The course is one of the two modules of the Nonlinear Control and Optimization course. The goal of the course is to let students familiarize with basic techniques for process planning and management. In particular, methods and algorithms of management science for modelling and solving complex decision problems will be presented. The theoretical tools will be illustrated using examples, coming from different fields, e.g. related to automation engineering, management and the economic field.
Course Prerequisites
Basic knowledge of maths, computer science, system and control theory for linear systems.
Teaching Methods
Lectures (hours/year in lecture theatre): 22 Practical class (hours/year in lecture theatre): 18 Practicals / Workshops (hours/year in lecture theatre): 14
Assessment Methods
Closed-book, closed-note written exam. Both knowledge of theory and skills in solving simple exercises will be tested. The exam lasts 3 hours and includes 4 exercises related to the main topics covered in class, for which the exam text and the appropriately structured sheet to be filled in with the complete resolution procedure are provided.
Texts
W. L. Winston, M. Venkataramanan. Introduction to Mathematical Programming: Applications and Algorithm. 4th ed., Duxbury Press, 2002.
S. Boyd & L. Vandenberghe, “Convex Optimization”, Cambridge University Press, 2004, ISBN 0521833787
C. Vercellis. Ottimizzazione: Teoria, metodi, applicazioni. McGraw-Hill, 2008. (in Italian).
Contents
AUTOMATION OF PRODUCTION PROCESSES. Modelling of production processes. Flexible production systems. Management science. Operations research for decision problems.
MATHEMATICAL PROGRAMMING FOR DECISION PROBLEMS. Modelling of decision problems: variables, cost and constraints. Basics of convex programming. Examples of decision problems including product mix, resource allocation, transport and portfolio selection problems.
LINEAR PROGRAMMING (LP) PROBLEMS. Geometry of LP. Fundamental theorem of LP. Algorithms for LP problems.
SIMPLEX METHOD: phase 1 and 2. Tableau form of the simplex method. Dual Programming.
GRAPH THEORY AND PATH OPTIMIZATION: Definitions of graphs and their basic elements. SST problem and its solution algorithms. Computational complexity.
MIXED-INTEGER LINEAR PROGRAMMING (MILP). The use of binary variables in optimization programs. Branch and bound algorithm. Extension also to the case of integer variables (and not only binary)
DYNAMIC PROGRAMMING: Bellman principle, cost-to-go and Bellman iterations. Application of dynamic programming to optimal control of finite state machines and shortest path problems. Dynamic programming applied to mobile robotics.
