Browsing by Subject "Mixed integer programming"

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Open Access
Examination timetabling problem
(2021-07) Şahin, Berk
Examination timetabling is a major challenge in most educational institutions. Since the underlying problem is NP-hard and real-life problems are too hard to solve to optimality, heuristic approaches are adopted as solution methodologies in general. The signiﬁcance of a fair exam schedule creates a need for exact solutions to the examination timetabling problem. In this thesis, we mainly focus on exact solution approaches for this problem and test their eﬃcacy on well-known benchmark problems from the literature as well as on Bilkent University’s data. Existing formulations used for the p-hub median hub location problem and the quadratic assignment problem in the literature are adapted to the examination timetabling problem and various Bender’s decomposition and branch and cut methodologies are tailored to these formulations. A novel compact formulation based on individual student schedules with reduced model dimensions is proposed. For the literature instances in which optimal values are not known, we could ﬁnd eﬀective lower bounds. For higher dimensions, we propose matheuristic approaches based on our proposed formulations. With this study, eﬀective lower bounds are found for unsolved problems and small-scale problems are solved to optimality in short computational times.
Open Access
Improving application behavior on heterogeneous manycore systems through kernel mapping
(2013) Albayrak, O. E.; Akturk, I.; Ozturk, O.
Many-core accelerators are being more frequently deployed to improve the system processing capabilities. In such systems, application mapping must be enhanced to maximize utilization of the underlying architecture. Especially, in graphics processing units (GPUs), mapping kernels that are part of multi-kernel applications has a great impact on overall performance, since kernels may exhibit different characteristics on different CPUs and GPUs. While some kernels run faster on GPUs, others may perform better in CPUs. Thus, heterogeneous execution may yield better performance than executing the application only on a CPU or only on a GPU. In this paper, we investigate on two approaches: a novel profiling-based adaptive kernel mapping algorithm to assign each kernel of an application to the proper device, and a Mixed-Integer Programming (MIP) implementation to determine optimal mapping. We utilize profiling information for kernels on different devices and generate a map that identifies which kernel should run where in order to improve the overall performance of an application. Initial experiments show that our approach can efficiently map kernels on CPUs and GPUs, and outperforms CPU-only and GPU-only approaches. © 2013 Elsevier B.V. All rights reserved.
Open Access
Optimization of transportation requirements in the deployment of military units
(Elsevier, 2007) Akgün, İ.; Tansel, B. Ç.
We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which analytical models do not exist. We propose a model for solving the problem and develop a solution methodology which involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branch-and-bound. The solution times for intermediate-sized problems are around 1 h at maximum, whereas it takes about a week in the Turkish Armed Forces to produce a suboptimal feasible solution based on trial-and-error methods. The proposed model can be used to evaluate and assess investment decisions in transportation infrastructure and transportation assets as well as to plan and execute cost-effective deployment operations at different levels of planning.
Open Access
Optimization of transportation requirements in the deployment of military units
(2005) Akgün, İbrahim
We study the deployment planning problem (DPP) that may roughly be defined as the problem of the planning of the physical movement of military units, stationed at geographically dispersed locations, from their home bases to their designated destinations while obeying constraints on scheduling and routing issues as well as on the availability and use of various types of transportation assets that operate on a multimodal transportation network. The DPP is a large-scale real-world problem for which no analytical models are existent. In this study, we define the problem in detail and analyze it with respect to the academic literature. We propose three mixed integer programming models with the objectives of cost, lateness (the difference between the arrival time of a unit and its earliest allowable arrival time at its destination), and tardiness (the difference between the arrival time of a unit and its latest arrival time at its destination) minimization to solve the problem. The cost-minimization model minimizes total transportation cost of a deployment and is of use for investment decisions in transportation resources during peacetime and for deployment planning in cases where the operation is not imminent and there is enough time to do deliberate planning that takes costs into account. The lateness and tardiness minimization models are of min-max type and are of use when quick deployment is of utmost concern. The lateness minimization model is for cases when the given fleet of transportation assets is sufficient to deploy units within their allowable time windows and the tardiness minimization model is for cases when the given fleet is not sufficient. We propose a solution methodology for solving all three models. The solution methodology involves an effective use of relaxation and restriction that significantly speeds up a CPLEX-based branchand-bound. The solution times for intermediate sized problems are around one hour at maximum for cost and lateness minimization models and around two hours for the tardiness minimization model. Producing a suboptimal feasible solution based on trial and error methods for a problem of the same size takes about a week in the current practice in the Turkish Armed Forces. We also propose a heuristic that is essentially based on solving the models incrementally rather than at one step. Computational results show that the heuristic can be used to find good feasible solutions for the models. We conclude the study with comments on how to use the models in the realworld.
Open Access
The robust spanning tree problem with interval data
(Elsevier, 2001) Yaman, H.; Karaşan, O. E.; Pınar, M. Ç.
Motivated by telecommunications applications we investigate the minimum spanning tree problem where edge costs are interval numbers. Since minimum spanning trees depend on the realization of the edge costs, we de5ne the robust spanning tree problem to hedge against the worst case contingency, and present a mixed integer programming formulation of the problem. We also de5ne some useful optimality concepts, and present characterizations for these entities leading to polynomial time recognition algorithms. These entities are then used to preprocess a given graph with interval data prior to the solution of the robust spanning tree problem. Computational results show that these preprocessing procedures are quite e9ective in reducing the time to compute a robust spanning tree.
Open Access
Toz deterjan için üretim planlama ve çizelgeleme sistemi tasarımı
(TMMOB Makina Mühendisleri Odası, 2009) Sepin, Tardu Selim; Yatkın, Mehmet Diyar; Eralp, Merve Nazlı; Memişoğlu, Gökhan; Taner, Mehmet Rüştü; Özcan, Mehmet; Akdemir, Deniz
Unilever Gebze Fabrikasının toz deterjan üretimi planlama sürecinde çizelgeleme işlemi için karar destek sisteminin eksikliği, ürün değişikliklerinin neden olduğu kurulum sayısının ve fırsat maliyetlerinin artmasına sebep olmaktadır. Projenin amacı, sürekli imalat yapısına sahip olan toz deterjan üretimine hızlı ve tutarlı sonuçlar veren, toplam kurulum sayı ve süresini en aza indirecek bir çizelgeleme sistemi tasarlanmasıdır. Problem dört aşamada incelenmiş; sırasıyla bütünleşik, bölünmüş, kısıtlı bölünmüş matematiksel modeller ve sezgisel metot ile çözülmüştür. Sonuçların karşılaştırılmasıyla sezgisel metodun kısa zamanda tutarlı çözümler verdiği görülmüş ve oluşturulan arayüzle sisteme entegre edilmiştir.