TecnoCampus Foundation
eCampus
University Business
eCampus

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General information

Subject type: Mandatory

Coordinator: Maria Dolors Celma Benaiges

Trimester: Second term

Credits: 3

Teaching staff: 

Rosa Herrero Antón

Academic year: 2025

Teaching course: 1

Languages ​​of instruction

  • Spanish

Classes are taught in Spanish, but some materials may be in English.

Competencies / Learning Outcomes

Basic skills

  • CB6-Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context

  • CB7. That students know how to apply the knowledge acquired and their ability to solve problems in new or little-known environments within broader (or multidisciplinary) contexts related to their area of ​​study. 

Specific skills

  • CE2. Apply tools and methodologies that facilitate creative and innovative thinking in everyday situations related to the supply chain environment and logistics and maritime businesses.

  • CE4. Strategically manage business innovation processes in the supply chain and the maritime business, from diagnosis to application, being able to align resources, capabilities and skills to implement them

  • CE7. Manage (plan, schedule and control) the flow of materials and information (supply chain flow) through the coordinated direction and management of the areas of purchasing, production and physical distribution of the company. 

Transversal competences

  • CT1. Show willingness to learn about new cultures, experiment with new methodologies and encourage international exchange in the context of logistics, supply chain and maritime business.

  • CT2. Demonstrate entrepreneurial leadership and leadership skills that build personal confidence and reduce risk aversion. 

  • CT3. Develop tasks applying the acquired knowledge with flexibility and creativity and adapting them to new contexts and situations. 

Presentation of the subject

This subject introduces students to mathematical modeling to solve logistics problems with uncertainty and risk.

 

 

Contents

Topic 1: Introduction 

1.1 Concept of mathematical model 

1.2 Types of systems 

1.3 Methodologies and algorithms 

Topic 2: Graph theory 

2.1 Definition, representation and topology 

2.2 Examples of application 

2.3 Matrices associated with a graph and isomorphism of graphs 

2.4 Algorithms in graphs 

2.4.1 Minimum partial tree and Prim and Kruskal algorithms 

2.4.2 Shortest path and Dijkstra algorithm 

2.4.3 Flow problem in a network and the Ford-Fulkerson algorithm 

Topic 3: Stochastic processes 

3.1 Definition of stochastic processes and random variables 

3.2 Examples and special cases 

3.3 Discrete-time Markov chain 

3.4 Continuous time Markov chain 

Topic 4: Trade Traveler Problem 

4.1 Definition of the problem 

4.2 Most used variants 

4.3 Resolution methodologies 

Topic 5: Vehicle Route Problem 

5.1 Definition of the problem 

5.2 Most used variants 

5.3 Resolution methodologies 

Topic 6: Nonlinear programming 

6.1 Definition and qualification of nonlinearity 

6.2 Examples 

6.3 Special case: problems with linear constraints 

6.4 Karush-Kuhn-Tucker conditions and interpretation of Lagrange multipliers 

6.5 Resolution methodologies 

Activities and evaluation system

With the aim of collecting evidence of the achievement of the expected learning outcomes, the following evaluative activities will be carried out.

10% Graph Theory: exercises to be solved in pairs through the virtual classroom based on the theoretical content. 

10% Stochastic Processes: exercises to be solved in pairs through the virtual classroom based on the theoretical content. 

15% Traveling Salesman Problem: exercises to be solved in pairs through the virtual classroom based on the theoretical content. 

15% Vehicle Routing Problem: exercises to be solved in pairs through the virtual classroom based on the theoretical content. 

50% Individual final exam: examination of the content of the entire subject. 

The final grade of each student will be calculated according to the corresponding percentages.

Considerations: 

- It is necessary to obtain a mark superior to 4 in the final examination to pass the asignatura. 

- The teacher will inform you of the dates and format for submitting the exercises. An activity not submitted or submitted late and without justification (judicial summons or medical matter) counts as a 0. 

- It is the responsibility of the student to avoid plagiarism in all its forms. In the case of detecting a plagiarism, regardless of its scope, in some activity will correspond to have a mark of 0. In addition, the teacher will communicate the situation so that applicable measures are taken in the matter of sanctioning regime. 

Bibliography

Basic

Golden, BL, Raghavan, S., Wasil, EA (2008). The vehicle routing problem: latest advances and new challenges (Vol. 43). Springer Science & Business Media.

Grassmann, WK, Tremblay, JP (2000). Logic and Discrete Mathematics. Prentice Hall.

Gutin, G., Punnen, AP (2006). The traveling salesman problem and its variations (Vol. 12). Springer Science & Business Media.

Hillier, FS, Lieberman, GJ (2016). Introduction to Operations Research. 10th. ed. McGraw-Hill Education.

Luenberger, DG, Ye, Y. (2015). Linear and Nonlinear Programming. 4th. ed. Springer.

Nelson, BL (2010). Stochastic modeling: analysis & simulation. Courier Corporation.

Taha, HA (2019). Operations Research: An Introduction. 10th ed. Pearson.

Complementary

Derbel, H., Jarboui, B., Siarry, P. (Eds.). (2020). Green Transportation and New Advances in Vehicle Routing Problems. 1st ed. Springer.

Moreno S., Ma. Isabel, Sistachs V., Vivian, Díaz G., L. (2016). Selection of models in binary logistic regression, a classic approach. VDM Verlag.