110311 - QUANTITATIVE METHODS I

Subject type: Mandatory

Coordinator: Josep López Xarbau

Trimester: First term

Credits: 6

Academic year: 2025

Teaching course: 3

• Catalan
• Spanish
• English

Materials written in different languages. Spoken language of the subject, Catalan. 

The subject of "Quantitative Methods I" is designed to enable participants to be able to develop an optimization model for a system design or management problem and to obtain and interpret the results corresponding to the model .

The classroom in which the subject is taught (physically or virtually) is a safe space, free of sexist, racist, homophobic, transphobic and discriminatory attitudes, whether towards students or teachers. We trust that together we can create a safe space where we can make mistakes and learn without having to suffer prejudice from others.

1. Mathematical programming.
   1. Problem modeling.
   2. Planning and programming of operations.
   3. Capacity dimensioning.
   4. Logistics optimization.

1. Linear programming.
   1. Simple method.
   2. Duality and sensitivity analysis.
   3. Entire schedule.
   4. Non-linear programming.
2. Graph theory.
   1. Representation of a graph.
   2. Minimum partial tree problem: Prim's algorithm.
   3. Shortest path problem: Dijkstra and Bellman-Kallaba algorithms.
   4. Maximum flow problem: Ford-Fulkerson algorithm.
3. Dynamic programming.
   1. Stages, states, decision variables and recurrence function.
   2. Deterministic dynamic programming.
   3. Random dynamic programming.
   4. Bellman's optimality principle.
4. Models of waiting lines.
   1. Parameters of a system of waiting lines.
   2. Parameters of waiting line models.
   3. Model results.
   4. Models based on birth and death processes.

Activities 1 to 4 will only be assessed if at least 80% of the practice sessions have been attended face-to-face and if the report corresponding to the campus task has been handed in within the indicated period. When a group activity is considered, the grade of the students in the same group may vary depending on the criteria established by the teaching staff responsible for the subject. It will be up to the teaching staff to decide whether to do an individualized assessment test in order to confirm the authorship of the reports delivered or if the result of the activities is not satisfactory.

Activities 1 to 4 are compulsory. If one of these activities is not delivered or its grade is lower than 4 out of 10, it will be considered as not presented in the final grade of the subject.

Activities 5 or 6 are individual and compulsory (activity 6 is only done if you need to recover activity 5). The final grade of the subject is the weighted sum of the grades of the activities if activity 5 is greater than or equal to 5 points out of 10, otherwise, the final grade will be that of activity 5. If the grade of activity activity 5 is greater than or equal to 5 points out of 10, the final grade is as follows:

Activity 1: 20%

Activity 2: 10%

Activity 3: 10%

Activity 4: 10%

Activity 5: 50%

Activity 6 corresponds to the recovery exam for activity 5. In activity 6, qualified students with a "Not Presented" or students who have passed the subject in the ordinary call cannot appear . Activity 6 only gives the option to pass the subject with a grade of 5 if the grade is equal to or higher than 5 out of 10, except in the case where the weighted average grade with the corresponding weights of the first four activities is equal or higher than 8. In this case, the final grade will correspond to the weighted average grade with the corresponding weights of activities 1, 2, 3, 4 and 6. If the grade for activity 6 is lower than 5 out of 10, the grade for activity 6 will be directly the grade for the subject.

Identification of plagiarism is considered a serious circumstance that may lead to a failing grade in the subject. In case of detection of plagiarism, the coordination of the degree will be informed so that the corresponding disciplinary measures can be taken.

For other aspects, the "Regulations for the evaluation of Degree courses of the TecnoCampus University Center" approved by the Governing Commission of the TecnoCampus University Center in the session of June 14, 2024, will be strictly followed.

Important:

Any form of academic fraud will be sanctioned in accordance with the regulations
evaluation of the center. In the event that signs of fraud are detected, including the improper use
of generative artificial intelligence tools, the subject's teachers will be able to
call the student for an individual interview with the aim of verifying
the authorship.

Hillier, Frederick S.; Lieberman, Gerald J. (2010). Introduction to Operations Research. McGraw-Hill.

Sallán Leyes, José María; Lordan, Oriol; Fernández Alarcón, Vicenç. Modeling and solving linear programming with R: OmniaScience, 2015.

Sallán, JM; Suñé, A; Fernández, V.; Fonollosa, JB (2006). Quantitative Methods of Industrial Organization I. Ediciones UPC.