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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical programming 86 (1999), S. 1-15 
    ISSN: 1436-4646
    Keywords: Key words: submodular flow problem – cycle canceling method – polynomial algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. Submodular flow problems, introduced by Edmonds and Giles [2], generalize network flow problems. Many algorithms for solving network flow problems have been generalized to submodular flow problems (cf. references in Fujishige [4]), e.g. the cycle canceling method of Klein [9]. For network flow problems, the choice of minimum-mean cycles in Goldberg and Tarjan [6], and the choice of minimum-ratio cycles in Wallacher [12] lead to polynomial cycle canceling methods. For submodular flow problems, Cui and Fujishige [1] show finiteness for the minimum-mean cycle method while Zimmermann [16] develops a pseudo-polynomial minimum ratio cycle method. Here, we prove pseudo-polynomiality of a larger class of the minimum-ratio variants and, by combining both methods, we develop a polynomial cycle canceling algorithm for submodular flow problems.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Annals of operations research 96 (2000), S. 287-315 
    ISSN: 1572-9338
    Keywords: dispatch ; local transport ; quadratic assignment ; stack ; 90Cxx ; 90C10 ; 90C27 ; 90C39
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract Real-time dispatch problems arise when preparing and executing the daily schedule of local transport companies. We consider the daily dispatch of transport vehicles like trams in storage yards. Immediately on arrival, each tram has to be assigned to a location in the depot and to an appropriate round trip of the next schedule period. In order to achieve a departure order satisfying the scheduled demand, shunting of vehicles may be unavoidable. Since shunting takes time and causes operational cost, the number of shunting movements should be minimized without violation of operational constraints. As an alternative, we may serve some round trips with trams of type differing from the requested type. In practice, the actual arrival order of trams may differ substantially from the scheduled arrival order. Then, dispatch decisions are due within a short time interval and have to be based on incomplete information. For such real-time dispatch problems, we develop combinatorial optimization models and exact as well as heuristic algorithms. Computational experience for real-world and random data shows that the derived methods yield good (often optimal) solutions within the required tight time bounds.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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