Endüstri Mühendisliği Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/279
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Article Citation - WoS: 12Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation With Two-Time Delays(Imr Press, 2023) Ambalarajan, Venkatesh; Sivakumar, Vinoth; Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; Murugadoss, Prakash RajBackground: Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. Methods: The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. Conclusions: The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.Article Citation - WoS: 4Citation - Scopus: 10Customer Order Scheduling With Job-Based Processing on a Single-Machine To Minimize the Total Completion Time(Growing Science, 2021) Yeloglu, Pinar; Catmakas, Hale Akkocaoglu; Cetinkaya, Ferda CanThis study considers a customer order scheduling (COS) problem in which each customer requests a variety of products (jobs) processed on a single flexible machine, such as the computer numerical control (CNC) machine. A sequence-independent setup for the machine is needed before processing each product. All products in a customer order are delivered to the customer when they are processed. The product ordered by a customer and completed as the last product in the order defines the customer order's completion time. We aim to find the optimal schedule of the customer orders and the products to minimize the customer orders' total completion time. We have studied this customer order scheduling problem with a job-based processing approach in which the same products from different customer orders form a product lot and are processed successively without being intermingled with other products. We have developed two mixed-integer linear programming models capable of solving the small and medium-sized problem instances optimally and a heuristic algorithm for large-sized problem instances. Our empirical study results show that our proposed tabu search algorithm provides optimal or near-optimal solutions in a very short time. We have also compared the job-based and order-based processing approaches for both setup and no-setup cases and observed that the job-based processing approach yields better results when jobs have setup times. (C) 2021 by the authors; licensee Growing Science, CanadaArticle Citation - Scopus: 2A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters' Route(Hindawi Ltd, 2021) Kirkavak, Nureddin; Alpay, Ayse Nilay; Ozaktas, HakanAverage waiting time is considered as one of the basic performance indicators for a bottleneck zone on a route for commuter traffic. It turns out that the average waiting time in a queue remains paradoxically unchanged regardless of how fast the queue dissolves for a single bottleneck problem. In this study, the paradox is verified theoretically for the deterministic case with constant arrival and departure rates. Consistent results with the deterministic case have also been obtained by simulation runs for which vehicle interarrival time is a random variable. Results are tabulated for interarrival times which have uniform, triangular, normal, and exponential distributions along with a statistical verification of the average waiting time paradox.