A Business Process Management System based on a General Optimium Criterion

Business Process Management Systems (BPMS) provide a broad range of facilities to manage operational business processes. These systems should provide support for the complete Business Process Management (BPM) life-cycle (16): (re)design, configuration, execution, control, and diagnosis of processes. BPMS can be seen as successors of Workflow Management (WFM) systems. However, already in the seventies people were working on office automation systems which are comparable with today’s WFM systems. Recently, WFM vendors started to position their systems as BPMS. Our paper’s goal is a proposal for a Tasks-to-Workstations Assignment Algorithm (TWAA) for assembly lines which is a special implementation of a stochastic descent technique, in the context of BPMS, especially at the control level. Both cases, single and mixed-model, are treated. For a family of product models having the same generic structure, the mixed-model assignment problem can be formulated through an equivalent single-model problem. A general optimum criterion is considered. As the assembly line balancing, this kind of optimisation problem leads to a graph partitioning problem meeting precedence and feasibility constraints. The proposed definition for the "neighbourhood" function involves an efficient way for treating the partition and precedence constraints. Moreover, the Stochastic Descent Technique (SDT) allows an implicit treatment of the feasibility constraint. The proposed algorithm converges with probability 1 to an optimal solution.BPMS, control assembly system, stochastic optimisation techniques, TWAA, SDT

Efficiency and Betweenness Centrality of Graphs and some Applications

The distance $d_{G}(i,j)$ between any two vertices $i$ and $j$ in a graph $G$ is the minimum number of edges in a path between $i$ and $j$. If there is no path connecting $i$ and $j$, then $d_G(i,j)=infty$. In 2001, Latora and Marchiori introduced the measure of efficiency between vertices in a graph. The efficiency between two vertices $i$ and $j$ is defined to be $in_{i,j}=frac{1}{d_G(i,j)}$ for all $ineq j$. The textit{global efficiency} of a graph is the average efficiency over all $ineq j$. The {it power of a graph} $G^m$ is defined to be $V(G^m)=V(G)$ and $E(G^m)={(u,v)|d_G(u,v)le m}$. In this paper we determine the global efficiency for path power graphs $P_n^m$, cycle power graphs $C_n^m$, complete multipartite graphs $K_{m,n}$, star and subdivided star graphs, and the Cartesian products $K_{n}times P_{m}^{t}$, $K_{n}times C_{m}^{t}$, $K_{m}times K_{n}$, and $P_{m}times P_{n}$. The concept of global efficiency has been applied to optimization of transportation systems and brain connectivity. We show that star-like networks have a high level of efficiency. We apply these ideas to an analysis of the Metropolitan Atlanta Rapid Transit Authority (MARTA) Subway system, and show this network is 82% as efficient as a network where there is a direct line between every pair of stations. From BOLD fMRI scans we are able to partition the brain with consistency in terms of functionality and physical location. We also find that football players who suffer the largest number of high-energy impacts experience the largest drop in efficiency over a season. Latora and Marchiori also presented two local properties. The textit{local efficiency} $E_{loc}=frac{1}{n}sumlimits_{iin V(G)}E_{glob}left(G_{i}right)$ is the average of the global efficiencies over the subgraphs $G_{i}$, the subgraph induced by the neighbors of $i$. The clustering coefficient of a graph $G$ is defined to be $CC(G)=frac{1}{n}sumlimits_{i}C_{i}$ where $C_{i}=|E(G_i)|/binom{|V(G_i)|}{2}$ is a degree of completeness of $G_{i}$. In this paper, we compare and contrast the two quantities, local efficiency and clustering coefficient. Betweenness centrality is a measure of the importance of a vertex to the optimal paths in a graph. Betweenness centrality of a vertex is defined as $bc(v)=sum_{x,y}frac{sigma_{xy}(v)}{sigma_{xy}}$ where $sigma_{xy}$ is the number of unique paths of shortest length between vertices $x$ and $y$. $sigma_{xy}(v)$ is the number of optimal paths that include the vertex $v$. In this paper, we examined betweenness centrality for vertices in $C_n^m$. We also include results for subdivided star graphs and $C_3$ star graphs. A graph is said to have unique betweenness centrality if $bc(v_i)=bc(v_j)$ implies $i=j$: the betweenness centrality function is injective over the vertices of $G$. We describe the betweenness centrality for vertices in ladder graphs, $P_2times P_n$. An appended ladder graph $U_n$ is $P_2times P_n$ with a pendant vertex attached to an tbl endtbr. We conjecture that the infinite family of appended graphs has unique betweenness centrality

Zero forcing sets and controllability of dynamical systems defined on graphs

In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence between the set of leaders rendering the network controllable and zero forcing sets is established. To illustrate the proposed results, special cases including path, cycle, and complete graphs are discussed. Moreover, as shown for graphs with a tree structure, the proposed results of the present paper together with the existing results on the zero forcing sets lead to a minimal leader selection scheme in particular cases

Efficient, Superstabilizing Decentralised Optimisation for Dynamic Task Allocation Environments

Decentralised optimisation is a key issue for multi-agent systems, and while many solution techniques have been developed, few provide support for dynamic environments, which change over time, such as disaster management. Given this, in this paper, we present Bounded Fast Max Sum (BFMS): a novel, dynamic, superstabilizing algorithm which provides a bounded approximate solution to certain classes of distributed constraint optimisation problems. We achieve this by eliminating dependencies in the constraint functions, according to how much impact they have on the overall solution value. In more detail, we propose iGHS, which computes a maximum spanning tree on subsections of the constraint graph, in order to reduce communication and computation overheads. Given this, we empirically evaluate BFMS, which shows that BFMS reduces communication and computation done by Bounded Max Sum by up to 99%, while obtaining 60-88% of the optimal utility