This textbook is primarily intended for students of a PhD programme, but it can also serve as a base for a graduate course.
It is assumed that the participant is already acquainted with the notions of optimal value (maximal value, minimal value) of function under constraints on arguments of that function.
Optimization model, i.e. the set of three elements:
- criterion function,
- maximization operator or minimization operator,
- set of constraints on arguments of the criterion function,
is a formal framework for modeling many economic and social phenomena, taking the form of decision making problems. By filling data into an optimization model we get an optimization problem. The values of arguments which yield the optimal value of the criterion function, i.e. the optimal solution} to the optimization problem, represent the most preferred decision variant. Considerations of that sort are the subject of Operations Research courses.
Optimization models are too often oversimplifications of decision problems met in practice. For instance, modeling company performance by an optimization model in which the criterion function is short term profit to be maximized, does not fully reflect the essence of business management. The company managing staff is accountable not only for short term profits, but also for actions which shall result in the company ability to generate a decent profit also in the future. This calls for management decisions and actions which ensure short term profitability, but also maintaining long term relations with clients, introducing innovative products, financing long-term investments, etc. Each of those additional but indispensable actions and their effects can be modeled separately, case by case, by an optimization model with an criterion function adequately selected. However, in each case the same set of constraints represents the range of company admissible actions. The aim and the scope of this textbook is to present methodologies and methods enabling modeling of such actions jointly.
This textbook is self-contained, to follow it the Reader does not need to refer to additional sources. However, the references given at the end can be a starting point for further research into methodologies and applications of decision making in the multiple criteria setting.