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  • Travelling Salesman Problem  (2)
  • Key words: Traveling Salesman Problem  (1)
  • 1
    Electronic Resource
    Electronic Resource
    On the symmetric travelling salesman problem I: Inequalities (1979)
    Springer
    Mathematical programming 16 (1979), S. 265-280 
    Details
    ISSN: 1436-4646
    Keywords: Linear Inequalities ; Convex Polytopes ; Facets ; Travelling Salesman Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We investigate several classes of inequalities for the symmetric travelling salesman problem with respect to their facet-defining properties for the associated polytope. A new class of inequalities called comb inequalities is derived and their number shown to grow much faster with the number of cities than the exponentially growing number of subtour-elimination constraints. The dimension of the travelling salesman polytope is calculated and several inequalities are shown to define facets of the polytope. In part II (“On the travelling salesman problem II: Lifting theorems and facets”) we prove that all subtour-elimination and all comb inequalities define facets of the symmetric travelling salesman polytope.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582116
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On the symmetric travelling salesman problem II: Lifting theorems and facets (1979)
    Springer
    Mathematical programming 16 (1979), S. 281-302 
    Details
    ISSN: 1436-4646
    Keywords: Linear Inequalities ; Convex Polytopes ; Facets ; Lifting Theorems ; Travelling Salesman Problem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Four lifting theorems are derived for the symmetric travelling salesman polytope. They provide constructions and state conditions under which a linear inequality which defines a facet of then-city travelling salesman polytope retains its facetial property for the (n + m)-city travelling salesman polytope, wherem ≥ 1 is an arbitrary integer. In particular, they permit a proof that all subtour-elimination as well as comb inequalities define facets of the convex hull of tours of then-city travelling salesman problem, wheren is an arbitrary integer.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01582117
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    Order picking in an automatic warehouse: Solving online asymmetric TSPs (1999)
    Springer
    Mathematical methods of operations research 49 (1999), S. 501-515 
    Details
    ISSN: 1432-5217
    Keywords: Key words: Traveling Salesman Problem ; online-algorithm ; automatic storage system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract. We report on a joint project with industry that had the aim to sequence transportation requests within an automatic storage system in such a way that the overall travel time is minimized. The manufacturing environment is such that scheduling decisions have to be made before all jobs are known. We have modeled this task as an online Asymmetric Traveling Salesman Problem (ATSP). Several heuristics for the online ATSP are compared computationally within a simulation environment to judge which should be used in practice. Compared to the priority rule used so far, the optimization package reduced the unloaded travel time by about 40%. Because of these significant savings our procedure was implemented as part of the control software for the stacker cranes of the storage systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s001860050064
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
    Fulltext
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