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  • 1
    Electronic Resource
    Electronic Resource
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing, Inc.
    Decision sciences 35 (2004), S. 0 
    ISSN: 1540-5915
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Economics
    Notes: The pressure to reduce inventory investments in supply chains has increased as competition expands and product variety grows. Managers are looking for areas they can improve to reduce inventories without hurting the level of service provided. Two areas that managers focus on are the reduction of the replenishment lead time from suppliers and the variability of this lead time. The normal approximation of lead time demand distribution indicates that both actions reduce inventories for cycle service levels above 50%. The normal approximation also indicates that reducing lead time variability tends to have a greater impact than reducing lead times, especially when lead time variability is large. We build on the work of Eppen and Martin (1988) to show that the conclusions from the normal approximation are flawed, especially in the range of service levels where most companies operate. We show the existence of a service-level threshold greater than 50% below which reorder points increase with a decrease in lead time variability. Thus, for a firm operating just below this threshold, reducing lead times decreases reorder points, whereas reducing lead time variability increases reorder points. For firms operating at these service levels, decreasing lead time is the right lever if they want to cut inventories, not reducing lead time variability.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 43 (1989), S. 1-29 
    ISSN: 1436-4646
    Keywords: p-nary group problem ; row module ; regular ; chain clutter ; Fulkerson property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The duality for group problems developed in [3] is restricted top-nary group problems. Results for ternary group problems are obtained similar to those obtained by Fulkerson and Lehman for the binary case. A complete facet description of the group polyhedron is available for a group problem having the Fulkerson property. A group problem has the Fulkerson property if its vertices are the facets of the blocking group problem and if its facets are the vertices of the blocking group problem. The Fulkerson property is a generalization of the max-flow min-cut theorem of Ford and Fulkerson which is interpreted as a statement about the pair of row modules arising from a group problem. We show that a group problem has the Fulkerson property if the corresponding row module is regular.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 81 (1998), S. 177-199 
    ISSN: 1436-4646
    Keywords: Network design ; Integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a directed graphG = (V,A), and a set of traffic demands to be shipped between pairs of nodes inV. Capacity has to be installed on the edges of this graph (in integer multiples of a base unit) so that traffic can be routed. In this paper we consider the problem of minimum cost installation of capacity on the arcs to ensure that the required demands can be shipped simultaneously between node pairs. We study two different approaches for solving problems of this type. The first one is based on the idea of metric inequalities (see Onaga and Kakusho, On feasibility conditions of multicommodity flows in networks, IEEE Transactions on Circuit Theory, CT-18 (4) (1971) 425–429.), and uses a formulation with only |A| variables. The second uses an aggregated multicommodity flow formulation and has |V||A| variables. We first describe two classes of strong valid inequalities and use them to obtain a complete polyhedral description of the associated polyhedron for the complete graph on three nodes. Next we explain our solution methods for both of the approaches in detail and present computational results. Our computational experience shows that the two formulations are comparable and yield effective algorithms for solving real-life problems. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 59 (1993), S. 87-115 
    ISSN: 1436-4646
    Keywords: Graph partition ; multiway cut ; polytope ; facet
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we describe several forms of thek-partition problem and give integer programming formulations of each case. The dimension of the associated polytopes and some basic facets are identified. We also give several valid and facet defining inequalities for each of the polytopes.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 50 (1994), S. 143-171 
    ISSN: 1572-9338
    Keywords: Steiner tree ; packing ; LP-relaxation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we consider the problem of packing Steiner trees in a graph. This problem arises during the global routing phase of circuit layout design. We consider various integer programming formulations and rank them according to lower bounds they provide as LP-relaxations. We discuss a solution procedure to obtain both lower and upper bounds using one of the LP-relaxations. Computational results to test the effectiveness of our procedures are provided.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 45 (1989), S. 35-47 
    ISSN: 1436-4646
    Keywords: Facets ; ternary ; covering ; packing
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider ternary matrices, i.e., integer matrices having all entries 0, 1 or 2. Three associated problems—the group problem, covering, and packing—are studied. General classes of vertices and facets are discussed in each case. Certain lifting procedures are also described. For all three problems techniques used are natural extensions of those used in the binary case.
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 64 (1994), S. 231-246 
    ISSN: 1436-4646
    Keywords: Steiner tree ; Polyhedron ; Facets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This is the second part of two papers addressing the study of the facial structure of the Steiner tree polyhedron. In this paper we identify several classes of facet defining inequalities and relate them to special classes of graphs on which the Steiner tree problem is known to be NP-hard.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 64 (1994), S. 209-229 
    ISSN: 1436-4646
    Keywords: Steiner tree ; Polyhedron ; Facets ; Projection
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we give some integer programming formulations for the Steiner tree problem on undirected and directed graphs and study the associated polyhedra. We give some families of facets for the undirected case along with some compositions and extensions. We also give a projection that relates the Steiner tree polyhedron on an undirected graph to the polyhedron for the corresponding directed graph. This is used to show that the LP-relaxation of the directed formulation is superior to the LP-relaxation of the undirected one.
    Type of Medium: Electronic Resource
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