Researcher:
Yıldırım, Emre Alper

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Emre Alper

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Yıldırım

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Yıldırım, Emre Alper

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2007 - 200912010 - 201910

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Now showing 1 - 10 of 11
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    Manufacturing parts sourcing with delayed transportation policy
    (Ieee, 2007) N/A; Department of Industrial Engineering; N/A; Department of Industrial Engineering; Department of Industrial Engineering; Erkan, Tuğçe; Sancak, Emre; Yıldırım, Emre Alper; Salman, Fatma Sibel; Undergraduate Student; Master Student; Faculty Member; Faculty Member; Department of Industrial Engineering; College of Engineering; N/A; College of Engineering; College of Engineering; N/A; N/A; 28415; 178838
    We propose a joint inventory and transportation policy for a manufacturer that needs to source multiple parts from a single supplier over a multiperiod planning horizon in order to facilitate its production plan. Instead of shipping trucks from the supplier to the manufacturer immediately whenever an order is given in a period, we allow delaying transportation to the next period in order to decrease the number of truck shipments with low truck loads. At the same time we maintain a minimum safety stock of each part at the manufacturer so that the production plan is not disrupted. We introduce a mixed integer programming model that represents the interdependency between ordering and transportation decisions and minimizes the sum of both transportation and inventory holding costs incurred to the manufacturer under the proposed policy. This model is utilized to improve the parts sourcing operations of a bus manufacturer in Istanbul with estimated sizeable savings on total costs.
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    Inner approximations of completely positive reformulations of mixed binary quadratic programs: a unified analysis
    (Taylor & Francis Ltd, 2017) Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering; 28415
    Every quadratic programming problem with a mix of continuous and binary variables can be equivalently reformulated as a completely positive optimization problem, that is, a linear optimization problem over the convex but computationally intractable cone of completely positive matrices. In this paper, we focus on general inner approximations of the cone of completely positive matrices on instances of completely positive optimization problems that arise from the reformulation of mixed binary quadratic programming problems. We provide a characterization of the feasibility of such an inner approximation as well as the optimal value of a feasible inner approximation. In particular, our results imply that polyhedral inner approximations are equivalent to a finite discretization of the feasible region of the original completely positive optimization problem. Our characterization yields, as a byproduct, an upper bound on the gap between the optimal value of an inner approximation and that of the original instance. We discuss the implications of this error bound for standard and box-constrained quadratic programs as well as general mixed binary quadratic programs with a bounded feasible region.
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    Joint routing, gateway selection, scheduling and power management optimization in wireless mesh networks
    (Institute of Industrial Engineers, 2012) Uzunlar, Onur; Gökbayrak, Kagan; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering; 28415
    The third generation (3G) wireless communications technology delivers user traffic in a single step to the wired network via base station; therefore it requires all base stations to be connected to the wired network. On the other hand, in the fourth generation (4G) communication systems, it is planned to have the base stations set up so that they can deliver each other's traffic to a small number of base stations equipped with wired connections. In order to improve system resiliency against failures, a mesh structure is preferred. The most important issue in Wireless Mesh Networks (WMN) is that the signals that are simultaneously transmitted on the same frequency channel can interfere with each other to become incomprehensible at the receiver end. It is possible to operate the links at different times or at different frequencies, but this also lowers capacity usage. In this paper, we tackle the planning problems of WMN, using 802.16 (Wi-MAX) protocol, such as deploying a given number of gateway nodes along with operational problems such as routing, management of power used by nodes and scheduling while maximizing the minimum service level provided. In order to be able to apply our results to real systems, we work with optimization models based on realistic assumptions such as physical interference and single path routing. We propose heuristic methods to obtain optimal or near optimal solutions in reasonable time. The models are applied to some cities in Istanbul and Ankara provinces.
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    An alternative polynomial-sized formulation and an optimization based heuristic for the reviewer assignment problem
    (Elsevier, 2019) Yeşilçimen, Ali; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering; 28415
    Peer review systems are based on evaluating a scholarly work, referred to as a proposal, by experts in that field. In such a system, we consider the reviewer assignment problem, i.e., the problem of assigning proposals to reviewers under the assumption that each reviewer returns her preferences using ordinal rankings. Motivated by the problem defined in Cook et al. (Management Science, 51:655-661, 2005), we focus on reviewer assignments so as to maximize the total number of pairwise comparisons of proposals while ensuring a balanced coverage of distinct pairs of proposals. We propose an alternative mixed integer linear programming formulation for the reviewer assignment problem. In contrast to the optimization model proposed by Cook et al. (2005), the size of our formulation is polynomial in the input size. We present a semidefinite programming relaxation of our optimization model. Furthermore, we propose an optimization based heuristic approach, in which an optimal solution of the linear programming relaxation or the semidefinite programming relaxation of our optimization model is rounded in a straight-forward fashion, followed by a local improvement scheme based on pairwise exchanges of proposals. Our computational results illustrate the effectiveness of our optimization model and our heuristic approach.
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    PublicationOpen Access
    A hierarchical solution approach for a multicommodity distribution problem under a special cost structure
    (Elsevier, 2012) Koca, Esra; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering
    Motivated by the spare parts distribution system of a major automotive manufacturer in Turkey, we consider a multicommodity distribution problem from a central depot to a number of geographically dispersed demand points. The distribution of the items is carried out by a set of identical vehicles. The demand of each demand point can be satisfied by several vehicles and a single vehicle is allowed to serve multiple demand points. For a given vehicle, the cost structure is dictated by the farthest demand point from the depot among all demand points served by that vehicle. The objective is to satisfy the demand of each demand point with the minimum total distribution cost. We present a novel integer linear programming formulation of the problem as a variant of the network design problem. The resulting optimization problem becomes computationally infeasible for real-life problems due to the large number of integer variables. In an attempt to circumvent this disadvantage of using the direct formulation especially for larger problems, we propose a Hierarchical Approach that is aimed at solving the problem in two stages using partial demand aggregation followed by a disaggregation scheme. We study the properties of the solution returned by the Hierarchical Approach. We perform computational studies on a data set adapted from a major automotive manufacturer in Turkey. Our results reveal that the Hierarchical Approach significantly outperforms the direct formulation approach in terms of both the running time and the quality of the resulting solution especially on large instances.
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    PublicationOpen Access
    Rounding on the standard simplex: regular grids for global optimization
    (Springer, 2014) Bomze, Immanuel M.; Gollowitzer, Stefan; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering
    Given a point on the standard simplex, we calculate a proximal point on the regular grid which is closest with respect to any norm in a large class, including all l(p)-norms for p >= 1 . We show that the minimal l(p)-distance to the regular grid on the standard simplex can exceed one, even for very fine mesh sizes in high dimensions. Furthermore, for p = 1, the maximum minimal distance approaches the l(1)-diameter of the standard simplex. We also put our results into perspective with respect to the literature on approximating global optimization problems over the standard simplex by means of the regular grid.
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    PublicationOpen Access
    Exact and heuristic approaches based on noninterfering transmissions for joint gateway selection, time slot allocation, routing and power control for wireless mesh networks
    (Elsevier, 2017) Gökbayrak, Kağan; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering
    Wireless mesh networks (WMNs) provide cost-effective alternatives for extending wireless communication over larger geographical areas. In this paper, given a WMN with its nodes and possible wireless links, we consider the problem of gateway node selection for connecting the network to the Internet along with operational problems such as routing, wireless transmission capacity allocation, and transmission power control for efficient use of wired and wireless resources. Under the assumption that each node of the WMN has a fixed traffic rate, our goal is to allocate capacities to the nodes in proportion to their traffic rates so as to maximize the minimum capacity-to-demand ratio, referred to as the service level. We adopt a time division multiple access (TDMA) scheme, in which a time frame on the same frequency channel is divided into several time slots and each node can transmit in one or more time slots. We propose two mixed integer linear programming formulations. The first formulation, which is based on individual transmissions in each time slot, is a straightforward extension of a previous formulation developed by the authors for a related problem under a different set of assumptions. The alternative formulation, on the other hand, is based on sets of noninterfering wireless transmissions. In contrast with the first formulation, the size of the alternative formulation is independent of the number of time slots in a frame. We identify simple necessary and sufficient conditions for simultaneous transmissions on different links of the network in the same time slot without any significant interference. Our characterization, as a byproduct, prescribes a power level for each of the transmitting nodes. Motivated by this characterization, we propose a simple scheme to enumerate all sets of noninterfering transmissions, which is used as an input for the alternative formulation. We also introduce a set of valid inequalities for both formulations. For large instances, we propose a three-stage heuristic approach. In the first stage, we solve a partial relaxation of our alternative optimization model and determine the gateway locations. This stage also provides an upper bound on the optimal service level. In the second stage, a routing tree is constructed for each gateway node computed in the first stage. Finally, in the third stage, the alternative optimization model is solved by fixing the resulting gateway locations and the routing trees from the previous two stages. For even larger networks, we propose a heuristic approach for solving the partial relaxation in the first stage using a neighborhood search on gateway locations. Our computational results demonstrate the promising performance of our exact and heuristic approaches and the valid inequalities
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    PublicationOpen Access
    Joint gateway selection, transmission slot assignment, routing and power control for wireless mesh networks
    (Elsevier, 2013) Gökbayrak, Kağan; Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering
    Wireless mesh networks (WMNs) provide cost effective solutions for setting up a communications network over a certain geographic area. In this paper, we study strategic problems of WMNs such as selecting the gateway nodes along with several operational problems such as routing, power control, and transmission slot assignment. Under the assumptions of the physical interference model and the tree-based routing restriction for traffic flow, a mixed integer linear programming (MILP) formulation is presented, in which the objective is to maximize the minimum service level provided at the nodes. A set of valid inequalities is derived and added to the model in an attempt to improve the solution quality. Since the MILP formulation becomes computationally infeasible for larger instances, we propose a heuristic method that is aimed at solving the problem in two stages. In the first stage, we devise a simple MILP problem that is concerned only with the selection of gateway nodes. In the second stage, the MILP problem in the original formulation is solved by fixing the gateway nodes from the first stage. Computational experiments are provided to evaluate the proposed models and the heuristic method.
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    PublicationOpen Access
    Analysis of copositive optimization based linear programming bounds on standard quadratic optimization
    (Springer, 2015) Department of Industrial Engineering; Sağol, Gizem; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; Graduate School of Sciences and Engineering; College of Engineering
    The problem of minimizing a quadratic form over the unit simplex, referred to as a standard quadratic optimization problem, admits an exact reformulation as a linear optimization problem over the convex cone of completely positive matrices. This computationally intractable cone can be approximated in various ways from the inside and from the outside by two sequences of nested tractable convex cones of increasing accuracy. In this paper, we focus on the inner polyhedral approximations due to YA +/- ldA +/- rA +/- m (Optim Methods Softw 27(1):155-173, 2012) and the outer polyhedral approximations due to de Klerk and Pasechnik (SIAM J Optim 12(4):875-892, 2002). We investigate the sequences of upper and lower bounds on the optimal value of a standard quadratic optimization problem arising from these two hierarchies of inner and outer polyhedral approximations. We give complete algebraic descriptions of the sets of instances on which upper and lower bounds are exact at any given finite level of the hierarchy. We identify the structural properties of the sets of instances on which upper and lower bounds converge to the optimal value only in the limit. We present several geometric and topological properties of these sets. Our results shed light on the strengths and limitations of these inner and outer polyhedral approximations in the context of standard quadratic optimization.
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    PublicationOpen Access
    On the accuracy of uniform polyhedral approximations of the copositive cone
    (Taylor _ Francis, 2012) Department of Industrial Engineering; Yıldırım, Emre Alper; Faculty Member; Department of Industrial Engineering; College of Engineering
    We consider linear optimization problems over the cone of copositive matrices. Such conic optimization problems, called copositive programs, arise from the reformulation of a wide variety of difficult optimization problems. We propose a hierarchy of increasingly better outer polyhedral approximations to the copositive cone. We establish that the sequence of approximations is exact in the limit. By combining our outer polyhedral approximations with the inner polyhedral approximations due to de Klerk and Pasechnik [SIAM J. Optim. 12 (2002), pp. 875-892], we obtain a sequence of increasingly sharper lower and upper bounds on the optimal value of a copositive program. Under primal and dual regularity assumptions, we establish that both sequences converge to the optimal value. For standard quadratic optimization problems, we derive tight bounds on the gap between the upper and lower bounds. We provide closed-form expressions of the bounds for the maximum stable set problem. Our computational results shed light on the quality of the bounds on randomly generated instances.