• Management Science and Financial Engineering
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• v.4 no.2
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• pp.1-13
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• 1998

The Shortest Path Problem in Time-dependent Networks, where the travel time of each link depends on the time interval, is not realistic since the model and its solution violate the Non-passing Property (NPP:often referred to as FIFO) of real phenomena. Furthermore, solving the problem needs much more computational and memory complexity than the general shortest path problem. A new model for Time-dependent Networks where the flow speeds of each link depend on time interval, is suggested. The model is more realistic since its solution maintains the NPP. Solving the problem needs just a little more computational complexity, and the same memory complexity, as the general shortest path problem. A solution algorithm modified from Dijkstra's label setting algorithm is presented. We extend this model to the problem of Minimum Expected Time Path in Time-dependent Stochastic Networks where flow speeds of each link change statistically on each time interval. A solution method using the Kth-shortest Path algorithm is presented.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.

• Bulletin of the Korean Chemical Society
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• v.25 no.2
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• pp.285-288
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• 2004

A canonical transformation changes variables such as coordinates and momenta to new variables preserving either the Poisson bracket or the commutation relations depending on whether the problem is classical or quantal respectively. Classically canonical transformations are well established as a powerful tool for solving differential equations. Quantum canonical transformations have been defined and used relatively recently because of the non-commutativeness of the quantum variables. Three elementary canonical transformations and their composite transformations have quantum implementations. Quantum canonical transformations have been mostly used in time-independent Schrodinger equations and a harmonic oscillator with time-dependent angular frequency is probably the only time-dependent problem solved by these transformations. In this work, we apply quantum canonical transformations to a harmonic oscillator in which both angular frequency and equilibrium position are time-dependent.

• Journal of Korean Institute of Industrial Engineers
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• v.37 no.2
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• pp.144-152
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• 2011

Most of the models for the vehicle routing problems studied in the literature assumed constant travel times. However, those approaches may give infeasible solutions when traffic congestion causes delays in travel time. To overcome such difficulty, there have been some researches considering the change of the travel time which is called the time dependent vehicle routing problem (TDVRP). TDVRP assumes that the travel time between two locations is not only affected by the distance traveled, but by many other factors including the time of the day. In this paper, we propose a branch-and-price algorithm to solve the TDVRP. The time dependent property of the travel time is dealt with an enumeration scheme with bounding procedures in the column generation procedure identifying a profitable route. The proposed algorithm guarantees the "Non-passing" property to be held in the solutions. The algorithm was tested on problems composed of the Solomon's benchmark instances for 25 and 50 nodes. Computational results are reported.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.463-472
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• 2011

In this paper we study the solvability of parabolic equations governed by the difference of time dependent subdifferential and time independent subdifferential in reflexive Banach spaces.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.27 no.2
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• pp.80-88
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• 2017

In this research a time dependent thermal and solutal convection was computationally investigated for the physical vapor transport of the mixture of $Hg_2Cl_2-I_2$ system with for the convective regime from thermal Rayleigh number of $2.16{\times}10^6$ up to $1.7{\times}10^7$ with marching time to a steady state problem. With time marching, the convective cells are decreased for the thermal Rayleigh number of $2.16{\times}10^6$, and increased for the thermal Rayleigh number of $1.7{\times}10^7$. The convective flow structures are found to be essentially time independent on the horizontal orientation of the enclosure with respect to the gravity vector, and on the other hand, time dependent on the vertical orientation of the enclosure with respect to the gravity vector.

• Transactions of Materials Processing
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• v.15 no.9 s.90
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• pp.679-685
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• 2006

New method for evaluation of heat transfer coefficient is proposed. In general, many researchers have been studied about inverse problem in order to calculate the heat transfer coefficient on three-dimensional heat conduction problem. But they can get the time-dependent heat transfer coefficient only through inverse problem. In order to acquire temperature-dependent heat transfer coefficient, it requires much time for numerous repetitive calculation and inconvenient manual modification. In order to solve these problems, we are using the SQP(Sequential Quadratic Programming) as an optimization algorithm. When the temperature history is given by experiment, the optimization algorithm can evaluate the temperature-dependent heat transfer coefficient with automatic repetitive calculation until difference between calculated temperature history and experimental ones is minimized. Finally, temperature-dependent heat transfer coefficient evaluated by developed program can used on various heat transfer problem.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1320-1326
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• 2002

In a one-dimensional heat conduction domain with heated and insulated walls, an integral approach is proposed to estimate time-dependent boundary heat flux without internal measurements. It is assumed that the expression of the heat flux is not known a priori. Hence, the present inverse heat conduction problem is classified as a function estimation problem. The spatial temperature distribution is approximated as a third-order polynomial of position, whose four coefficients are determined from the heat fluxes and the temperatures at both ends at each measurement. After integrating the heat conduction equation over spatial and time domain, respectively, a simple and non-iterative recursive equation to estimate the time-dependent boundary heat flux is derived. Several examples are introduced to show the effectiveness of the present approach.

• Korean Management Science Review
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• v.30 no.1
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• pp.15-24
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• 2013

We consider the single machine scheduling problem with a rate-modifying activity and time-dependent deterioration after the activity. The class of scheduling problems with rate-modifying activities and the class of scheduling problems with time-dependent processing times have been studied independently. However, the integration of these classes is motivated by human operators of tasks who has fatigue while carrying out the operation of a series of tasks. This situation is also applicable to machines that experience performance degradation over time due to mal-position or mal-alignment of jobs, abrasion of tools, and scraps of operations, etc. In this study, the integration of the two classes of scheduling problems is considered. We present a mathematical model to determine job-sequence and a position of a rate-modifying activity for the integration problem. Since the model is difficult to solve as the size of real problem being very large, we propose genetic algorithms. The performance of the algorithms are compared with optimal solutions with various problems.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.4
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• pp.788-792
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• 2010

The problem of delay-dependent and parameter-dependent robust stability condition for discrete-time uncertain singular systems with polytopic uncertainty and interval time-varying delay is considered. A new robust stability condition based on parameter-dependent Lyapunov function is derived in terms of LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general condition for both singular and non-singular systems. A numerical example is presented to demonstrate the effectiveness of the proposed method.