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Credits  Dept. 

7.5 (6.0 ECTS)  EIO 
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This subject presents some of the fundamental methods of operations research. Operations research is a discipline based on the formulation of models and the development and application of algorithms for solving problems in decision making. The subject also goes into the modelling languages and software vital to effective problem solving. The subject has a practical orientation. Students are introduced to several applications of the model and algorithms that may come into play complex problems they will come across in the future, both in technical and managerial fields.
Estimated time (hours):
T  P  L  Alt  Ext. L  Stu  A. time 
Theory  Problems  Laboratory  Other activities  External Laboratory  Study  Additional time 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

1,0  0  0  0  0  0  0  1,0  
 Operational research, Mathematical Programming and Optimisation. Models.
 Classification of problems and solution algorithms. 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

8,0  2,0  2,0  0  0  8,0  0  20,0  
Basic properties of linear programming.
 Computational complexity of linear programming.  The Simplex algorithm (first version, matricial format). 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

10,0  4,0  4,0  0  0  12,0  0  30,0  
 The theory sessions will cover:  Basic properties of problems exhibiting a network structure:  Types of network flow models. Examples.  Simplex algorithm for the minimum cost problem in network flows.  Shortest path algorithms for positive costs (Dijkstra) and labelcorrecting"). Algorithms for the maximum flow problem. 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

4,0  1,0  1,0  0  0  4,0  0  10,0  
Branch and bound algorithm.


T  P  L  Alt  Ext. L  Stu  A. time  Total  

4,0  2,0  0  0  0  4,0  0  10,0  
Basic properties of nonlinear programming.


T  P  L  Alt  Ext. L  Stu  A. time  Total  

6,0  2,0  0  0  0  6,0  0  14,0  
 Heuristic methods for solving the sequencing of tasks.  Heuristic methods for designing networks.  Heuristic methods for tackling itineraries. 

T  P  L  Alt  Ext. L  Stu  A. time  Total  

2,0  0  0  0  0  1,0  0  3,0 
Total per kind  T  P  L  Alt  Ext. L  Stu  A. time  Total 
43,0  15,0  17,0  0  10,0  45,0  0  130,0  
Avaluation additional hours  5,0  
Total work hours for student  135,0 
This will include theory, problem, and lab sessions. The basic knowledge contained in the course will be introduced in the theory sessions. The problems dealt with in the practical sessions will be directly based on the theory taught. The lab sessions will involve solving reallife mediumsized cases in which students will formulate and solve problems using modelling software and appropriate "solvers".
The final grade (NF) is calculate thus: NF= 0.7*NT+0.3*NP, with NT being the theory grade and NP the grade for the practical work.
NT: This part exam will be be calculated as NT/2 where students obtain a grade of 4 or over. The final exam will be calculated as NT/2 for those students who obtained a grade of 4 or higher, and as NT for the remaining students.
NP: There will be two practical assignments. These will be carried out during class time in the lab. Each assignment will consist of modelling and solving a case using AMPL modellingoptimisation software. Each practical assignment will be marked as NP/2.
Students will need have acquired basic knowledge of the following from previous courses. In particular, basic knowledge of:
 programming
 algebra (operations with matrices and vectors)
 data structures for graphs
 Basic algorithms for graphs.