Browsing by Subject "Computational results"

Now showing 1 - 14 of 14

Open Access
A beam search algorithm to optimize robustness under random machine breakdowns and processing time variability
(Institute of Industrial Engineers, 2007) Gören, S.; Sabuncuoğlu, İhsan
The vast majority of the machine scheduling research assumes complete information about the scheduling problem and a static environment in which scheduling systems operate. In practice, however, scheduling systems are subject to considerable uncertainty in dynamic environments. The ability to cope with the uncertainty in scheduling process is becoming increasingly important in today's highly dynamic and competitive business environments. In the literature, two approaches have appeared as the effective way: reactive and proactive scheduling. The objective in reactive scheduling is to revise schedules as necessary, while proactive scheduling attempts to incorporate future disruptions when generating schedules. In this paper we take a proactive scheduling approach to solve a machine scheduling problem with two sources of uncertainty: processing time variability and machine breakdowns. We define two robustness measures and develop a heuristic based on beam search methodology to optimize them. The computational results show that the proposed algorithms perform significantly better than a number of heuristics available in the literature.
Open Access
Benchmark Solutions of Large Problems for Evaluating Accuracy and Efficiency of Electromagnetics Solvers
(IEEE, 2011) Ergul, O.; Gürel, Levent
We present a set of benchmark problems involving conducting spheres and their solutions using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). Accuracy of the implementation is tested by comparing the computational results with analytical Mie-series solutions. Reference solutions are made available on an interactive website to evaluate and compare the accuracy and efficiency of fast solvers. We also demonstrate the capabilities of our solver on real-life problems involving complicated targets, such as the Flamme.
Open Access
Bicriteria multiresource generalized assignment problem
(John Wiley & Sons, 2014) Karsu, O.; Azizoglu, M.
In this study,we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches.
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
Discrete time/cost trade-off problem: a decomposition-based solution algorithm for the budget version
(Pergamon Press, 2010-04) Hazır, O.; Haouari, M.; Erel, E.
This paper investigates the budget variant of the discrete time/cost trade-off problem (DTCTP). This multi-mode project scheduling problem requires assigning modes to the activities of a project so that the total completion time is minimized and the budget and the precedence constraints are satisfied. This problem is often encountered in practice as timely completion of the projects without exceeding the budget is crucial. The contribution of this paper to the literatures is to describe an effective Benders Decomposition-based exact algorithm to solve the DTCTP instances of realistic sizes. Although Benders Decomposition often exhibits a very slow convergence, we have included several algorithmic features to enhance the performance of the proposed tailored approach. Computational results attest to the efficacy of the proposed algorithm, which can solve large-scale instances to optimality.
Open Access
Double bound method for solving the p-center location problem
(Elsevier, 2013) Calik, H.; Tansel, B. C.
We give a review of existing methods for solving the absolute and vertex restricted p-center problems on networks and propose a new integer programming formulation, a tightened version of this formulation and a new method based on successive restrictions of the new formulation. A specialization of the new method with two-element restrictions obtains the optimal p-center solution by solving a series of simple structured integer programs in recognition form. This specialization is called the double bound method. A relaxation of the proposed formulation gives the tightest known lower bound in the literature (obtained earlier by Elloumi et al., [1]). A polynomial time algorithm is presented to compute this bound. New lower and upper bounds are proposed. Problems from the OR-Library [2] and TSPLIB [3] are solved by the proposed algorithms with up to 3038 nodes. Previous computational results were restricted to networks with at most 1817 nodes.
Open Access
An integrated approach for airline scheduling, aircraft fleeting and routing with cruise speed control
(Elsevier, 2016) Gürkan, H.; Gürel, S.; Aktürk, M. S.
To place an emphasis on profound relations among airline schedule planning problems and to mitigate the effect of unexpected delays, we integrate schedule design, fleet assignment and aircraft routing problems within a daily planning horizon while passengers' connection service levels are ensured via chance constraints. We propose a nonlinear mixed integer programming model due to the nonlinear fuel consumption and CO2 emission cost terms in the objective function, which is handled by second order conic reformulation. The key contribution of this study is to take into account the cruise time control for the first time in an integrated model of these three stages of airline operations. Changing cruise times of flights in an integrated model enables to construct a schedule to increase utilization of fuel efficient aircraft and even to decrease total number of aircraft needed while satisfying the same service level and maintenance requirements for aircraft fleeting and routing. There is a critical tradeoff between the number of aircraft needed to fulfill the required flights and overall operational expenses. We also propose two heuristic methods to solve larger size problems. Finally, computational results using real data obtained from a major U.S. carrier are presented to demonstrate potential profitability in applying the proposed solution methods.
Open Access
Mixed-integer second-order cone programming for lower hedging of American contingent claims in incomplete markets
(2013) Pınar, M. Ç.
We describe a challenging class of large mixed-integer second-order cone programming models which arise in computing the maximum price that a buyer is willing to disburse to acquire an American contingent claim in an incomplete financial market with no arbitrage opportunity. Taking the viewpoint of an investor who is willing to allow a controlled amount of risk by replacing the classical no-arbitrage assumption with a "no good-deal assumption" defined using an arbitrage-adjusted Sharpe ratio criterion we formulate the problem of computing the pricing and hedging of an American option in a financial market described by a multi-period, discrete-time, finite-state scenario tree as a large-scale mixed-integer conic optimization problem. We report computational results with off-the-shelf mixed-integer conic optimization software.
Open Access
The multi-terminal maximum-flow network-interdiction problem
(2011) Akgün, İ.; Tansel, B. Ç.; Wood, R. K.
This paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K ≥ 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the post-interdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E. © 2011 Elsevier B.V. All rights reserved.
Open Access
New formulations for the hop-constrained minimum spanning tree problem via Sherali and Driscoll's tightened Miller-Tucker-Zemlin constraints
(Elsevier, 2010) Akgün, İbrahim
Given an undirected network with positive edge costs and a natural number p, the hop-constrained minimum spanning tree problem (HMST) is the problem of finding a spanning tree with minimum total cost such that each path starting from a specified root node has no more than p hops (edges). In this paper, the new models based on the Miller-Tucker-Zemlin (MTZ) subtour elimination constraints are developed and computational results together with comparisons against MTZ-based, flow-based, and hop-indexed formulations are reported. The first model is obtained by adapting the MTZ-based Asymmetric Traveling Salesman Problem formulation of Sherali and Driscoll [18] and the other two models are obtained by combining topology-enforcing and MTZ-related constraints offered by Akgün and Tansel (submitted for publication) [20] for HMST with the first model appropriately. Computational studies show that the best LP bounds of the MTZ-based models in the literature are improved by the proposed models. The best solution times of the MTZ-based models are not improved for optimally solved instances. However, the results for the harder, large-size instances imply that the proposed models are likely to produce better solution times. The proposed models do not dominate the flow-based and hop-indexed formulations with respect to LP bounds. However, good feasible solutions can be obtained in a reasonable amount of time for problems for which even the LP relaxations of the flow-based and hop-indexed formulations can be solved in about 2 days. © 2010 Elsevier Ltd. All rights reserved.
Open Access
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.
Open Access
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.
Open Access
A strong conic quadratic reformulation for machine-job assignment with controllable processing times
(Elsevier, 2009) Aktürk, M. S.; Atamtürk, A.; Gürel, S.
We describe a polynomial-size conic quadratic reformulation for a machine-job assignment problem with separable convex cost. Because the conic strengthening is based only on the objective of the problem, it can also be applied to other problems with similar cost functions. Computational results demonstrate the effectiveness of the conic reformulation.
Open Access
Volumetric plasmonic resonator architecture for thin-film solar cells
(AIP Publishing, 2011-03-04) Sefunc, M.A.; Okyay, Ali Kemal; Demir, Hilmi Volkan
We propose and demonstrate a design concept of volumetric plasmonic resonators that relies on the idea of incorporating coupled layers of plasmonic structures embedded into a solar cell in enhanced optical absorption for surface-normal and off-axis angle configurations, beyond the enhancement limit of individual plasmonic layers. For a proof-of-concept demonstration in a thin-film organic solar cell that uses absorbing materials of copper phthalocyanine/perylene tetracarboxylic bisbenzimidazole, we couple two silver grating layers such that the field localization is further extended within the volume of active layers. Our computational results show a maximum optical absorption enhancement level of ∼67% under air mass 1.5 global illumination considering both polarizations.