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  • Articles  (227)
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  • 11
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    Springer
    In: 4OR
    Publication Date: 2018-03-05
    Description: Fritz John and Karush–Kuhn–Tucker necessary conditions for local LU-optimal solutions of the constrained interval-valued optimization problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators are established. Under suitable assumptions on the generalized convexity of objective and constraint functions, sufficient conditions for LU-optimal solutions are given. The dual problems of Mond–Weir and Wolfe types are studied together with weak and strong duality theorems for them.
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 12
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    Springer
    In: 4OR
    Publication Date: 2018-03-05
    Description: In the context of recreational routing, the problem of finding a route which starts and ends in the same location (while achieving a length between specified upper and lower boundaries) is a common task, especially for tourists or cyclists who want to exercise. The topic of finding a tour between a specified starting and ending location while minimizing one or multiple criteria is well covered in literature. In contrast to this, the route planning task in which a pleasant tour with length between a maximum and a minimum boundary needs to be found is relatively underexplored. In this paper, we provide a formal definition of this problem, taking into account the existing literature on which route attributes influence cyclists in their route choice. We show that the resulting problem is NP-hard and devise a branch-and-bound algorithm that is able to provide a bound on the quality of the best solution in pseudo-polynomial time. Furthermore, we also create an efficient heuristic to tackle the problem and we compare the quality of the solutions that are generated by the heuristic with the bounds provided by the branch-and-bound algorithm. Also, we thoroughly discuss the complexity and running time of the heuristic.
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 13
    Publication Date: 2018-03-05
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 14
    Publication Date: 2018-03-05
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 15
    Publication Date: 2018-03-05
    Description: In this paper, we consider a multi-source Weber problem of m new facilities with respect to n demand regions in order to minimize the sum of the transportation costs between these facilities and the demand regions. We find a point on the border of each demand region from which the facilities serve the demand regions at these points. We present an algorithm including a location phase and an allocation phase in each iteration for solving this problem. An algorithm is also proposed for carrying out the location phase. Moreover, global convergence of the new algorithm is proved under mild assumptions, and some numerical results are presented.
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 16
    Publication Date: 2018-03-05
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 17
    Publication Date: 2018-03-05
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 18
    Publication Date: 2018-03-05
    Description: We introduce and prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints that has been proposed by Liberti (4OR 5(3):231–245, 2007 , https://doi.org/10.1007/s10288-006-0015-3 ). The new conditions resolve inconsistencies that can occur when the original method is used. We also present a mixed-integer linear program to compute a minimally sized linearization. When all the assignment constraints have non-overlapping variable support, this program is shown to have a totally unimodular constraint matrix. Finally, we give a polynomial-time combinatorial algorithm that is exact in this case and can be used as a heuristic otherwise.
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 19
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    Springer
    In: 4OR
    Publication Date: 2017-04-27
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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  • 20
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    Springer
    In: 4OR
    Publication Date: 2017-03-04
    Description: Seaborne trade is the lynchpin in almost every international supply chain, and about 90% of non-bulk cargo worldwide is transported by container. In this survey we give an overview of data-driven optimization problems in liner shipping. Research in liner shipping is motivated by a need for handling still more complex decision problems, based on big data sets and going across several organizational entities. Moreover, liner shipping optimization problems are pushing the limits of optimization methods, creating a new breeding ground for advanced modelling and solution methods. Starting from liner shipping network design , we consider the problem of container routing and speed optimization . Next, we consider empty container repositioning and stowage planning as well as disruption management . In addition, the problem of bunker purchasing is considered in depth. In each section we give a clear problem description, bring an overview of the existing literature, and go in depth with a specific model that somehow is essential for the problem. We conclude the survey by giving an introduction to the public benchmark instances LINER-LIB. Finally, we discuss future challenges and give directions for further research.
    Print ISSN: 1619-4500
    Electronic ISSN: 1614-2411
    Topics: Mathematics
    Published by Springer
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