ISEN 320: Operations Research I 

Free Resources 

Below are links to helpful, free resources to use during the class. I took this class with Dr. Aprahamian during the Fall 2022 semester.  Here is some advice for ISEN 320:

• The first part of the class, learning how to write mathematical equations (linear program and integer program) to model optimization scenarios, is best accomplished by sheer practice. The problems follow a certain pattern when writing the equations, so the best way to be able to recognize the patterns on the test is to repeat a variety of problems. 

• For the simplex method, it is essential to understand how to properly do the row operations within each tableau to be able to find the correct answer. One small algebra mistake can be costly. That's why you can use the automatic Simplex Method Calculator below to help you find where you made a mistake. 

Quick Guides

Quick Guide 3: Simplex Method  

Contains key points on the definition of simplex method and basic/non-basic variables, step-by-step procedure/ example for the standard simplex method, explanation of alternative optimal solutions and unboundedness, Bland’s rule of termination. 

Quick Guide 4: Big M & Two Phase Initialization  

Contains key points on when to use initialization, definition of artificial variables, step-by-step procedure/ example for the two phase method, step-by-step procedure/ example for the big M method, the fundamental theorem of LPs. 

Quick Guide 5: Graphical Solutions  

Contains key points on step-by-step procedure/ example to find graphical solutions, plotting the feasible region, creating isotropic lines, effects of the objective function on the feasible region, unbounded and infeasible graphical solutions, classifying constraints as binding or non-binding. 

Quick Guide 6: Duality Part 1  

Contains key points on the definition of duality, the general form of the primal/ dual LPs, and example of creating the dual from the primal, definition of weak duality, definition of strong duality, how to find the optimal dual values, applied example problem.

Quick Guide 7: Duality Part 2

Contains key points on the definition of complementary slackness, example of complementary slackness conditions, using complementary slackness to check if an LP is optimal, example of determining the optimal solution of primal/ dual LPs, special rules for converting a primal into a dual LP, the economic interpretation of dual LPs, shadow price definition, applied example of dual LP economic interpretation. 

Quick Guide 8: Sensitivity Analysis

Contains key points on the definition of sensitivity analysis, the general format of variables in the simplex tableau, effects of changing a basic variables' value with example, effects of changing a non-basic variables' value with example, effects of changing a right hand side of a constraint with example.