LOG733 Exact Optimization Methods in Logistics (Spring 2023)

About the course

The course will mainly focus on solving problems from logistics formulated as deterministic optimization models. Examples of problems include production problems, shortest path and knapsack problems. Modeling will be covered only briefly, as this is supposed to be known in advance. Problems treated include Linear Programming (LP) problems and Discrete Optimization problems. Emphasis will be put on the Simplex algorithm for Linear Programming and Branch and Bound search for discrete problems, but dynamic programming and other solution methods will also be treated.

The course is connected to the following study programs

• Master of Science in Logistics
• Master of Science in Economics and Business Administration
• Exchange programme - Master's level

Recommended requirements

LOG725 Transportation and Distribution is recommended. Some mathematical or quantitative background is needed.

The student's learning outcomes after completing the course

Knowledge

After completing this course, the students should be able to:

• describe a taxonomy for mathematical models based on the demarcation between static and dynamic models, linear and nonlinear models, integer and continuous variables, and deterministic and stochastic models
• define the following objects from linear algebra: scalars, vectors, and matrices
• define the following operations from linear algebra: scalar/dot/inner products, addition, and multiplication of matrices, and taking the transpose and the inverse of a matrix
• explain four assumptions of linear programming problems: proportionality, additivity, divisibility, and certainty
• explain the relationship between the primal and the dual of a linear programming problem
• describe the principles of dynamic programming

 

Skills

After completing this course, the students should be able to:

• represent a system of linear equations using matrix notation, and solve systems using the Gauss-Jordan method
• represent and solve linear programming problems with two variables using the graphical method
• reformulate a linear programming problem to standard form and augmented form
• execute the simplex algorithm in tabular form to solve linear programming problems
• find the dual of a linear programming problem
• perform sensitivity analyses for linear programming problems to calculate the effects of changes in objective function coefficients and right-hand side coefficients
• solve integer programming problems and binary integer programming problems using branch-and-bound with LP-relaxations being solved using the (dual) simplex method
• solve binary integer programming problems using implicit enumeration
• generate Gomory cuts and solve integer programming problems using a cutting plane algorithm
• formulate and solve deterministic problems using dynamic programming

 

General competence

After completing this course, the students should be able to:

• work independently or in small groups to solve tasks that require patience, a high degree of precision, and the ability to conduct and verify numerical calculations

Forms of teaching and learning

3 hours of lectures per week.

Coursework requirements - conditions for taking the exam

• Mandatory coursework: Assignment(s)
• Courseworks given: 2
• Courseworks required: 2
• Presence: Not required
• Comment: There will be two mandatory assignments, both needs to be passed in order to take the final exam.

Examination

• Form of assessment: School assessment

• Proportion: 100%

• Duration: 4 hours

• Grouping: Individual

• Grading scale: Letter (A - F)

• Supported material:Kalkulator med tomt minne+generell ordbok morsmål/norsk/engelsk i papirformat