Browsing by Author "Yaman, H."

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Open Access
Allocation Strategies in Hub Networks
(Elsevier, 2011-06-11) Yaman, H.
In this paper, we study allocation strategies and their effects on total routing costs in hub networks. Given a set of nodes with pairwise traffic demands, the p-hub median problem is the problem of choosing p nodes as hub locations and routing traffic through these hubs at minimum cost. This problem has two versions; in single allocation problems, each node can send and receive traffic through a single hub, whereas in multiple allocation problems, there is no such restriction and a node may send and receive its traffic through all p hubs. This results in high fixed costs and complicated networks. In this study, we introduce the r-allocation p-hub median problem, where each node can be connected to at most r hubs. This new problem generalizes the two versions of the p-hub median problem. We derive mixed-integer programming formulations for this problem and perform a computational study using well-known datasets. For these datasets, we conclude that single allocation solutions are considerably more expensive than multiple allocation solutions, but significant savings can be achieved by allowing nodes to be allocated to two or three hubs rather than one. We also present models for variations of this problem with service quality considerations, flow thresholds, and non-stop service.
Open Access
A branch and cut algorithm for hub location problems with single assignment
(Springer, 2005) Labbé, M.; Yaman, H.; Gourdin, E.
The hub location problem with single assignment is the problem of locating hubs and assigning the terminal nodes to hubs in order to minimize the cost of hub installation and the cost of routing the traffic in the network. There may also be capacity restrictions on the amount of traffic that can transit by hubs. The aim of this paper is to investigate polyhedral properties of these problems and to develop a branch and cut algorithm based on these results.
Open Access
A branch-and-cut algorithm for the hub location and routing problem
(Elsevier, 2014) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
We study the hub location and routing problem where we decide on the location of hubs, the allocation of nodes to hubs, and the routing among the nodes allocated to the same hubs, with the aim of minimizing the total transportation cost. Each hub has one vehicle that visits all the nodes assigned to it on a cycle. We propose a mixed integer programming formulation for this problem and strengthen it with valid inequalities. We devise separation routines for these inequalities and develop a branch-and-cut algorithm which is tested on CAB and AP instances from the literature. The results show that the formulation is strong and the branch-and-cut algorithm is able to solve instances with up to 50 nodes.
Open Access
A branch-and-cut algorithm for two-level survivable network design problems
(Elsevier, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
This paper approaches the problem of designing a two-level network protected against single-edge failures. The problem simultaneously decides on the partition of the set of nodes into terminals and hubs, the connection of the hubs through a backbone network (first network level), and the assignment of terminals to hubs and their connection through access networks (second network level). We consider two survivable structures in both network levels. One structure is a two-edge connected network, and the other structure is a ring. There is a limit on the number of nodes in each access network, and there are fixed costs associated with the hubs and the access and backbone links. The aim of the problem is to minimize the total cost. We give integer programming formulations and valid inequalities for the different versions of the problem, solve them using a branch-and-cut algorithm, and discuss computational results. Some of the new inequalities can be used also to solve other problems in the literature, like the plant cycle location problem and the hub location routing problem.
Open Access
A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations
(Elsevier Ltd, 2017) Ozbaygin G.; Ekin Karasan O.; Savelsbergh M.; Yaman, H.
We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set. © 2017 Elsevier Ltd
Open Access
A capacitated hub location problem under hose demand uncertainty
(Elsevier, 2017) Meraklı, M.; Yaman, H.
In this study, we consider a capacitated multiple allocation hub location problem with hose demand uncertainty. Since the routing cost is a function of demand and capacity constraints are imposed on hubs, demand uncertainty has an impact on both the total cost and the feasibility of the solutions. We present a mathematical formulation of the problem and devise two different Benders decomposition algorithms. We develop an algorithm to solve the dual subproblem using complementary slackness. In our computational experiments, we test the efficiency of our approaches and we analyze the effects of uncertainty. The results show that we obtain robust solutions with significant cost savings by incorporating uncertainty into our problem.
Open Access
Concentrator location in telecommunications
(Springer, 2004) Yaman, H.
We survey the main results in the author's PhD Thesis presented in December 2002 at the Université Libre de Bruxelles and supervised by Prof. Martine Labbé. The dissertation is written in English and is available at smg.ulb.ac.be. Several versions of concentrator location problems in telecommunication networks are studied. The thesis presents a list of polyhedral results for these problems and a branch and cut algorithm for the most general problem introduced.
Open Access
Continuous knapsack sets with divisible capacities
(Springer, 2016) Wolsey, L. A.; Yaman, H.
We study two continuous knapsack sets (Formula presented.) and (Formula presented.) with (Formula presented.) integer, one unbounded continuous and (Formula presented.) bounded continuous variables in either (Formula presented.) or (Formula presented.) form. When the coefficients of the integer variables are integer and divisible, we show in both cases that the convex hull is the intersection of the bound constraints and (Formula presented.) polyhedra arising as the convex hulls of continuous knapsack sets with a single unbounded continuous variable. The latter convex hulls are completely described by an exponential family of partition inequalities and a polynomial size extended formulation is known in the (Formula presented.) case. We also provide an extended formulation for the (Formula presented.) case. It follows that, given a specific objective function, optimization over both (Formula presented.) and (Formula presented.) can be carried out by solving (Formula presented.) polynomial size linear programs. A further consequence of these results is that the coefficients of the continuous variables all take the values 0 or 1 (after scaling) in any non-trivial facet-defining inequality of the convex hull of such sets.
Open Access
Formulations and valid inequalities for the heterogeneous vehicle routing problem
(Springer, 2006) Yaman, H.
We consider the vehicle routing problem where one can choose among vehicles with different costs and capacities to serve the trips. We develop six different formulations: the first four based on Miller-Tucker-Zemlin constraints and the last two based on flows. We compare the linear programming bounds of these formulations. We derive valid inequalities and lift some of the constraints to improve the lower bounds. We generalize and strengthen subtour elimination and generalized large multistar inequalities.
Open Access
Generating facets for the independence system
(Society for Industrial and Applied Mathematics, 2009) Fouilhoux, P.; Labbé, M.; Mahjoub, A. R.; Yaman, H.
In this paper, we present procedures to obtain facet-defining inequalities for the independence system polytope. These procedures are defined for inequalities which are not necessarily rank inequalities. We illustrate the use of these procedures by der iving strong valid inequalities for the acyclic induced subgraph, triangle free induced subgraph, bipartite induced subgraph, and knapsack polytopes. Finally, we derive a new family of facet-defining ineq ualities for the independence system polytope by adding a set of edges to antiwebs.
Open Access
Health network mergers and hospital re-planning
(Palgrave Macmillan Ltd., 2010) Güneş, E. D.; Yaman, H.
This paper presents an integer programming formulation for the hospital re-planning problem which arises after hospital network mergers. The model finds the best re-allocation of resources among hospitals, the assignment of patients to hospitals and the service portfolio to minimize the system costs subject to quality and capacity constraints. An application in the Turkish hospital networks case is illustrated to show the implications of consolidation of health insurance funds on resource allocations and flow of patients in the system.
Open Access
The hierarchical hub median problem with single assignment
(Elsevier, 2009) Yaman, H.
We study the problem of designing a three level hub network where the top level consists of a complete network connecting the so-called central hubs and the second and third levels are unions of star networks connecting the remaining hubs to central hubs and the demand centers to hubs and central hubs, respectively. The problem is to decide on the locations of a predetermined number of hubs and central hubs and the connections in order to minimize the total routing cost in the resulting network. This problem includes the classical p-hub median problem as a special case. We also consider a version of this problem where service quality considerations are incorporated through delivery time restrictions. We propose mixed integer programming models for these two problems and report the outcomes of a computational study using the CAB data and the Turkey data.
Open Access
Hierarchical multimodal hub location problem with time-definite deliveries
(Elsevier, 2012) Alumur, S. A.; Yaman, H.; Kara, B. Y.
Hierarchical multimodal hub location problem is a cost-minimizing hub covering problem where two types of hubs and hub links, accounting for ground and air transportation, are to be established, while ensuring time-definite deliveries. We propose a mixed-integer programming formulation and perform a comprehensive sensitivity analysis on the Turkish network. We show that the locations of airport hubs are less sensitive to the cost parameters compared to the locations of ground hubs and it is possible to improve the service quality at not much additional cost in the resulting multimodal networks. Our methodology provides the means for a detailed trade-off analysis.
Open Access
Hierarchical Survivable Network Design Problems
(Elsevier, 2016) Rodríguez-Martín, I.; Salazar-González, J-J.; Yaman, H.
We address the problem of designing two-level networks protected against single edge failures. A set of nodes must be partitioned into terminals and hubs, hubs must be connected through a backbone network, and terminals must be assigned to hubs and connected to them through access networks, being the objective to minimize the total cost. We consider two survivable structures, two-edge connected (2EC) networks and rings, in both levels of the network. We present an integer programming formulation for these problems, solve them using a branch-and-cut algorithm, and show some computational results.
Open Access
Humanitarian logistics under uncertainty: planning for sheltering and evacuation
(Springer Cham, 2023-05-09) Bayram, V.; Y. Kara, Bahar; Saldanha-da-Gama, F.; Yaman, H.; Eiselt, H. A.; Marianov, V.
This chapter focuses on a major area emerging in the context of humanitarian logistics: emergency evacuation planning and management. Two major aspects are covered: shelter site location and evacuation traffic assignment. Both are discussed separately before an integrated problem is considered. Throughout the chapter, uncertainty in the underlying parameters is assumed. The major sources of uncertainty analyzed are the demand for sheltering and capacity of the edges in the underlying network. Congestion issues emerge in this context that are also considered. Different paradigms for capturing uncertainty are considered for illustrative purposes, namely, robust optimization, chance-constrained programming, and stochastic programming.
Open Access
The integer knapsack cover polyhedron
(Society for Industrial and Applied Mathematics, 2007) Yaman, H.
We study the integer knapsack cover polyhedron which is the convex hull of the set of vectors x ∈ ℤ+ n that satisfy C T x ≥ b, with C ∈ ℤ++ n and 6 ∈ ℤ++. We present some general results about the nontrivial facet-defining inequalities. Then we derive specific families of valid inequalities, namely, rounding, residual capacity, and lifted rounding inequalities, and identify cases where they define facets. We also study some known families of valid inequalities called 2-partition inequalities and improve them using sequence-independent lifting.
Open Access
An intermodal multicommodity routing problem with scheduled services
(2012) Ayar, B.; Yaman, H.
We study a multicommodity routing problem faced by an intermodal service operator that uses ground and maritime transportation. Given a planning horizon, a set of commodities to be picked up at their release times and to be delivered not later than their duedates, the problem is to decide on routes for these commodities using trucks and scheduled and capacitated maritime services at minimum cost of transportation and stocking at the seaports. Two mixed integer programming formulations and valid inequalities are proposed for this problem. The results of a computational study to evaluate the strength of the linear programming relaxations and the solution times are reported.
Open Access
The latest arrival hub location problem for cargo delivery systems with stopovers
(Elsevier, 2007) Yaman, H.; Kara, B. Y.; Tansel, B. C.
In this paper, we concentrate on the service structure of ground-transportation based cargo delivery companies. The transient times that arise from nonsimultaneous arrivals at hubs (typically spent for unloading, loading, and sorting operations) can constitute a significant portion of the total delivery time for cargo delivery systems. The latest arrival hub location problem is a new minimax model that focuses on the minimization of the arrival time of the last item to arrive, taking into account journey times as well as the transient times at hubs. We first focus on a typical cargo delivery firm operating in Turkey and observe that stopovers are essential components of a ground-based cargo delivery system. The existing formulations of the hub location problem in the literature do not allow stopovers since they assume direct connections between demand centers and hubs. In this paper, we propose a generic mathematical model, which allows stopovers for the latest arrival hub location problem. We improve the model using valid inequalities and lifting. We present computational results using data from the US and Turkey.
Open Access
Linear inequalities among graph invariants: using graPHedron to uncover optimal relationships
(John Wiley & Sons, 2008) Christophe, J.; Dewez, S.; Doignon, J-P.; Fasbender, G.; Grégoire, P.; Huygens, D.; Labbé, M.; Elloumi, S.; Mélot, H.; Yaman, H.
Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph vertices, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a "small" number of vertices. It greatly helps in conjecturing optimal linear inequalities, which are then hopefully proved for any number of vertices. Two examples are investigated here for the class of connected graphs. First, all the optimal linear inequalities for the stability number and the number of edges are obtained. To this aim, a problem of Ore (1962) related to the Turán Theorem (1941) is solved. Second, several optimal inequalities are established for three invariants: the maximum degree, the irregularity, and the diameter.
Open Access
Lot sizing with piecewise concave production costs
(Institute for Operations Research and the Management Sciences (I N F O R M S), 2014) Koca, E.; Yaman, H.; Aktürk, M. S.
We study the lot-sizing problem with piecewise concave production costs and concave holding costs. This problem is a generalization of the lot-sizing problem with quantity discounts, minimum order quantities, capacities, overloading, subcontracting or a combination of these. We develop a dynamic programming algorithm to solve this problem and answer an open question in the literature: we show that the problem is polynomially solvable when the breakpoints of the production cost function are time invariant and the number of breakpoints is fixed. For the special cases with capacities and subcontracting, the time complexity of our algorithm is as good as the complexity of algorithms available in the literature. We report the results of a computational experiment where the dynamic programming is able to solve instances that are hard for a mixed-integer programming solver. We enhance the mixed-integer programming formulation with valid inequalities based on mixing sets and use a cut-and-branch algorithm to compute better bounds. We propose a state space reduction-based heuristic algorithm for large instances and show that the solutions are of good quality by comparing them with the bounds obtained from the cut-and-branch.