An extension of the Disjunctive Model, eeciently representing Jobshop Scheduling (JS) problem, to more general Resource-Constrained Project Scheduling (RCPS) problem is proposed. The extension considers diierent groups of resources used by activities in diierent amounts limited to a constant value in every moment of the project duration. A solution to the problem is represented by a project res...

Aim of this presentation is to introduce a tabu search algorithm for a general scheduling problem modeled by means of the alternative graph. The alternative graph is a mathematical model, which is based on a generalization of the disjunctive graph of Roy and Sussman [6]. It allows a detailed representation of many scheduling problems. It was successfully applied to several real world environmen...

The behavior of the disjunctive operator, defined by Balas, Ceria and Cornuéjols, in the context of the “antiblocker duality diagram” associated with the stable set polytope,QSTAB(G), of a graph and its complement, was first studied byAguilera, Escalante and Nasini. The authors prove the commutativity of this diagram in any number of iterations of the disjunctive operator. One of the main conse...

In the field of cooperative games there is an extensive literature that studies situations of restricted cooperation. Myerson (1979) introduced communication graph games, where players can only cooperate if they are connected in an undirected graph representing the communication possibilities. The Myerson value of such a game is obtained by taking the Shapley value of the corresponding restrict...

For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges of the original graph. It is shown that the problem b...

The scheduling of manufacturing processes aims to find sequences of jobs on given machines optimal by a selected criterion, e.g. minimal completion time of all operations. With respect to NP-hardness of these problems and the necessity to solve them by heuristic methods, the problem representation and the effectiveness of their procedures is substantial for computations to be completed in a rea...

Each (nondeterministic) multilective VLSI-circuit C of area A can be simulated by an oblivious (disjunctive) branching program of width exp(O(A)) which has the same multiplicity of reading as C. That is why exponential lower bounds on the width of (disjunctive) oblivious branching programs of linear depth provide lower bounds of order Sl(nlm2’), 0 <a < i, on the area of (nondeterministic) multi...

For the classical minimum spanning tree problem we introduce disjunctive constraints for pairs of edges which can not be both included in the spanning tree at the same time. These constraints are represented by a conflict graph whose vertices correspond to the edges of the original graph. Edges in the conflict graph connect conflicting edges of the original graph. It is shown that the problem b...

A set D of vertices in a graph G is disjunctive dominating if every vertex not adjacent to or has at least two distance 2 from it . The domination number, γ d ( ), the minimum cardinality We show that T tree order n with l leaves and s support vertices, then n-l +3/4≤ )≤ n+l +s/4. Moreover, we characterize families trees which attain these bounds.

In 2002, Aguilera et al. analyzed the performance of the disjunctive lift-and-project operator defined by Balas, Ceria and Cornuéjols on covering and packing polyhedra, in the context of blocking and antiblocking duality. Their results generalize Lovász’s Perfect Graph Theorem and a theorem of Lehman on ideal clutters. This study motivated many authors to work on the same ideas, providing alter...