110311 - QUANTITATIVE METHODS I

Subject type: Mandatory

Coordinator: Julián Horrillo Tello

Trimester: First term

Credits: 6

The subject will be taught in English. Students will be able to address the teacher in the language that is most comfortable for them.

Subject framed in the field of operational research. The subject aims to introduce students to the problems and possibilities of quantitative methods in industrial organization, and to train the student to obtain models in the context of industrial organization based on linear programming and programming dynamic In addition, the fundamental concepts of queuing and graph theory are studied, and their application to the resolution of problems specific to industrial organization. Finally, basic concepts related to business applications are introduced.

As prerequisites for taking the subject, it is recommended that students have passed all the subjects of the first two years of the degree studies.

At the end of the course the student must be able to:

• LO1: Interpret the types of models: linear, non-linear, binary (CE 22).

• LO3: Identify tools for optimizing models that have a single objective or several objectives (CE 22).

• LO4: Apply the basic knowledge of the techniques and models of operational research and be able to project them to applications of the industrial organization (CE 22).

• R5: Manage the models of queuing systems and apply them in the industrial organization (CE 22).

• R6: Design appropriate models for problems related to industrial organization (CE 22).

Theoretical sessions: master class, lectures, presentations.

Guided learning: seminars, forums and debates, case studies, use of computer tools applied to the subject, visits to real environments.

Autonomous learning: Problem solving, research and critical reading of articles, non-contact tutorials

Content title 1: Linear programming

Learning time: Large group: 8h, Small group: 4h, Self study: 18h    
Description:

• Review of concepts
• Dual problem of a linear problem
• Sensitivity analysis
• Transportation problem
• Entire programming
• Modeling with linear programming
• Introduction to nonlinear programming

Related activities:

1- Practical activities. Two laboratory sessions where you will work with R software to solve Linear Programming problems. The students will have to deliver an independent resolution activity as proposed by the teachers.
2- Exercises of practical application of the concepts exposed in class.
3- 1st Exam: where the concepts acquired by the student will be evaluated.

Content title 2: Graph theory

Learning time: Large group: 8h, Small group: 4h, Self study: 18h    
Description:

• Introduction
• Representation of a graph
• Minimum partial tree problem: Prim algorithm
• Shortest path problem: Dijkstra and Bellman-Kallaba algorithms
• Maximum flow problem: Ford-Fulkerson algorithm

Related activities:

1- Practical activities. Two laboratory sessions where you will work with R software to solve graph problems. The students will have to deliver an independent resolution activity as proposed by the teachers.
2- Exercises of practical application of the concepts exposed in class.
3- 1st Exam: where the concepts acquired by the students will be evaluated.

Content title 3: Dynamic programming

Learning time: Large group: 8h, Small group: 4h, Self study: 18h  
Description:

• Introduction
• Stages, states, decision variables and recurrence function
• Deterministic dynamic programming
• Random dynamic programming

Related activities:

1- Practical activities. Two laboratory sessions where you will work with R software to solve Dynamic Programming problems. The students will have to deliver an independent resolution activity as proposed by the teachers.
2- Exercises of practical application of the concepts exposed in class.
4- 2nd Exam: where the concepts acquired by the students will be evaluated.

Content title 4:  Waiting line models

Learning time: Large group: 8h, Small group: 4h, Self study: 18h  
Description:

• Parameters of a waiting line system
• Parameters of waiting line models
• Model results
• Birth and death processes
• Models based on birth and death processes
• Costs of a waiting line system

Related activities:

1- Practical activities. Two laboratory sessions where you will work with R software to solve waiting line problems. The students will have to deliver an independent resolution activity as proposed by the teachers.
2- Exercises of practical application of the concepts exposed in class.
4- 2nd Exam: where the concepts acquired by the students will be evaluated.

Content title 5:  Business applications

Learning time: Large group: 8h, Small group: 4h, Self study: 18h   
Description:

• Planning and scheduling operations
• Logistics management
• Quality management
• Maintenance management

Related activities:

1- Practical activities. Two laboratory sessions where you will work with R software and other software solutions to solve application problems of the concepts achieved. The students will have to deliver an independent resolution activity as proposed by the teachers.
2- Exercises of practical application of the concepts exposed in class.
4- 2nd Exam: where the concepts acquired by the students will be evaluated.

Activity title 1:  Practical activities
Learning time: Small group: 20h, Self study: 40h  
General description: practical activities related to the 5 main topics of the subject, in which students will work on different computer applications that will facilitate the resolution of the proposed activities and the analysis of the information.
Support material: installable software, and technical and user guides provided by the teacher.
Competences: CE 22, CB 5, CT 2
Deliverables and links to the evaluation: Reports containing the reasoning and proposed solutions to the questions asked in the statement.
Specific objectives: at the end of the activity the student must be able to know the usefulness of the different tools that have been used, and their practical application to real situations in a business environment.

Tactivity title 2:  Exercises

Learning time: Large group: 12h, Self study: 24h   
General description: activities related to the 5 main topics of the subject, proposed by the teachers, to facilitate the learning of the different concepts introduced in the subject.
Support material: notes of the subject and statements of the exercises provided by the teacher.
Competences: CE 22, CB 5, CT 2
Deliverable and links to the evaluation: reports containing the reasoning and the proposed solutions to the questions asked in the statement.
Specific objectives: at the end of the exercises, the students must be able to understand the situation, develop a diagnosis of the situation, and come up with a solution to the problem.

Activity title 3:  1 exam

Learning time: Large group: 2h, Self study: 13h  
General description: realization of a theoretical examination and of problems of the first 2 subjects of the asignatura.
Support material: bibliography and methodological guides of the subject.
Competences: CE 22, CB 5
Deliverable and links with the evaluation: resolution of the test. This activity represents 30% of the final grade of the subject
Specific objectives: eminently evaluative objective of the degree of achievement of theoretical knowledge and its application to practical situations. Collect information for individual summative assessment.

Activity title 4:   2 exam

Learning time: Large group: 2h, Self study: 13h   
General description: realization of a theoretical examination and of problems of the last 3 subjects of the asignatura.
Support material: bibliography and methodological guides of the subject.
Competences: CE 22, CB 5
Deliverable and links with the evaluation: resolution of the test. This activity represents 30% of the final grade of the subject
Specific objectives: eminently evaluative objective of the degree of achievement of theoretical knowledge and its application to practical situations. Collect information for individual summative assessment.

The assessment will consist of a grade obtained from the continuous assessment, attendance and exams according to the following percentages:

• Partial examination Parts 1 and 2: 30%.
• Practical activities: 30%.
• Exercises: 10%.
• Partial examination Parts 3, 4 and 5: 30%.

The minimum mark of the exams must be 3,5 in order to be computable with the rest of the assessment.
Recovery: Those who pass the recovery test will get a pass mark of 5.0 at most.

It will be up to the teachers of the subject to decide on the possibility of adding activities that allow the recovery of the suspended activities.

For the practical activities, if the result of their evaluation is not satisfactory, or the teachers consider it opportune they will be able to summon the members of a group to the realization of a test of individualized evaluation.

Rules for carrying out the activities

For each activity, teachers will report on the particular rules and conditions that govern them. This information will be communicated in the physical classroom or published in the virtual classroom.

One-on-one activities presuppose the student's commitment to carry them out individually. All activities in which the student does not fulfill this commitment regardless of their role (origin or destination) will be considered suspended.

Likewise, the activities to be carried out in groups presuppose the commitment on the part of the students who make it up to carry them out within the group.

All activities in which the group has not respected this commitment regardless of its role (origin or destination) will be considered suspended. The responsibility for the results of the work lies with the group, and not with the individuals who make it up. In any case, teachers can, based on the information they have, customize the grade for each member of the group.

Any undelivered activity will be considered scored with zero points. It is optional for teachers to accept or not deliveries outside the deadlines indicated. In the event that these late deliveries are accepted, it is up to the teacher to decide whether to apply a penalty and the amount thereof.

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

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

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

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