Industrial Optimization: Models & Linear Programming

Overview

Introduces the theory, computation, and application of deterministic models to represent industrial operations. Includes linear programming formulation and solution using spreadsheet and algebraic languages software; simplex, big-M, revised simplex, and dual simplex algorithms for solving linear programs; introduction to the theory of simplex.

Syllabus

Introduction to Operations Research and Linear Programming

In this module, we will introduce OR including its brief history, methodologies that comprise the OR discipline etc. In addition, we will show its relationship to other disciplines, such as applied mathematics, computer science, industrial engineering, systems engineering, and economics. Then, we will introduce LP and its applications. Finally, we will illustrate an example of LP formulation and graphical solution.

Generalized LP Model and LINGO Software

In this module, we will introduce a commercial LP software package, LINGO. A very small problem (Wyndor Glass Co. prototype example) was introduced in Module 1 to illustrate the LP model, a problem small enough to solve graphically. We will now generalize the LP model for any application or problem size.

Introduction to Simplex

George Dantzig’s development of the simplex method made it possible to systematically solve incredibly complex problems. Simplex method, combined with powerful computer applications that perform the calculations contained in the simplex method, have made the use of Linear Programming applicable in many different fields. The correct use of the simplex method gives you the ability to construct and answer complex questions consisting of hundreds or thousands of dimensions, and makes you an invaluable member of a project team. In this module, we will introduce the simplex method for solving LP problems.

Simplex Continued—Breaking Ties and Dealing with Non-Standard Forms

Earlier, we demonstrated the simplex method on a LP that is in a standard form, i.e., the problem is maximization, all functional constraints are "≤" inequalities, and all variables are non-negative. However, it is very rare that a real-world problem is in a standard form. How, then, do we solve problems which are in non-standard forms? Instead of developing many variations of the simplex method, where its steps depend on each particular type of non- standard form, we transform the problem to the standard form and use the same simplex algorithm without any change in its rules.