Mathematical programming is an applied course that focuses on solving optimization problems involving linear functions of variables that satisfy linear inequalities. Such problems are important and numerous, including personnel and equipment assignments, optimal use of limited resources, distribution of goods through a transportation network, investment portfolio funding, project or maintenance scheduling, and many more. In this course, we concentrate on understanding the theory and implementation of the simplex algorithm, a powerful tool for solving linear programming problems.

Topics include linear optimization models, development and theory of the simplex algorithm, duality, sensitivity analysis, integer programming, and applications.

The textbook is An Introduction to Linear Programming and Game Theory, 3rd Edition, by P. R. Thie and G.E. Keough. Here's a copy of the syllabus and here's an errata sheet of typos for the first printing of the textbook.

Academic integrity is taken seriously and University procedures will be followed for any cases of cheating. See here for a description of these procedures.

Office Hours: (365 Carney, 2-3769) Mon. 1-2, Wed. 2-3, Fri. 11-12, or by appointment.

We will be using LP Assistant, a Java-based application written by Prof. Jerry Keough, Assoc. Professor Emeritus, Boston College. It can be downloaded from here.

 

Calendar of classes, homework assignments, and exams.

Note: this is a work in progress and no doubt will be changed; check back for updates.

Date	Section/Topic Covered		HW assigned	HW due
September
9	[2.2] intro; trail mix: ex.1, ex. 2, graphing feasible region; level curves of objective function
11	[2.2] trail mix finished: corner points, intro to sensitivity analysis; blending with percentages; production models begun		HW#1: due September 18
14	[2.3] production models, overtime
16	[2.3, 3.10, 2.4] Excel formulation and solutions; transportation model;
18	[2.5, 3.1] dynamic programming  model; end of Chapter 2. Chapter 3 begun: standard form of a LPP		HW#2: due September 25	HW#1
21	[3.2] systems of linear equations, canonical form of a LPP and basic solutions
23	[3.2] feasible basic solns vs corner points; LP Assistant demo
25	[3.3] feasible basic solns- geometric approach; introduction to simplex algorithm		HW#3: due October 5	HW#2
28	[3.4] theory of simplex algorithm Thms. 1 and 2
30	[3.4] Thm. 3
October
2	[3.5] simplex algorithm, example by hand			HW#3
5	[3.5] examples, LP Assistant
7	[3.6] artificial variables intro		HW#4: due October 14
9	[3.7] artificial variables: ex's
14	[3.7] artificial variables: ex's and redundant equations			HW#4
16	[3.8] cycling example, convergence theorem for simplex algorithm, corollary
19	Exam 1
21	[4.1] intro to dual: ICP and DOP
23	[4.2] def. of dual; max and min form of LPP
26	[4.2, 4.3] finding the dual interpretation of the dual
28	[4.3] more dual interpretations
30	[4.4] the duality theorem		HW#5: due November 6
November
2	[4.4] proof of duality thm corollaries
4	[4.4] reading soln to dual from final tableau
6	[4.4] reading soln to dual from final tableau			HW#5
9	more duality
11	[4.5] using CST		HW#6: due November 18
13	[5.2] B*, A*, c*, z_0*
16	[5.3] changes in the objective function
18	5.3 concluded		practice problems and soln	HW#6
20	[5.4] adding a new variable
23	Exam 2
30	[5.5] change in constraint constant [5.6] dual simplex algorithm
December
2	integer programming examples
4	integer programming models
7	integer prog. models
9	[8.4] data envelopment analysis
11	last day; review
14	Final 9:00 am