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In batch production systems, multiple items can be processed in the same batch if they share sufficiently similar production parameters. We consider the batch consolidation problem of minimizing the number of batches of a finite set of items. This article focuses on the case in which only one or two items can be processed in a single batch. The problem is NP ‐hard and cannot be approximated within...
We study the minimization of ADMs (Add‐Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all‐to‐all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor C and N, the size of the ring. We first study exhaustively the cases C = 1, C = 2, and...
This article investigates the relationship between resource allocation and early‐start policies (ES‐policies), which are a type of scheduling policies introduced for stochastic scheduling and which can be represented by a directed acyclic graph. We present a formal treatment of resource flows as a representation of resource‐allocation decisions, extending the existing literature. Our results lead...
A set S of vertices is defined to be a power dominating set (PDS) of a graph G if every vertex and every edge in G can be monitored by the set S according to a set of rules for power system monitoring. The minimum cardinality of a PDS of G is its power domination number. In this article, we find upper bounds for the power domination number of some families of Cartesian products of graphs: the cylinders...
In this article, we present a stochastic shortest path problem that we refer to as the Most Likely Path Problem (MLPP). We demonstrate that optimal solutions to the MLPP are not composed of optimal subpaths, which limits the computational tractability of exact solution methods. On series‐parallel networks, we produce analytical bounds for the MLPP's optimality indices, the probabilities of given paths...
This article examines the complexity of resource‐allocation decisions for resource‐constrained project scheduling. The allocation decisions are modeled by means of precedence networks and are closely related to ES‐policies, which are a type of scheduling policies introduced for stochastic scheduling. We find that even a number of ‘surrogate’ objective functions, whose use has recently been proposed...
In this article, we propose a global optimization technique (Big Segment Small Segment) for solving single facility location problems on a network when the location of the facility can either at nodes or along the links of the network. Some multiple facility location problems can be solved by recursively solving single facility problems. The technique is tested on five problems: the mixed weights...
In this article, we describe how to construct physical computer network topologies, which can support the establishment of overlays that reduce or increase the distances between nodes. Reducing pairwise distances (i.e., compression) implies that the overlay enjoys significantly lower inter‐node latencies compared to the ambient physical network; such an overlay can be used to implement a “high‐performance...
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