Aggregation errors in project scheduling

It is shown that aggregation leads to errors in network models projects problems with restricted resources. In consequence of aggregation an optimal solution of network problem has systematic mistakes in resources evaluation and project schedules look like better than indeed. As illustration the results of computer experiments on real-life data are presented.

Optimization of Shortest Path Problem using Dijkstra’s Algorithm in Imprecise Environment

Dijkstra algorithm is a widely used algorithm to find the shortest path between two specified nodes in a network problem. In this paper, a generalized fuzzy Dijkstra algorithm is proposed to find the shortest path using a new parameterized defuzzification method. Here, we address most important issue like the decision maker’s choice. A numerical example is used to illustrate the efficiency of the proposed algorithm.

OPTIMIZATION PROBLEMS OF MODERNIZATION OF THE CAPACITY OF ARCS OF FAULT-TOLERANT NETWORKS

Mathematical models of two classes of problems of modernization of the capacity of arcs of fault-tolerant oriented networks are considered. A network is considered to be fault-tolerant for which it is possible to satisfy all the demands for the transmission of flows when there will be one, but any failure, from all possible single network failures. For the first class of problems (problem A), all possible paths in the network can be used for the transmission of flows. For the second class of problems (problem P), only paths from a predetermined set of paths are used to transfer flows. Mathematical models are represented by linear, Boolean and nonlinear programming problems with a block structure of the constraint matrix.The material of the article is presented in five sections. The first section describes the concepts of a single failure and the scenario of network failures, the content of optimization problems A and P for modernization of capacity of arcs of a fault-tolerant network, a test network (6 vertices and 19 arcs) to test algorithms for solving the problems of modernization of fault-tolerant networks. In the second section, basic models of linear programming problems for finding the capacities of arcs of the fault-tolerant physical structure of a network (problem A) and the fault-tolerant logical structure of a network (problem P) are described, and their properties are considered. The third section describes problems A and P in the form of mixed Boolean linear programming models. Optimal solutions of problem A for various failure scenarios are given for the example of the test network. The solutions were found using the Gurobi program from the NEOS server, where the mathematical model of problem A is described in the AMPL modeling language.The fourth section describes nonlinear convex programming models for problems A and P, developed to find the optimal capacities of fault-tolerant networks according to the selected criterion, and a decomposition algorithm for their solution. The fifth section describes software in the FORTRAN programming language for the decomposition algorithm based on efficient implementations of Shor’s r-algorithms. The decomposition algorithm is compared with the IPOPT program based on the results of solving test problems.