• Transactions of the Korean Society of Automotive Engineers
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• v.5 no.1
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• pp.216-216
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• 1997

We developed the durability estimation and design systems to minimize the volume, considering the durability, efficiency, and design requirements of worm gears. That is, we consider each kind of factors affecting on durability on the basis of AGMA Standard for the cylindrical and double-enveloping worm gears. We also estimate input power on the basis of wear and durability, bending strength and deflection of worm shaft, and we developed the durability estimation and design systems of power transmission worm gears introducing the optimal design method on the personal computer to be easily used in field. Also, we developed a method which converts the design variables obtained from the optimal design method to integer values(number of worm threads, number of worm threads, number of worm wheel teeth, etc.,) to be used in real design and production. The developed durability estimation and design method can be easily applied to the design of worm gears used as power transmission devices in machineries and is expected to be used for weight minimization of worm gear unit.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.3
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• pp.224-229
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• 2008

In the paper, a new Constraint algorithm is proposed to solve the fan-in problem occurred in the encoding circuitry of an ADC. The Flash ADC architecture uses a Double-Base Number System(DBNS). The DBNS has been known to represent the Multidimensional Logarithmic Number System (MDLNS) used for implementing the multiplier accumulator architecture of FIR filter in Digital Signal Processing (DSP) applications. The authors use the DBNS with the base 2 and 3 in designing ADC encoder circuits, which is called as Double Base Integer Encoder(DBIE). A symmetric map is analyzed first, and then asymmetric map is followed to provide addition ready DBNS for DSP circuitry. The simulation results of the DBIE circuits in 6-bit and 8-bit ADC show the effectiveness of the Constraint algorithm with $0.18{\mu}m$ CMOS technology. The DBIE yields faster processing speed compared to the speed of Fat Tree Encoder (FAT) circuits by 17% at more power consumption by 39%.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.21-25
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• 2009

In this paper, we study the problem to fit a piecewise-quadratic polynomial curve to points in the plane. The curve consists of quadratic polynomial segments and two points are connected by a segment. But it passes through a subset of points, and for the points not to be passed, the error between the curve and the points is estimated in $L^{\infty}$ metric. We consider two optimization problems for the above problem. One is to reduce the number of segments of the curve, given the allowed error, and the other is to reduce the error between the curve and the points, while the curve has the number of segments less than or equal to the given integer. For the number n of given points, we propose $O(n^2)$ algorithm for the former problem and $O(n^3)$ algorithm for the latter.

• Journal of applied mathematics & informatics
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• v.39 no.1_2
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• pp.13-29
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• 2021

For a graph G = (V, E), a vertex coloring (or, simply, a coloring) of G is a function C : V (G) → {1, 2, …, k} (using the non-negative integers {1, 2, …, k} as colors). We say that a coloring of a graph G is injective if for every vertex v ∈ V (G), all the neighbors of v are assigned with distinct colors. The injective chromatic number χi(G) of a graph G is the least k such that there is an injective k-coloring [6]. In this paper, we study a natural variation of the injective coloring problem: coloring the edges of a graph under the same constraints (alternatively, to investigate the injective chromatic number of line graphs), we define the k- injective edge coloring of a graph G as a mapping C : E(G) → {1, 2, …, k}, such that for every edge e ∈ E(G), all the neighbors edges of e are assigned with distinct colors. The injective chromatic index χ′in(G) of G is the least positive integer k such that G has k- injective edge coloring, exact values of the injective chromatic index of different families of graphs are obtained, some related results and bounds are established. Finally, we define the injective clique number ωin and state a conjecture, that, for any graph G, ωin ≤ χ′in(G) ≤ ωin + 2.

• Journal of Intelligence and Information Systems
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• v.16 no.2
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• pp.129-141
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• 2010

An Internet shopping mall for clothing operates a warehouse for packing and shipping products to fulfill its orders. All the products in the warehouse are put into the boxes of same brands and the boxes are stored in a row on shelves equiped in the warehouse. To make picking and managing easy, boxes of the same brands are located side by side on the shelves. When new products arrive to the warehouse for storage, the products of a brand are put into boxes and those boxes are located adjacent to the boxes of the same brand. If there is not enough space for the new coming boxes, however, some boxes of other brands should be moved away and then the new coming boxes are located adjacent in the resultant vacant spaces. We want to minimize the movement of the existing boxes of other brands to another places on the shelves during the warehousing of new coming boxes, while all the boxes of the same brand are kept side by side on the shelves. Firstly, we define the adjacency of boxes by looking the shelves as an one dimensional series of spaces to store boxes, i.e. cells, tagging the series of cells by a series of numbers starting from one, and considering any two boxes stored in the cells to be adjacent to each other if their cell numbers are continuous from one number to the other number. After that, we tried to formulate the problem into an integer programming model to obtain an optimal solution. An integer programming formulation and Branch-and-Bound technique for this problem may not be tractable because it would take too long time to solve the problem considering the number of the cells or boxes in the warehouse and the computing power of the Internet shopping mall. As an alternative approach, we designed a fast heuristic method for this reallocation problem by focusing on just the unused spaces-empty cells-on the shelves, which results in an assignment problem model. In this approach, the new coming boxes are assigned to each empty cells and then those boxes are reorganized so that the boxes of a brand are adjacent to each other. The objective of this new approach is to minimize the movement of the boxes during the reorganization process while keeping the boxes of a brand adjacent to each other. The approach, however, does not ensure the optimality of the solution in terms of the original problem, that is, the problem to minimize the movement of existing boxes while keeping boxes of the same brands adjacent to each other. Even though this heuristic method may produce a suboptimal solution, we could obtain a satisfactory solution within a satisfactory time, which are acceptable by real world experts. In order to justify the quality of the solution by the heuristic approach, we generate 100 problems randomly, in which the number of cells spans from 2,000 to 4,000, solve the problems by both of our heuristic approach and the original integer programming approach using a commercial optimization software package, and then compare the heuristic solutions with their corresponding optimal solutions in terms of solution time and the number of movement of boxes. We also implement our heuristic approach into a storage location assignment system for the Internet shopping mall.

• Health Policy and Management
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• v.3 no.2
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• pp.159-176
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• 1993

The utilization of outpatient care services involves two steps of sequential decisions. The first step decision is about whether to initiate the utilization and the second one is about how many more visits to make after the initiation. Presumably, the initiation decision is largely made by the patient and his or her family, while the number of additional visits is decided under a strong influence of the physician. Implication is that the analysis of the outpatient care utilization requires to specify each of the two decisions underlying the utilization as a distinct stochastic process. This paper is concerned with the number of physician visits, which is, by definition, a discrete variable that can take only non-negative integer values. Since the initial visit is considered in the analysis of whether or not having made any physician visit, the focus on the number of visits made in addition to the initial one must be enough. The number of additional visits, being a kind of count data, could be assumed to exhibit a Poisson distribution. However, it is likely that the distribution is over dispersed since the number of physician visits tends to cluster around a few values but still vary widely. A recently reported study of outpatient care utilization employed an analysis based upon the assumption of a negative binomial distribution which is a type of overdispersed Poisson distribution. But there is an indication that the use of Poisson distribution making adjustments for over-dispersion results in less loss of efficiency in parameter estimation compared to the use of a certain type of distribution like a negative binomial distribution. An analysis of the data for outpatient care utilization was performed focusing on an assessment of appropriateness of available techniques. The data used in the analysis were collected by a community survey in Hwachon Gun, Kangwon Do in 1990. It was observed that a Poisson regression with adjustments for over-dispersion is superior to either an ordinary regression or a Poisson regression without adjustments oor over-dispersion. In conclusion, it seems the most approprite to assume that the number of physician visits made in addition to the initial visist exhibits an overdispersed Poisson distribution when outpatient care utilization is studied based upon a model which embodies the two-part character of the decision process uderlying the utilization.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• Journal of Digital Contents Society
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• v.3 no.2
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• pp.221-233
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• 2002

In this paper, we present integer programming models and algorithms for the Capacitated Facility Location-Allocation Problem (CFLP). The models and algorithms can be used for the design of logistics networks and for the location of telecommunication facilities. We are given a set of candidate facility installation sites, one type of facility for each candidate site with its capacity and installation cost, a set of customers with their demand requirement, and flow cost for one unit of demand flow from each customer to each candidate site. (CFLP) is to determine the number of facilities for each candidate site and the set of customers which are connected to each site with minimum cost, while satisfying the demand requirement of each customer and constraints imposed on the allocation of customers to facilities. We present two integer programming models for (CFLP), and devise a branch-and-cut algorithm and a branch-and-price algorithm for the problem.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.39 no.1
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• pp.98-104
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• 2016

With the development of modern science and technology, weapon systems such as tanks, submarines, combat planes, radar are also dramatically advanced. Among these weapon systems, the ballistic missile, one of the asymmetric forces, could be considered as a very economical means to attack the core facilities of the other country in order to achieve the strategic goals of the country during the war. Because of the current ballistic missile threat from the North Korea, establishing a missile defense (MD) system becomes one of the major national defense issues. This study focused on the optimization of air defense artillery units' deployment for effective ballistic missile defense. To optimize the deployment of the units, firstly this study examined the possibility of defense, according to the presence of orbital coordinates of ballistic missiles in the limited defense range of air defense artillery units. This constraint on the defense range is originated from the characteristics of anti-ballistic missiles (ABMs) such as PATRIOT. Secondly, this study proposed the optimized mathematical model considering the total covering problem of binary integer programming, as an optimal deployment of air defense artillery units for defending every core defense facility with the least number of such units. Finally, numerical experiments were conducted to show how the suggested approach works. Assuming the current state of the Korean peninsula, the study arbitrarily set ballistic missile bases of the North Korea and core defense facilities of the South Korea. Under these conditions, numerical experiments were executed by utilizing MATLAB R2010a of the MathWorks, Inc.

• Journal of Korean Society of Transportation
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• v.31 no.2
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• pp.80-89
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• 2013

The purpose of this research is to optimize the line planning of the intercity passenger railway. In this study, the line planning problem has been formulated into a mixed integer programming by minimizing both user costs (passenger's total travel time) and operator costs (operation, maintenance and vehicle costs) with multiple train types. As a solution algorithm, the branch-and-bound method is used to solve this problem. The change of travel demand, train speed and the number of schedules have been tested through sensitivity analysis. The optimal stop-schedules and frequency as well as system split with respect to each train type have been found in the case study of Kyoung-bu railway line in Korea. The model and results of this research are useful to make a decision for railway operation strategy, to analyze the efficiency of new railway systems and to evaluate the social costs of users and operators.