Authors:Gizem Temelcan, Mustafa Sivri, Inci Albayrak Pages: 47 - 54 Abstract: Nonlinear equations arise frequently while modeling chemistry, physics, economy and engineering problems. In this paper, a new iterative approach for finding a solution of a nonlinear equations system (NLES) is presented by applying a linearization technique. The proposed approach is based on computational method that converts NLES into a linear equations system by using Taylor series expansion at the chosen arbitrary nonnegative initial point. Using the obtained solution of the linear equations system, a linear programming (LP) problem is constructed by considering the equations as constraints and minimizing the objective function constructed as the summation of balancing variables. At the end of the presented algorithm, the exact solution of the NLES is obtained. The performance of the proposed approach has been demonstrated by considering different numerical examples from literature. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00684 Issue No:Vol. 10, No. 1 (2020)

Authors:Raheleh Khanduzi, Asyieh Ebrahimzadeh, Samaneh Panjeh Ali Beik Pages: 55 - 65 Abstract: This paper elaborated an effective and robust metaheuristic algorithm with acceptable performance based on solution accuracy. The algorithm applied in solution of the optimal control of fractional Volterra integro-differential (FVID) equation which be substituted by nonlinear programming (NLP). Subsequently the FIVD convert the problem to a NLP by using spectral collocation techniques and thereafter we execute the grey wolf optimizer (GWO) to improve the speed and accuracy and find the solutions of the optimal control and state as well as the optimal value of the cost function. It is mentioned that the utilization of the GWO is simple, due to the fact that the GWO is global search algorithm, the method can be applied to find optimal solution of the NLP. The efficiency of the proposed scheme is shown by the results obtained in comparison with the local methods. Further, some illustrative examples introduced with their approximate solutions and the results of the present approach compared with those achieved using other methods. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00753 Issue No:Vol. 10, No. 1 (2020)

Authors:Nihal Ozgur, Nihal Taş, James Francis Peters Pages: 66 - 72 Abstract: We present a new type of activation functions for a complex-valued neural network (CVNN). A proposed activation function is constructed such that it fixes a given ellipse. We obtain an application to a complex-valued Hopfield neural network (CVHNN) using a special form of the introduced complex functions as an activation function. Considering the interesting geometric properties of the plane curve ellipse such as focusing property, we emphasize that these properties may have possible applications in various neural networks. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00756 Issue No:Vol. 10, No. 1 (2020)

Authors:Hatıra Günerhan Pages: 73 - 77 Abstract: In this work, we have used reduced differential transform method (RDTM) to compute an approximate solution of the Two-Dimensional Convection-Diffusion equations (TDCDE). This method provides the solution quickly in the form of a convergent series. Also, by using RDTM the approximate solution of two-dimensional convection-diffusion equation is obtained. Further, we have computed exact solution of non-homogeneous CDE by using the same method. To the best of my knowledge, the research work carried out in the present paper has not been done, and is new. Examples are provided to support our work. PubDate: 2020-01-14 DOI: 10.11121/ijocta.01.2020.00781 Issue No:Vol. 10, No. 1 (2020)

Authors:Onur Alp İlhan, Hasan Bulut, Tukur Abdulkadir Sulaiman, Haci Mehmet Baskonus Pages: 1 - 8 Abstract: The analytical solution of the longitudinal wave equation in the MEE circular rod is analyzed by the powerful sine-Gordon expansion method. Sine - Gordon expansion is based on the well-known wave transformation and sine - Gordon equation. In the longitudinal wave equation in mathematical physics, the transverse Poisson MEE circular rod is caused by the dispersion. Some solutions with complex, hyperbolic and trigonometric functions have been successfully implemented. Numerical simulations of all solutions are given by selecting the appropriate parameter values. The physical meaning of the analytical solution explaining some practical physical problems is given. PubDate: 2019-09-04 DOI: 10.11121/ijocta.01.2020.00837 Issue No:Vol. 10, No. 1 (2019)

Authors:Banu Yetkin Ekren, Bartu Arslan Pages: 9 - 16 Abstract: Since it affects the performance of whole supply chain significantly, definition of correct inventory control policy in a supply chain is critical. Recent technological development enabled real time visibility of a supply network by horizontal integration of each node in a supply network. By this opportunity, inventory sharing among stocking locations is also possible in the effort of cost minimization in supply chain management. Hence, lateral transshipment gained popularity and studies seeking the best lateral-transshipment policy is still under research. In this study, we aim to compare different lateral-transshipment policies for an s, S inventory control problem for a single-echelon supply chain network system. In this work, we consider a supply network with three stocking locations which may perform lateral transshipment among them when backorder takes place. We develop the simulation models of the systems in ARENA 14.5 commercial software and compare the performance of the policies by minimizing the total cost under a pre-defined fill rate constraint by using an optimization tool, OptQuest, integrated in that software. The results show that lateral transshipment works well compared to the scenario when there is no lateral transshipment policy in the network. PubDate: 2019-09-16 DOI: 10.11121/ijocta.01.2020.00789 Issue No:Vol. 10, No. 1 (2019)

Authors:Elif G. Dayıoğlu, Kenan Karagül, Yusuf Şahin, Michael G. Kay Pages: 17 - 25 Abstract: In this study, procedures are presented that can be used to determine the routes of the packages transported within a modular storage system. The problem is a variant of robot motion planning problem. The structures of the procedures are developed in three steps for the simultaneous movement of multiple unit-sized packages in a modular warehouse. The proposed heuristic methods consist of route planning, tagging, and main control components. In order to demonstrate the solution performance of the methods, various experiments were conducted with different data sets and the solution times and qualities of the proposed methods were compared with previous studies. It was found that the proposed methods provide better solutions when taking the number of steps and solution time into consideration. PubDate: 2019-09-19 DOI: 10.11121/ijocta.01.2020.00752 Issue No:Vol. 10, No. 1 (2019)

Authors:Özgün Yücel, Önder Bulut Pages: 26 - 36 Abstract: This study considers a make-to-stock production system with multiple identical parallel servers, fixed production start-up costs and lost sales. Processing times are assumed to be two-phase Coxian random variables that allows us to model the systems having rework or remanufacturing operations. First, the dynamic programming formulation is developed and the structure of the optimal production policy is characterized. Due to the highly dynamic nature of the optimal policy, as a second contribution we propose an easy-to-apply production policy. The proposed policy makes use of the dynamic state information and controlled by only two parameters. We test the performance of the proposed policy at several instances and reveal that it is near optimal. We also assess the value of dynamic state information in general by comparing the proposed policy with the well-known static inventory position based policy. PubDate: 2019-09-24 DOI: 10.11121/ijocta.01.2020.00801 Issue No:Vol. 10, No. 1 (2019)

Authors:Gülçin Bektur Pages: 37 - 46 Abstract: In this study, a multi-resource agent bottleneck generalized assignment problem (MRBGAP) is addressed. In the bottleneck generalized assignment problem (BGAP), more than one job can be assigned to an agent, and the objective function is to minimize the maximum load over all agents. In this problem, multiple resources are considered and the capacity of the agents is dependent on these resources and it has minimum two indices. In addition, agent qualifications are taken into account. In other words, not every job can be assignable to every agent. The problem is defined by considering the problem of assigning jobs to employees in a firm. BGAP has been shown to be NP- hard. Consequently, a multi-start iterated tabu search (MITS) algorithm has been proposed for the solution of large-scale problems. The results of the proposed algorithm are compared by the results of the tabu search (TS) algorithm and mixed integer linear programming (MILP) model. PubDate: 2019-10-06 DOI: 10.11121/ijocta.01.2020.00796 Issue No:Vol. 10, No. 1 (2019)