Browsing by Subject "Valid inequality"

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    Comparison of the formulations for a hub-and-spoke network design problem under congestion
    (Elsevier, 2016) Kian, Ramer; Kargar, Kamyar
    In this paper, we study the hub location problem with a power-law congestion cost and propose an exact solution approach. We formulate this problem in a conic quadratic form and use a strengthening method which rests on valid inequalities of perspective cuts in mixed integer nonlinear programming. In a numerical study, we compare two well known types of mathematical modeling in the hub-location problems which are solved with different branch and cut strategies. The strength and weakness of the formulations are summarized based on an extensive numerical study over the CAB data set. © 2016 Elsevier Ltd
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    Hub location problems: the location of interacting facilities
    (Springer, 2011) Kara, Bahar Y.; Taner, Mehmet R.; Eiselt, H. A.; Marianov, V.
    O’Kelly’s (1986) classical paper started a new research stream by identifying a connection between spatial interaction models and location theory. The traditional spatial interaction theory applies models of travel behavior to investigate demand patterns between fixed locations. Location theory, on the other hand, takes demand as given, assumes a simple view of travel behavior, and focuses on finding the best location for facilities.
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    A polyhedral study of multiechelon lot sizing with intermediate demands
    (Institute for Operations Research and the Management Sciences (I N F O R M S), 2012) Zhang, M.; Küçükyavuz, S.; Yaman, H.
    In this paper, we study a multiechelon uncapacitated lot-sizing problem in series (m-ULS), where the output of the intermediate echelons has its own external demand and is also an input to the next echelon. We propose a polynomial-time dynamic programming algorithm, which gives a tight, compact extended formulation for the two-echelon case (2-ULS). Next, we present a family of valid inequalities for m-ULS, show its strength, and give a polynomial-time separation algorithm. We establish a hierarchy between the alternative formulations for 2-ULS. In particular, we show that our valid inequalities can be obtained from the projection of the multicommodity formulation. Our computational results show that this extended formulation is very effective in solving our uncapacitated multi-item two-echelon test problems. In addition, for capacitated multi-item, multiechelon problems, we demonstrate the effectiveness of a branch-and-cut algorithm using the proposed inequalities.
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    The ring/κ-rings network design problem: model and branch-and-cut algorithm
    (John Wiley & Sons, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
    This article considers the problem of designing a two-level network where the upper level consists of a backbone ring network connecting the so-called hub nodes, and the lower level is formed by access ring networks that connect the non-hub nodes to the hub nodes. There is a fixed cost for each type of link, and a facility opening cost associated to each hub. The number of nodes in each access ring is bounded, and the number of access rings connected to a hub is limited to κ, thus resulting in a ring/κ-rings topology. The aim is to decide the hubs to open and to design the backbone and access rings to minimize the installation cost. We propose a mathematical model, give valid inequalities, and describe a branch-and-cut algorithm to solve the problem. Computational results show the algorithm is able to find optimal solutions on instances involving up to 40 nodes within a reasonable time.
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    Time constrained maximal covering salesman problem with weighted demands and partial coverage
    (Elsevier Ltd, 2016) Ozbaygin, G.; Yaman, H.; Karasan, O. E.
    In a routing framework, it may not be viable to visit every single customer separately due to resource limitations or efficiency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in which the aim is to find a tour visiting a subset of customers so that the amount of demand covered within a limited time is maximized. We provide flow and cut formulations and derive valid inequalities. Since the connectivity constraints and the proposed valid inequalities are exponential in the size of the problem, we devise different branch-and-cut schemes. Computational experiments performed on a set of problem instances demonstrate the effectiveness of the proposed valid inequalities in terms of strengthening the linear relaxation bounds as well as speeding up the solution procedure. Moreover, the results indicate the superiority of using a branch-and-cut methodology over a flow-based formulation. Finally, we discuss the relation between the problem parameters and the structure of optimal solutions based on the results of our experiments. © 2016 Elsevier Ltd