General information


Subject type: Mandatory

Coordinator: Jesus Ezequiel Martínez Marín

Trimester:2

Credits: 3

Teaching staff: Rosa Herrero Antón

Description


Mathematical Models for Logistics. 

 

This subject has methodological and digital resources to make possible its continuity in non-contact mode in the case of being necessary for reasons related to the Covid-19. In this way, the achievement of the same knowledge and skills that are specified in this teaching plan will be ensured.

The TecnoCampus will make available to teachers and students the digital tools needed to carry out the course, as well as guides and recommendations that facilitate adaptation to the non-contact mode.

Learning outcomes


Model and solve logistical problems with uncertainty and risk 

Programming mathematical models in Logistics 

Working methodology


The subject uses the following work methodologies: 

Master class, case study, collaborative learning and problem solving. 

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 

Learning activities


The subject uses the following work methodologies: 

Master class, case study, collaborative learning and problem solving. 

Evaluation system


In order to gather evidence of the achievement of the expected learning outcomes, the following evaluative activities will be carried out: 

  
A1. Exercise at home: Graf theory (10%) 

Exercises to be solved through the virtual classroom based on the theoretical content. 

  
A2. Exercise at home: Stochastic Processes (10%) 

Exercises to be solved through the virtual classroom based on the theoretical content. 

  
A3. Exercise at home: Business Traveler problem (15%) 

Exercises to be solved through the virtual classroom based on the theoretical content. 

  
A4. Exercise at home: Vehicle Route Problem (15%) 

Exercises to be solved through the virtual classroom based on the theoretical content. 

  
A5. Final exam (50%) 

Examination of the content of the whole subject. 

  
The mark of each student will be calculated following the corresponding percentages: 

Final grade = A1 0,1 + A2 0,1 + A3 0,15 + A4 0,15 + A5 0,5 

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

- The teacher will inform of the dates and format of the delivery of the exercises at home. An activity not delivered or delivered late and without justification (court 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. 

References


Basic

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

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

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

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

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

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

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