Interaktivní přístupy k řešení vícekriteriálních problémů v projektovém řízení

The paper deals with authors‘ research in the field of application of multiple criteria programming
algorithms in project management problems. It combines algorithms of finding critical path in
AON networks with methods of project cost minimizations. For this purpose a software realization
of ALOP (Aspiration Levels Oriented Procedure) method is presented.
First of all commonly used Activity on Arc project network model is modified to Activity on Node
model. Each task duration is limited by lower and upper bound and these bounds correspond to
maximum and minimum acceptable costs. Inverse proportion between task duration and task cost
is supposed. Nonlinear cost curves are approximated by linear ones.
On these assumptions the multiple criteria linear programming model is defined, where project
duration is set as the first criteria function, cost minimization as another. Interactive solution of this
cost – duration minimization problem (cost minimization versus due date optimization) is provided
using ALOP Method, its software realization (Excel Add In Tool Alokosa) respectively.
Alokosa is an interactive procedure for multiosbjective linear programming problems, where the
decision space is determined by linear constraints and linear objective functions. The decision maker
states aspiration levels for each criteria value. The problem can have a unique nondominated
solution, or can be feasible or infeasible. In case of nondominated problem solution the module
Alokosa calculates all objective function and variable values. In case of feasible problem, it offers
proposed changes of aspiration levels by which a nondominated solution is obtained in the next
step. In case of infeasible problem the module Alokosa offers necessary changes in aspiration
levels by which the nearest nondominated solution can be found. All outputs of this module are in
the form of interactive spreadsheet.
The demo example of cost-due date optimization problem solving is shown and analyzed at the
end of our paper.