Operational Research I

COURSE CONTENT

Section 1: Introduction to Decision Making, Decisions & Problems, Process & Conditions of Decision Making.

Section 2: Operational Research, Introduction, Historical Review, Operational Research Problems, Problem Solving Process and Methodology, Applications in Engineering discipline.

Section 3: Mathematical Programming, Linear Programming, Introduction, Concepts, Formulation and fundamental components of a Linear Programming problem, Mathematical modeling of problems.

Section 4: Graphical solution of Linear Programming problems, Algebraic calculation of extreme points, Revised Linear Programming problem, Multiple optima, Infeasible solutions, Presenting computational (software) Tools by realizing related exercises (Microsoft Excel)

Section 5: Simplex method, Symbols, Definitions, Simplex algorithm, Solving Linear Programming problems, Interpreting the final Simplex tableau, Presenting computational (software) tools by realizing related exercises (Solver @ Microsoft Excel, LINDO).

Section 6: Sensitivity analysis, Variations of objective function coefficients, Variations of constant terms of the constraints.

Section 7: Duality theory, Dual prices, Shadow prices, Extra cost, Primal and dual problem relations, Presenting computational (software) Tools by realizing related exercises (Solver @ Microsoft Excel, LINDO).

Section 8: Examples of Linear Programming with application in Engineering discipline and Industry. Presenting computational (software) Tools by realizing related exercises (Solver @ Microsoft Excel, LINDO, GAMS).

Section 9: Minimization Problems, Problems with Constraints >=. Artificial variables. Big M method, Adapted use of Simplex Method, Common errors & weaknesses of Linear Programming models.

Section 10: Integer Linear Programming, Concepts, Purpose, Formulation and fundamental components of Integer and Mixed Integer Linear Programming problems, 0-1 variables, Mathematical modeling of problems, Branch and bound method, Special logical relations & constraints, Presentation of Integer Programming problems.

Section 11: Introducing Non-linear Programming problems, Handling non-linear mathematical relationships, Linearization techniques.

LEARNING OUTCOMES

The course aims to educate undergraduate students in the scientific field of Operational Research and Management Science (Decision Making) presenting applications in the Engineering discipline. The purpose is to familiarize students with the basic knowledge, methods, techniques, and skills required for the analysis, modeling and optimization of systems and solving decision-making problems that often are related with the allocation of limited resources among competitive activities.

The course focuses on Mathematical Programming, specifically Linear Programming and proceeds to learning the fundamentals of Integer and Mixed Integer Linear Programming.

Under this course, the students are expected to:

• Understand the importance of Decision Making, the procedure and the quantitative methods that provide support.
• Identify and match the problem having to deal with typical Operational Research problems.
• Formulate and model a Decision Making problem in the context of typical Mathematical Programming framework.
• Choose the most appropriate method for solving optimization problems.
• Understand and interpret the results of the solution process and identify the most important parameters of the problem.
• Make a 360^o evaluation under multiple dimensions considered about the effect of the solutions outcome.
• Use modern computational (software) tools to construct and solve optimization problems as well as to analyze the solution derived.