweeney & Williams [you'll find this book in the library: english version]
Slides	[7 Duality & Sensitivity] ResAllocation.xls
Assignment	[Assignment 5] (use the provided data files - do NOT change them!) templates ass5_hireandfire_template.mos ass5_incrementalPriceBreaks_template.mos solutions ass5_hireandfireBackOrder.mos ass5_cocoMultiPeriodPermClosure.mos.mos

Lesson 6	Final Exam
Date	April 30, 2009, (10-12h, Seminarraum 2)
Topics	to be announced (basically just everything we've covered so far)
Final Grades	grades.txt