SA305 – Linear Programming Spring 2014
Last updated: January 6, 2014
Course coordinator
Asst. Prof. Nelson Uhan, uhan@usna.edu
Course description
Operations research (OR) is a broad field which, loosely speaking, investigates how mathematical techniques can be used to solve “real-life” decision-making problems. This course provides an introduction to linear programming, a fundamental technique used in OR. In particular, the course focuses on formulating mathematical optimization models (also called mathematical programs ), and understanding the mathematical underpinnings of linear programming algorithms.
Textbook
D. Rader,
Deterministic Operations Research: Models and Methods in Linear Optimization
, Wiley, 2010.
Schedule This schedule is subject to change.
Unit
Overview
Modeling
Week Topic Readings Homework
1 Introduction to operations research 1.1
1/7 – 1/10 Introduction to optimization modeling, classification of optimization models 1.2, 1.3
Graphical solution of optimization models, sensitivity analysis 1.2
1.1abcd using trial-and-error
1.1abcd, 1.2
2 Resource allocation models, introduction to GMPL and GUSEK
1/13 – 1/17 Work scheduling models
Blending models
3 Production process models
1/20 – 1/24 Production process models, cont.
2.1
2.2
2.4
2.5
2.5
2.1, 2.3*
2.6
2.11*, 2.12
2.9
2.10*
4
1/27 – 1/31
5
Multiperiod models
Sets, summations, for statements
Resource allocation models, revisited
Work scheduling models, revisited
2/3 – 2/7 Blending models, revisited
Production process models, revisited
6 Multiperiod models, revisited
2/10 – 2/14 Review
Exam 1
2.6
2.3
2.1
2.2
2.4
2.5
2.6
inventory, finco
2.3
† , 2.24
† , diet* †
2.6
† (challenge: 2.7, 2.8)
2.13*
2.9
†
2.20
†
† , 2.14
, 2.10
†
, 2.22
†
†
, 2.16
†
* = Formulate a model on paper and write accompanying GMPL code.
† = Formulate a model using symbolic input parameters.
1

Unit
Algorithms
Duality
Modeling revisited
Week Topic
7 Introduction to algorithm design
2/17 – 2/21 Improving search: finding better solutions
8 Improving search: convexity and optimality
2/24 – 2/28 Improving search: review
Geometry and algebra of corner points
9 Geometry and algebra of corner points, cont., fundamental theorem of LP
3/3 – 3/7 Linear programs in canonical form
Basic solutions in canonical form LPs
10
3/10 – 3/14
Spring Break
11 The simplex method
3/17 – 3/21 The simplex method, cont.
The simplex method: review
12 Degeneracy, convergence, multiple optimal solutions
3/24 – 3/28 The two-phase simplex method
Bounds and the dual LP
13 Weak and strong duality, complementary slackness
3/31 – 4/4 Review
Exam 2
14 Duality review, maximin objectives
4/7 – 4/11 Maximin and minimax objectives
LP duality and game theory
15 An economic interpretation of LP duality
4/14 – 4/18 Introduction to networks and the shortest path problem
Modeling with the shortest path problem
16 Modeling with the shortest path problem, cont.
4/21 – 4/25 Review
Review
17
4/28 – 4/29
Review
8.1
8.1
8.1
8.3
8.4
9.1, 9.2
9.3
Readings Homework
5.1–5.2
6.1–6.2
6.1, 6.2, 6.8, 6.9
6.14, 6.18
6.3
6.1–6.3
7.1
7.1–7.2
2.8, 7.3
7.3
7.2, 7.3
7.4
7.14
7.16, 7.17
8.1, 8.2
8.3, 8.8
8.7
8.11ab, 8.12a
9.1, 9.2, 9.3, 9.4
9.5, 9.7
9.1–9.3, 2.7
pirates* †
2.7
2.30
† handout rock-paper-scissors
9.6
2.9
2.9
2.9
cars
2.42
rental*
2.39
* = Formulate a model on paper and write accompanying GMPL code.
† = Formulate a model using symbolic input parameters.
2