Browsing by Subject "Mixed Integer Programming"

Now showing 1 - 6 of 6

Open Access
The hub covering problem over incomplete hub networks
(2006) Kalaycılar, Murat
The rising trend in the transportation and telecommunication systems increases the importance of hub location studies in recent years. Hubs are special types of facilities in many-to-many distribution systems where flows are consolidated and disseminated. Analogous to location models, p-hub median, p-hub center and hub covering problems have been studied in the literature. In this thesis, we focus on a special type of hub covering problem which we call as “Hub Covering Problem over Incomplete Hub Networks”. Most of the studies in the hub location literature assume that the hub nodes are fully interconnected. We observe that, especially in cargo delivery systems, hub network is not complete. Thus, in this study we relax this fundamental assumption and propose integer programming models for single and multi allocation cases of the hub covering problem. We also propose three heuristics for both single and multi allocation cases of the problem. During the computational performance of proposed models and heuristics, CAB data was used. Results and comparisons of these heuristics will also be discussed.
Open Access
Improving application behavior on heterogeneous manycore systems through kernel mapping
(2013) Albayrak, Ömer Erdil
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 thesis, 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 or energy consumption 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. Some part of this work is published in 41st International Conference on Parallel Processing Workshops (ICPPW), 2012 [1], and submitted to Parallel Computing journal (ParCo) [2].
Open Access
Min-degree constrained minimum spanning tree problem: New formulation via Miller-Tucker-Zemlin constraints
(Elsevier, 2010-01) Akgun, I.; Tansel, B.
Given an undirected network with positive edge costs and a positive integer d > 2, the minimum-degree constrained minimum spanning tree problem is the problem of finding a spanning tree with minimum total cost such that each non-leaf node in the tree has a degree of at least d. This problem is new to the literature while the related problem with upper bound constraints on degrees is well studied. Mixed-integer programs proposed for either type of problem is composed, in general, of a tree-defining part and a degree-enforcing part. In our formulation of the minimum-degree constrained minimum spanning tree problem, the tree-defining part is based on the Miller-Tucker-Zemlin constraints while the only earlier paper available in the literature on this problem uses single and multi-commodity flow-based formulations that are well studied for the case of upper degree constraints. We propose a new set of constraints for the degree-enforcing part that lead to significantly better solution times than earlier approaches when used in conjunction with Miller-Tucker-Zemlin constraints. © 2009 Elsevier Ltd. All rights reserved
Open Access
Modeling and optimization of Central Ring Transportation System (CRTS) in Turkish Land Forces
(2003) Akmeşe, Hamdi Ünal
This thesis shows how Turkish Land Forces can optimally meet delivery and pick-up demands of its units via Central Ring Transportation System. A mixed integer programming model is proposed, and for the implementation of the model, mathematical modeling software GAMS is used. The model is implemented for three different fleet sizes of vehicles (4-vehicle, 5-vehicle, 6- vehicle) with taking eight-week data of 2002 into account. How transportation costs are affected by the number of vehicles is investigated, and an ideal number of vehicles and the optimal routes to be followed are proposed.
Open Access
Organ transplantation logistics : case for Turkey
(2012) Çay, Pelin
Organ transplantation is one of the fundamental and effective treatment techniques for the patients who have critical health problems. However, while 3,930 organs were transplanted to the patients in 2011, there still exist 20,954 people waiting for a suitable organ as of April 2012 in Turkey. Even though the exact numbers are different; the situation of well developed countries like USA is not very different in terms of organ donation and patient ratio. Thus; matching - defined as finding the best recipient for a donated organ- is very crucial for the overall organ transplantation process. There are mainly two different ways of matching in the applications: centralized and hierarchical method. In the centralized method, all patients and donors are monitored and matching is coordinated centrally. In the hierarchical method, the matching process is coordinated via a bottom-up hierarchy. The application in Turkey is also hierarchical, coordinated by nine regional coordination centers and one national coordination center. Due to the nature of the matching application in Turkey, the cluster of each regional coordination center is crucial. There are many dynamics of the transplantation process like cold ischemia time -the duration that the organ survives without blood circulation-, operation times and specialized hospitals and teams. In this thesis, we study the organ transplantation logistics mainly focusing on the Turkish application. We provide mathematical models that consider the problem specific requirements like ischemia time. We also consider two-mode transportation since airplanes or helicopters are also used widely in organ transportation. Finally, we also developed a simulation model to observe the hierarchical nature of the system and to evaluate the performance of the mathematical model outputs. Both mathematical model and simulation model outcomes based on Turkish data were compared with actual regional coordination center locations of Turkey.
Open Access
Pricing and hedging of contingent claims in incomplete markets
(2010) Camcı, Ahmet
In this thesis, we analyze the problem of pricing and hedging contingent claims in the multi-period, discrete time, discrete state case. We work on both European and American type contingent claims. For European contingent claims, we analyze the problem using the concept of a “λ gain-loss ratio opportunity”. Pricing results which are somewhat different from, but reminiscent of, the arbitrage pricing theorems of mathematical finance are obtained. Our analysis provides tighter price bounds on the contingent claim in an incomplete market, which may converge to a unique price for a specific value of a gain-loss preference parameter imposed by the market while the hedging policies may be different for different sides of the same trade. The results are obtained in the simpler framework of stochastic linear programming in a multiperiod setting. They also extend to markets with transaction costs. Until now, determining the buyer’s price for American contingent claims (ACC) required solving an integer program unlike European contingent claims for which solving a linear program is sufficient. We show that a relaxation of the integer programming problem which is a linear program, can be used to get the buyer’s price for an ACC. We also study the problem of computing the lower hedging price of an American contingent claim in a market where proportional transaction costs exist. We derive a new mixed-integer linear programming formulation for calculating the lower hedging price. We also present and discuss an alternative, aggregate formulation with similar properties. Our results imply that it might be optimal for the holder of several identical American claims to exercise portions of the portfolio at different time points in the presence of proportional transaction costs while this incentive disappears in their absence. We also exhibit some counterexamples for some new ideas based on our work. We believe that these counterexamples are important in determining the direction of research on the subject.