110311 - QUANTITATIVE METHODS I

Subject type: Mandatory

Coordinator: Joan Triadó Aymerich

Trimester: First term

Credits: 6

• English

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.

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.

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 deliveries of the exercises, cases and practical activities, to be taken into account in the evaluation of the subject, must be delivered before the established deadline.
The minimum grade for the exam must be 3,5 for it to be computable with the rest of the assessment.

Recovery:

• The theoretical part of the subject (Partial exams) can be retaken as long as and when the student has appeared for the two partial theory exams in ordinary call. The recovery test will cover all the content covered in theory. The maximum grade for the recovery test for the theoretical part is limited to 5.
• Continuous assessment activities (exercises, case studies and practical activities) cannot be recovered under any circumstances.

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; Suñé, A; Fernández, V.; Fonollosa, JB (2006). Quantitative Methods of Industrial Organization II. UPC editions.

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