Operational Research

Learning Outcomes

Upon successful completion of the course, the student will be able to:

• Know/state mathematical theory (concepts, theorems, proofs) which related to the course in question.
• Recognize the mathematical formulas related to the theory and to describe the solution methods (e.g. Method M)
• Distinguish different cases of linear problems programming and explain their use in relation to the given mathematical problem. (e.g. Binary theory, the transference problem.)
• Compute basic elements of the theory (e.g. solution via the Simplex technique).
• Understand, distinguish, and resolve the different cases of the issues that concern integer programming (Branch and bound, the partition problem, the minimum set overlap problem, dynamic programming, the knapsack problem (generalized knapsack)
• Fix problems with the local search method (e.g. Neighborhood Structure, methods neighborhood search, the street vendor problem, graph partitioning.)
• Explain and solve problems using Heuristic algorithms (Techniques performance evaluation, reachability ratio, the nodal overlap problem (vertex covering), maximum independent subset, upper and lower bounds, empirical evaluation of heuristics).
• Combine mathematical theory with problems of an economic nature that fall within in the course and to successfully proceed to exemplify them.

Indicative Module Content

Business research models, complexity of algorithms, NP-hard problems. Linear programming: Simplex algorithm, Binary theory, the problem transportation. Integer programming: Branch and bound, the partition problem, the minimum set overlap problem, dynamic programming, the knapsack problem, generalized knapsack. Heuristic algorithms: Performance evaluation techniques, reachability ratio, the vertex covering problem, maximum independent subset, upper and lower bounds, empirical evaluation of heuristic methods. Local search methods: Neighborhood structure, neighborhood search methods, the traveling salesperson problem, graph partitioning. Simulated annealing: The Metropolis algorithm, applications, the maximum intersection problem.