LOG904-126 Decision Modeling and Metaheuristics (Autumn 2024)

About the course

The seminar provides an introduction to the most effective Operations Research and Management Science techniques in the context of Optimization. It has two parts, the first one is based on mathematical models, and the second part on algorithmic coding. In the first part we apply the Linear Programming (LP), Integer LP and Non-LP methods in the Excel Solver to target logistic problems. We follow a modeling approach, from developing a mathematical model, selecting the appropriate solving method, to finally analyzing the results. Special emphasis is given to complex problems, such as multi-objective optimization.

In the second part we target metaheuristic methodologies, the class of modern heuristic procedures, which are able to handle large difficult problems. We cover two of the most efficient methodologies: GRASP and tabu search. We show how to apply them, when the classic optimization methods fail to solve a problem, by implementing an algorithm in Visual Basic for Excel.

Contents

1. Modeling and Mathematical Programming

 

We target valid models that accurately represent relevant characteristics of the optimization problem. We cover linear programming from a modeling approach; making emphasis in the Excel implementations. We target the different types of problems in terms of their results: One Single Optimal Solution, Alternate Optimal Solutions, Unbounded Solutions, and Infeasibility.

2. Integer Models

 

In this model, one or more variables in an LP problem must assume an integer value. We study the classical approach implemented in Excel to face problems in this model: the branch and bound methodology, based on the linear programming relaxation. We include Network flow problems, which constitute a class of important logistic problems.

3. Global and Multi-Objective Optimization

 

We cover those problems with a nonlinear objective function and/or one or more nonlinear constraints. They are formulated and implemented in virtually the same way as linear problems. However, the mathematics involved in solving NLPs is quite different than for LPs. Additionally, we cover problems with two or more objectives. We solve these problems, in which the different objectives are in conflict, with a goal programming approach.

4. Metaheuristics I

 

These methodologies are the class of modern heuristic procedures which are able to handle large difficult problems. In this section we cover memory-less methodologies, such as GRASP. We will implement the first two with the Visual Basic for Excel language.

5. Metaheuristics II

 

In this section we target advanced methods, which are mainly based in memory-based designs. They include Tabu Search and Strategic Oscillation. We implement it with the Visual Basic for Excel language.

The course is connected to the following study programs

• Master of Science in Logistics
• Experience-based Master in Logistics
• Master of Science in Sustainable Energy Logistics
• Exchange programme - Master's level
• Master of Science in Sustainable Transport and Urban Mobility

Recommended requirements

 Basic knowledge in optimization.

 Basic linear programming

The student's learning outcomes after completing the course

To learn how to translate business situations into formal models, identify the relevant data and investigate how those models enhance decision making.

Knowledge:

 Optimization models: linear, integer, and non-linear programming.

 Complex and mixed models: Multi-objective optimization

 Algorithm design. Visual basic in Excel

 

Skills:

 Given an optimization problem, be able to create mathematical models first with variables, functions and constraints, and then implement the model in the spreadsheets language.

 Identify the appropriate solver in Excel for an optimization problem. Analyze its outcomes.

 Create an algorithm and implement it in computer code to find good solutions for an optimization problems.

 Find and analyze results for a given problem.

 

General competence:

 Become proficient in fact-based management.

 Be able to analyze a real situation to identify the optimization problems involved, and to propose solutions to them based on mathematical models and algorithms.

Forms of teaching and learning

This is an applied course in which students will be exposed to a variety of decision modeling applications from business to industry with emphasis in supply chain management. The course will show how to use Excel spreadsheet to solve them effectively, and to create algorithms to obtain good solutions.

We alternate in the clasroom short theoretical descriptions with their applications in problem solving. Students will work on their computers to solve the problems themselves based on the teacher’s descriptions. It is very dynamic and with interaction, with questions and class participation.

Schedule:

From October 10th (Monday) to October 14th 202 (Friday) a daily class from 9:15 to 12:00. They follow the standard schedule: 9:15 – 10:00 + 10:15 – 11:00 + 11:15 – 12:00. These classes combine theory and exercises and the students have to brought their laptop computers to the classroom. They are complemented with two sessions on applications: Monday and Wednesday from 13:15 to 15:00.

Examination

Form of assessment: Open book exam: Solve two optimization problems with Excel.

• Proportion: 50 %

• Duration: 2 hours Friday 10:00 – 12:00

• Grouping: Individually

• Grading scale: Letter (A - F)

• Support material:

 

Homework (project):

Form of assessment: Implementation of a metaheuristic algorithm in Visual Basic for Excel (or similar computer language).

• Proportion: 50%

• Duration: Deadline: Saturday 23:00.

• Grouping: Group of 2 students

• Grading scale: Letter (A - F)

• Support material: