@article {1538, title = {Multiple instance classification via quadratic programming}, journal = {Journal of Global Optimization}, year = {2022}, pages = {1{\textendash}32}, author = {Emel {\c S}eyma K{\"u}{\c c}{\"u}ka{\c s}c{\i} and Mustafa Gokce Baydogan and Z C Ta{\c s}k{\i}n} } @article {1540, title = {A branch-and-price algorithm for parallel machine campaign planning under sequence dependent family setups and co-production}, journal = {Computers \& Operations Research}, volume = {135}, year = {2021}, pages = {105430}, doi = {https://doi.org/10.1016/j.cor.2021.105430}, author = {Serkan Kalay and Z C Ta{\c s}k{\i}n} } @article {1539, title = {A Branch-Price-and-Cut Algorithm for Optimal Decoding of LDPC Codes}, journal = {Journal of Global Optimization}, volume = {81}, year = {2021}, pages = {805{\textendash}834}, doi = {https://doi.org/10.1007/s10898-021-01073-4}, author = {Banu Kabakulak and Z C Ta{\c s}k{\i}n and Ali Emre Pusane} } @article {1542, title = {An Exact Cutting Plane Algorithm to Solve the Selective Graph Coloring Problem in Perfect Graphs}, journal = {European Journal of Operational Research}, volume = {291(1)}, year = {2021}, pages = {67{\textendash}83}, doi = {https://doi.org/10.1016/j.ejor.2020.09.017}, author = {Oylum {\c S}eker and Ekim, Tinaz and Z C Ta{\c s}k{\i}n} } @article {1424, title = {A linear programming approach to multiple instance learning}, journal = {Turkish Journal of Electrical Engineering \& Computer Sciences}, volume = {29}, year = {2021}, pages = {2186{\textendash}2201}, author = {Emel {\c S}eyma K{\"u}{\c c}{\"u}ka{\c s}c{\i} and Mustafa Gokce Baydogan and Z C Ta{\c s}k{\i}n} } @article {1541, title = {Single Machine Campaign Planning under Sequence Dependent Family Setups and Co-Production}, journal = {Journal of the Operational Research Society}, volume = {72}, year = {2021}, pages = {2091{\textendash}2111}, doi = {https://doi.org/10.1080/01605682.2020.1772016}, author = {Serkan Kalay and Z C Ta{\c s}k{\i}n} } @article {1426, title = {A branch-and-cut algorithm for a bipartite graph construction problem in digital communication systems}, journal = {Networks}, volume = {75}, year = {2020}, pages = {137-157}, abstract = {

Abstract We study a bipartite graph (BG) construction problem that arises in digital communication systems. In a digital communication system, information is sent from one place to another over a noisy communication channel using binary symbols (bits). The original information is encoded by adding redundant bits, which are then used to detect and correct errors that may have been introduced during transmission. Harmful structures, such as small cycles, severely deteriorate the error correction capability of a BG. We introduce an integer programming formulation to generate a BG for a given smallest cycle length. We propose a branch-and-cut algorithm for its solution and investigate the structural properties of the problem to derive valid inequalities and variable fixing rules. We also introduce heuristics to obtain feasible solutions for the problem. The computational experiments show that our algorithm can generate BGs without small cycles in an acceptable amount of time for practically relevant dimensions.

}, keywords = {bipartite graphs, branch-and-cut algorithm, integer programming, symmetry, telecommunications, valid inequalities}, doi = {https://doi.org/10.1002/net.21914}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/net.21914}, author = {Banu Kabakulak and Z C Ta{\c s}k{\i}n and Pusane, Ali E.} } @article {1428, title = {On the Construction of Regular QC-LDPC Codes With Low Error Floor}, journal = {IEEE Communications Letters}, volume = {24}, year = {2020}, pages = {25-28}, doi = {10.1109/LCOMM.2019.2953058}, author = {Sar{\i}duman, Abdullah and Pusane, Ali E. and Z C Ta{\c s}k{\i}n} } @article {1425, title = {Decentralized decomposition algorithms for peer-to-peer linear optimization}, journal = {RAIRO-Oper. Res.}, volume = {54}, year = {2020}, pages = {1835-1861}, doi = {10.1051/ro/2019097}, url = {https://doi.org/10.1051/ro/2019097}, author = {Aydin, M. Asli and Z C Ta{\c s}k{\i}n} } @article {1427, title = {A strong integer programming formulation for hybrid flowshop scheduling}, journal = {Journal of the Operational Research Society}, volume = {71}, year = {2020}, pages = {2042-2052}, doi = {10.1080/01605682.2019.1654414}, url = {https://doi.org/10.1080/01605682.2019.1654414}, author = {Ali Tamer {\"U}nal and Semra A{\u g}ral{\i} and Z C Ta{\c s}k{\i}n} } @article {1433, title = {A column generation heuristic for {VMAT} planning with adaptive {CVaR} constraints}, journal = {Physics in Medicine {\&} Biology}, volume = {64}, year = {2019}, month = {oct}, pages = {205024}, abstract = {

In this study we develop an efficient computational procedure that generates medically acceptable treatment plans for volumetric modulated arc therapy with constant gantry speed. Our proposed method is a column generation heuristic based on a mixed integer linear programming model, where the objective function contains minimization of total monitor unit of the treatment plan and dose-volume requirements are included as conditional value-at-risk constraints. Our heuristic generates a full treatment arc for the restricted master problem and calibrates the right hand side parameters of the conditional value-at-risk constraints in the first phase. In the second phase, this initial solution is improved by performing column generation. This is a fully automated procedure and produces treatment plans in a single call without any human intervention. We evaluate its performance on real prostate cancer data by comparing the quality of the generated plans with those obtained by a widely used commercial treatment planning system. Our analysis shows that the results are promising, and the generated plans satisfy the prescription restrictions and require fewer monitor units on average compared to the ones obtained using Eclipse.

}, doi = {10.1088/1361-6560/ab416e}, url = {https://doi.org/10.1088/1361-6560/ab416e}, author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel and Hatice Bilge and Nazmiye D{\"o}nmez Kesen and Murat Okutan and Ethem Nezih Oral} } @article {1431, title = {A decomposition approach to solve the selective graph coloring problem in some perfect graph families}, journal = {Networks}, volume = {73}, year = {2019}, pages = {145-169}, abstract = {

Graph coloring is the problem of assigning a minimum number of colors to all vertices of a graph such that no two adjacent vertices receive the same color. The selective graph coloring problem is a generalization of the standard graph coloring problem; given a graph with a partition of its vertex set into clusters, the objective is to choose exactly one vertex per cluster so that, among all possible selections, the number of colors necessary to color the vertices in the selection is minimum. This study focuses on a decomposition based exact solution framework for selective coloring in some perfect graph families: in particular, permutation, generalized split, and chordal graphs where the selective coloring problem is known to be NP-hard. Our method combines integer programming techniques and combinatorial algorithms for the graph classes of interest. We test our method on graphs with different sizes and densities, present computational results and compare them with solving an integer programming formulation of the problem by CPLEX, and a state-of-the art algorithm from the literature. Our computational experiments indicate that our decomposition approach significantly improves solution performance in low-density graphs, and regardless of edge-density in the class of chordal graphs.

}, keywords = {chordal graphs, decomposition algorithm, generalized split graphs, integer programming, partition coloring, permutation graphs, selective graph coloring}, doi = {https://doi.org/10.1002/net.21850}, url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/net.21850}, author = {{\c S}eker, Oylum and Ekim, Tinaz and Z C Ta{\c s}k{\i}n} } @article {1432, title = {The determination of optimal treatment plans for Volumetric Modulated Arc Therapy (VMAT)}, journal = {European Journal of Operational Research}, volume = {272}, year = {2019}, pages = {372-388}, abstract = {

The success of radiation therapy depends on the ability to deliver the proper amount of radiation to cancerous cells while protecting healthy tissues. As a natural consequence, any new treatment technology improves quality standards concerning primarily this issue. Similar to the widely used Intensity Modulated Radiation Therapy (IMRT), the radiation resource is outside of the patient{\textquoteright}s body and the beam is shaped by a multi-leaf collimator mounted on the linear accelerator{\textquoteright}s head during the state-of-the-art Volumetric Modulated Arc Therapy (VMAT) as well. However, unlike IMRT, the gantry of the accelerator may rotate along one or more arcs and deliver radiation continuously. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution; but the apertures are interdependent and optimal treatment planning problem cannot be decomposed into simpler independent subproblems as a consequence. In this work, we consider optimal treatment planning problem for VMAT. First, we formulate a mixed-integer linear program minimizing total radiation dose intensity subject to clinical requirements embedded within the constraints. Then, we develop efficient solution procedures combining Benders decomposition with certain acceleration strategies. We investigate their performance on a large set of test instances obtained from an anonymous real prostate cancer data.

}, keywords = {algorithms, Benders decomposition, integer programming, Radiation therapy, VMAT}, issn = {0377-2217}, doi = {https://doi.org/10.1016/j.ejor.2018.06.023}, url = {https://www.sciencedirect.com/science/article/pii/S0377221718305514}, author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel} } @article {1434, title = {Minimum cost noncrossing flow problem on layered networks}, journal = {Discrete Applied Mathematics}, volume = {261}, year = {2019}, pages = {2-21}, abstract = {

In this work we focus on an extension of the minimum cost flow problem in layered networks. Feasible arc flows must satisfy a specific compatibility restriction in addition to flow balance and capacity restrictions. Namely, at most one of the crossing arcs is allowed to have positive flow on it. This variant of the minimum cost flow problem, which we call the minimum cost noncrossing flow problem, can frequently be encountered in real life. The determination of optimal temporal quay crane allocations to berthed vessels in container terminals, and optimal train schedules through the stations on the same railroad line are two examples. We first analyze the complexity of the problem and show that the noncrossing flow problem is in fact NP-complete in a layered network. Then, we introduce mixed-integer linear programming formulations and discuss a polynomially solvable special case. Next we show a sufficient condition for the existence of a crossing in an optimal solution, which can be used for preprocessing the arcs in order to reduce the problem size. Our computational experiments on a large test set show that our preprocessing algorithm can significantly reduce the number of arcs.

}, keywords = {integer programming, Layered networks, Network flows, Noncrossing flow}, issn = {0166-218X}, doi = {https://doi.org/10.1016/j.dam.2018.09.016}, url = {https://www.sciencedirect.com/science/article/pii/S0166218X18304815}, author = {I. Kuban Altinel and Necati Aras and Zeynep {\c S}uvak and Z C Ta{\c s}k{\i}n} } @article {1430, title = {Optimization{\textendash}based decoding algorithms for LDPC convolutional codes in communication systems}, journal = {IISE Transactions}, volume = {51}, year = {2019}, pages = {1061-1074}, abstract = {

AbstractIn a digital communication system, information is sent from one place to another over a noisy communication channel. It may be possible to detect and correct errors that occur during the transmission if one encodes the original information by adding redundant bits. Low{\textendash}Density Parity{\textendash}Check (LDPC) convolutional codes, a member of the LDPC code family, encode the original information to improve error correction capability. In practice these codes are used to decode very long information sequences, where the information arrives in subsequent packets over time, such as video streams. We consider the problem of decoding the received information with minimum error from an optimization point of view and investigate integer programming{\textendash}based exact and heuristic decoding algorithms for its solution. In particular, we consider relax{\textendash}and{\textendash}fix heuristics that decode information in small windows. Computational results indicate that our approaches identify near{\textendash}optimal solutions significantly faster than a commercial solver in high channel error rates. Our proposed algorithms can find higher quality solutions compared with the state of the art iterative decoding heuristic.

}, doi = {10.1080/24725854.2018.1550692}, url = {https://doi.org/10.1080/24725854.2018.1550692}, author = {Banu Kabakulak and Z C Ta{\c s}k{\i}n and Ali Emre Pusane} } @article {1429, title = {Using branch-and-price to determine optimal treatment plans for volumetric modulated arc therapy (VMAT)}, journal = {Computers \& Operations Research}, volume = {110}, year = {2019}, pages = {1-17}, abstract = {

Volumetric Modulated Arc Therapy (VMAT) is the state-of-the-art technique for external radiation therapy treatment. In this method, radiation can be delivered continuously on one or more arcs during the rotation of the gantry of the linear accelerator. This property makes VMAT powerful in obtaining high conformal plans in terms of dose distribution within short treatment times. However, the apertures composed by the leaves of the multileaf collimator (MLC) system that shapes continuously the radiation are interdependent, which makes treatment planning hard. We propose a mixed integer linear programming model for VMAT planning problem and exact branch-and-price algorithms to solve it. The objective of the model is to minimize total radiation that is delivered to the patient, and pricing subproblem is decomposable by rows of the MLC and can be solved as a shortest path problem. We generate a large set of test instances from a real data set and evaluate the performance of the proposed branch-and-price algorithm. Computational results reveal that new algorithms are efficient and capable of finding optimal solutions for large problem instances.

}, keywords = {Branch-and-price, Column generation, integer programming, Radiation therapy, Shortest path problem, VMAT}, issn = {0305-0548}, doi = {https://doi.org/10.1016/j.cor.2019.05.018}, url = {https://www.sciencedirect.com/science/article/pii/S0305054819301315}, author = {P{\i}nar Dursun and Z C Ta{\c s}k{\i}n and I. Kuban Altinel} } @article {1435, title = {Integer Programming Formulations and Benders Decomposition for the Maximum Induced Matching Problem}, journal = {INFORMS Journal on Computing}, volume = {30}, year = {2018}, pages = {43-56}, abstract = {

We investigate the maximum induced matching problem (MIM), which is the problem of finding an induced matching having the largest cardinality on an undirected graph. The problem is known to be NP-hard for general graphs. We first propose a vertex-based integer programming formulation for MIM, which is more compact compared to an edge-based formulation found in the literature. We also introduce the maximum weight induced matching problem (MWIM), which generalizes MIM so that vertices and edges have weights. We adapt the edge-based formulation to MWIM, and propose a quadratic programming formulation of MWIM based on our vertex-based formulation. We then linearize our quadratic programming formulation, and devise a Benders decomposition algorithm that exploits a special structure of the linearized formulation. We also propose valid inequalities and formulation tightening procedures to improve the efficiency of our approach. Our computational tests on a large suite of randomly generated graphs show that our vertex-based formulation and decomposition approach significantly improve the solvability of MIM and MWIM, especially on dense graphs. The online appendix and data are available at https://doi.org/10.1287/ijoc.2017.0764.

}, doi = {10.1287/ijoc.2017.0764}, url = {https://doi.org/10.1287/ijoc.2017.0764}, author = {Ahat, Bet{\"u}l and Ekim, Tinaz and Z C Ta{\c s}k{\i}n} } @article {1488, title = {A parallel machine lot-sizing and scheduling problem with a secondary resource and cumulative demand}, journal = {International Journal of Production Research}, volume = {56}, year = {2018}, pages = {3344-3357}, abstract = {

We investigate a parallel machine multi-item lot-sizing and scheduling problem with a secondary resource, in which demands are given for the entire planning horizon rather than for every single period. All-or-nothing assumption of the discrete lot-sizing and scheduling problem is valid so that a machine is either idle or works at full capacity in a period. The objective is to minimise the number of setups and teardowns. We prove that the problem is NP-hard and present two equivalent formulations. We show some properties of the optimal objective value, give optimality conditions and suggest a heuristic algorithm. We discuss and formulate two possible extensions related to real-life applications. Finally, we carry out computational experiments to compare the two formulations, to determine the effect of our proposed modeling improvements on solution performance, and to test the quality of our heuristic.

}, doi = {10.1080/00207543.2017.1406675}, url = {https://doi.org/10.1080/00207543.2017.1406675}, author = {Murat G{\"u}ng{\"o}r and Ali Tamer {\"U}nal and Z C Ta{\c s}k{\i}n} } @article {1130, title = {Branch-cut-price algorithms for solving a class of search problems on general graphs}, journal = {Networks}, volume = {70}, year = {2017}, pages = {4-18}, doi = {http://doi.org/10.1002/net.21740}, author = {Z C Ta{\c s}k{\i}n and J. Cole Smith} } @article {1090, title = {Employee Scheduling in Service Industries with Flexible Employee Availability and Demand}, journal = {Omega}, volume = {66}, year = {2017}, pages = {159-169}, doi = {http://dx.doi.org/10.1016/j.omega.2016.03.001}, author = {Semra A{\u g}ral{\i} and Z C Ta{\c s}k{\i}n and Ali Tamer {\"U}nal} } @article {1089, title = {Optimal Berth Allocation, Time-variant Quay Crane Assignment and Scheduling with Crane Setups in Container Terminals}, journal = {European Journal of Operational Research}, volume = {254}, year = {2016}, pages = {985-1001}, doi = {http://dx.doi.org/10.1016/j.ejor.2016.04.022}, author = {Yavuz Boga{\c c} T{\"u}rkogullari and Z C Ta{\c s}k{\i}n and Necati Aras and I. Kuban Altinel} } @article {785, title = {A column generation approach for evaluating delivery efficiencies of collimator technologies in IMRT treatment planning}, journal = {Physics in Medicine and Biology}, volume = {60}, year = {2015}, pages = {1989-2004}, author = {Merve G{\"o}ren and Z C Ta{\c s}k{\i}n} } @article {786, title = {Mathematical Programming-Based Sales and Operations Planning at Vestel Electronics}, journal = {Interfaces}, volume = {45}, year = {2015}, pages = {325-340}, doi = {http://dx.doi.org/10.1287/inte.2015.0793}, author = {Z C Ta{\c s}k{\i}n and Semra A{\u g}ral{\i} and Ali Tamer {\"U}nal and Vahdet Belada and Filiz G{\"o}kten-Y{\i}lmaz} } @article {671, title = {An Integer Programming-Based Search Technique for Error-Prone Substructures of LDPC Codes}, journal = {AEU - International Journal of Electronics and Communications}, volume = {68}, year = {2014}, pages = {1097-1105}, doi = {10.1016/j.aeue.2014.05.012}, author = {Abdullah Sar{\i}duman and Ali Emre Pusane and Z C Ta{\c s}k{\i}n} } @article {TurkogullariEtAl2014, title = {Optimal berth allocation and time-invariant quay crane assignment in container terminals}, journal = {European Journal of Operational Research}, volume = {235}, number = {1}, year = {2014}, pages = {88{\textendash}101}, doi = {http://dx.doi.org/10.1016/j.ejor.2013.10.015}, author = {Yavuz Boga{\c c} T{\"u}rkogullari and Z C Ta{\c s}k{\i}n and Necati Aras and I. Kuban Altinel} } @inbook {aras2014simultaneous, title = {Simultaneous Optimization of Berth Allocation, Quay Crane Assignment and Quay Crane Scheduling Problems in Container Terminals}, booktitle = {Operations Research Proceedings 2012}, year = {2014}, pages = {101{\textendash}107}, publisher = {Springer International Publishing}, organization = {Springer International Publishing}, author = {Necati Aras and T{\"u}rko{\u g}ullar{\i}, Yavuz and Z C Ta{\c s}k{\i}n and I. Kuban Altinel} } @article {TaskinCevik2013, title = {Combinatorial Benders Cuts for Decomposing IMRT Fluence Maps Using Rectangular Apertures}, journal = {Computers and Operations Research}, volume = {40(9)}, year = {2013}, pages = {2178{\textendash}2186}, doi = {http://dx.doi.org/10.1016/j.cor.2011.07.005}, author = {Z C Ta{\c s}k{\i}n and Mucahit Cevik} } @article {BodurEtAl2013, title = {Decomposition Algorithms for Solving the Minimum Weight Maximal Matching Problem}, journal = {Networks}, volume = {62}, number = {4}, year = {2013}, pages = {273{\textendash}287}, doi = {http://dx.doi.org/10.1002/net.21516}, author = {Merve Bodur and Ekim, Tinaz and Z C Ta{\c s}k{\i}n} } @article {AgraliEtAl2012, title = {A Facility Location Model with Safety Stock Costs: Analysis of the Cost of Single-Sourcing Requirements}, journal = {Journal of Global Optimization}, volume = {54(3)}, year = {2012}, pages = {551-581}, doi = {http://dx.doi.org/10.1007/s10898-011-9777-z}, author = {Semra A{\u g}ral{\i} and Joseph Geunes and Z C Ta{\c s}k{\i}n} } @article {TaskinEkim2012, title = {Integer Programming Formulations for the Minimum Weighted Maximal Matching Problem}, journal = {Optimization Letters}, volume = {6(6)}, year = {2012}, pages = {1161-1171}, doi = {http://dx.doi.org/10.1007/s11590-011-0351-x}, author = {Z C Ta{\c s}k{\i}n and Ekim, Tinaz} } @article {TaskinEtAl2012, title = {Mixed-Integer Programming Techniques for Decomposing IMRT Fluence Maps Using Rectangular Apertures}, journal = {Annals of Operations Research}, volume = {196(1)}, year = {2012}, pages = {799-818}, doi = {http://dx.doi.org/10.1007/s10479-010-0767-1}, author = {Z C Ta{\c s}k{\i}n and J. Cole Smith and H. Edwin Romeijn} } @article {TaskinEtAl2010a, title = {Optimal Multileaf Collimator Leaf Sequencing in IMRT Treatment Planning}, journal = {Operations Research}, volume = {58}, number = {3}, year = {2010}, pages = {674{\textendash}690}, doi = {http://dx.doi.org/10.1287/opre.1090.0759}, author = {Z C Ta{\c s}k{\i}n and J. Cole Smith and H. Edwin Romeijn and James F. Dempsey} } @article {TaskinEtAl2009a, title = {Cutting Plane Algorithms for Solving a Stochastic Edge-Partition Problem}, journal = {Discrete Optimization}, volume = {6}, number = {4}, year = {2009}, pages = {420-435}, doi = {http://dx.doi.org/10.1016/j.disopt.2009.05.004}, author = {Z C Ta{\c s}k{\i}n and J. Cole Smith and Shabbir Ahmed and Andrew J. Schaefer} } @article {TaskinUnal2009, title = {Tactical Level Planning in Float Glass Manufacturing with Co-Production, Random Yields and Substitutable Products}, journal = {European Journal of Operational Research}, volume = {199}, number = {1}, year = {2009}, pages = {252-261}, doi = {http://dx.doi.org/10.1016/j.ejor.2008.11.024}, author = {Z C Ta{\c s}k{\i}n and Ali Tamer {\"U}nal} } @article {MenEtAl2007, title = {An Exact Approach to Direct Aperture Optimization in IMRT Treatment Planning}, journal = {Physics in Medicine and Biology}, volume = {52}, number = {24}, year = {2007}, pages = {7333-7352}, doi = {http://dx.doi.org/10.1088/0031-9155/52/24/009}, author = {Chunhua Men and H. Edwin Romeijn and Z C Ta{\c s}k{\i}n and James F. Dempsey} }