To acquire solid knowledge on the fundamental modalities necessary to classify, mathematically formulate and solve problems of optimization applications in the logistic field, not necessarily limited to the specific themes addressed in the course.

It is desirable that the student has already taken the basic mathematics examinations scheduled. In the case in point, having already taken the Operational Research exam (if inserted in their study plan) can facilitate the learning of some topics included in the course program.

NETWORK OPTIMIZATION PROBLEMS
Graphs and networks. Transportation problem. PL formulation. Network interpretation. Initial solution. Stepping stone method. MODI method.
Examples. Assignment problem. Integer programming formulation. Continuous relaxation. Hungarian method. Outline of total unimodularity.
Examples. Maximum flow problem. Ford-Fulckerson algorithm. Optimality. Maximum flow and minimum cut theorem. Construction of a minimum capacity cut. Examples. Minimum cost path. Dijkstra algorithm. Examples. Trees. Minimum spanning tree with Prim algorithm. Minimum path tree with Dijkstra algorithm. Examples. Critical path method. Examples. PERT.

ROUTING AND FLEET MANAGEMENT
Routing problems: introduction to the TSP: examples, formulation, computational complexity. Triangular inequality. TSP: heuristics and exact algorithms. Types of heuristics. Heuristics of the nearest node, of insertion and of the double covering tree. TSP: savings heuristic, 2-OPT, 3-OPT, of Lin-Kernighan. Exact algorithms. Asymmetric TSP. VRP: exact and heuristic algorithms. Heuristics of savings or Clark-Wright. Examples. Cluster-first, Route-second. Theorems on the TSP. Route-first, Cluster-second. Heuristics OR-OPT. Chinese postman. Necessary and sufficient conditions for the existence of Eulerian circuits. End-pairing and Fleury algorithms. Rural Postman Problem: definition, examples, heuristics.

FORECASTING TECHNIQUES
Taxonomy and examples. Subjective and objective forecasts. Causal models. Least squares method, correlation and linear regression. Time series: stationary series. Introduction to the moving average. Moving average and exponential leveling. Statistical properties: advantages, disadvantages and examples. Average age of data in the moving average and exponential smoothing. Series with trends, forecasts in the periods following the first, elementary technique, linear regression, double moving average, Holt method (or double exponential damping), examples. Seasonality, seasonal factors estimation, deseasonalization, elementary technique, revised exponential mean method, examples. Winters method.

Giuseppe Bruno,
Operations Management. Modelli e Metodi per la Logistica,
Edizioni Scientifiche Italiane (collana Ingegneria economico-gestionale),
ISBN: 88-495-1032-2.

Frederick S. Hillier, Gerald J. Lieberman,
Ricerca operativa,
Ottava edizione, McGraw-Hill,
ISBN: 88-386-6242-8.

Gianpaolo Ghiani, Roberto Musmanno,
Modelli e Metodi per l'Organizzazione dei Sistemi Logistici,
Pitagora Editrice Bologna,
ISBN: 88-371-1204-1.

Slides can be found on the teacher's web page, at http://www.units.it/coslovich

NETWORK OPTIMIZATION PROBLEMS
Graphs and networks. Transportation problem. PL formulation. Network interpretation. Initial solution. Stepping stone method. MODI method.
Examples. Assignment problem. Integer programming formulation. Continuous relaxation. Hungarian method. Outline of total unimodularity.
Examples. Maximum flow problem. Ford-Fulckerson algorithm. Optimality. Maximum flow and minimum cut theorem. Construction of a minimum capacity cut. Examples. Minimum cost path. Dijkstra algorithm. Examples. Trees. Minimum spanning tree with Prim algorithm. Minimum path tree with Dijkstra algorithm. Examples. Critical path method. Examples. PERT.

ROUTING AND FLEET MANAGEMENT
Routing problems: introduction to the TSP: examples, formulation, computational complexity. Triangular inequality. TSP: heuristics and exact algorithms. Types of heuristics. Heuristics of the nearest node, of insertion and of the double covering tree. TSP: savings heuristic, 2-OPT, 3-OPT, of Lin-Kernighan. Exact algorithms. Asymmetric TSP. VRP: exact and heuristic algorithms. Heuristics of savings or Clark-Wright. Examples. Cluster-first, Route-second. Theorems on the TSP. Route-first, Cluster-second. Heuristics OR-OPT. Chinese postman. Necessary and sufficient conditions for the existence of Eulerian circuits. End-pairing and Fleury algorithms. Rural Postman Problem: definition, examples, heuristics.

FORECASTING TECHNIQUES
Taxonomy and examples. Subjective and objective forecasts. Causal models. Least squares method, correlation and linear regression. Time series: stationary series. Introduction to the moving average. Moving average and exponential leveling. Statistical properties: advantages, disadvantages and examples. Average age of data in the moving average and exponential smoothing. Series with trends, forecasts in the periods following the first, elementary technique, linear regression, double moving average, Holt method (or double exponential damping), examples. Seasonality, seasonal factors estimation, deseasonalization, elementary technique, revised exponential mean method, examples. Winters method.

Classic frontal lessons on the blackboard, with the use, in addition, of projected slides. Examples of the theory presented, also with projection of spreadsheets compiled in the classroom to stimulate student participation.

All information related to the lessons (suspensions or transfers), exams etc. are published on a web page maintained by the teacher, at the address http://www.units.it/coslovich In this page, you can find previous written topics exam, slides used by the teacher during lessons and other resources. It represents an efficient communication channel, usually much appreciated by students.

Oral exams.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs)