• Journal of the Korean School Mathematics Society
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• v.23 no.2
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• pp.179-201
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• 2020

The purpose of this study is to analyze tasks reflected in Korean and US textbooks according to the mathematical modeling perspectives, and then to compare the diversity of learning opportunities given to students from both countries. For this, we analyzed mathematical modeling tasks of textbooks based on three aspects: mathematical modeling process, data, and expression. Results are as follows. First, with respect to modeling process, Korean textbook provides a high percentage of the task at all stages of modeling than US textbook. Second, with respect to data, both countries' textbooks have the highest percentage of matching task. Korean textbooks have a large gap in data characteristics by textbook. Third, with respect to expression, both countries' textbooks have the highest percentage of text and picture. Korean textbooks have a large gap in the type of expression than US textbooks, and some textbooks have no other expression except for text and picture. Fourth, tasks were analyzed by integrating the three features. The three features were not combined in various ways. It is necessary to diversify the integration of the three features.

• Journal of the Korean Operations Research and Management Science Society
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• v.13 no.2
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• pp.9-17
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• 1988

This vehicle scheduling problem with multiple depots and multiple vehicle types (VMM) is to determine the optimal vehicle routes to minimize the total travel costs. The object of this paper is to develope an exact algorithm for the VMM. In this paper the VMM is transformed into a mathematical model of the vehicle problem with multiple depots. Then an efficient branch and bound algorithm is developed to obtain an exact solution for this model. In order to enhance the efficiency, this algorithm emphasizes the follows; First, a heuristic algorithm is developed to get a good initial upper bound. Second, an primal-dual approach is used to solve subproblems which are called the quasi-assignment problem, formed by branching strategy is presented to reduce the number of the candidate subproblems.

• Journal of the Korean Operations Research and Management Science Society
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• v.19 no.2
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• pp.119-128
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• 1994

There are three important regions im Multiple Objective Linear Programming (MOLP). One is the region of efficient solutions, another is the region of weight to be used for finding efficient solutions, the third is the region of efficient (nondominated) objective values. In this paper, first, we find the condition of extreme point in the region of efficient objective values. Second, we find that the sum of the dimension of the weight region and the dimension of efficient objective values region is constant. Using the above, it is shown that we find the shape and dimension of weight region corresponding to the given region or efficient objective values and vice versa.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.2
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• pp.83-101
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• 1998

Assembly U-lines are increasingly accepted in industry, especially just-in-time production systems, for the efficient utilization of workforce. In this paper, we present an integer programming formulation and a branch-and-bound method for balancing the U-line with the objective of minimizing the number of workstations with a fixed cycle time. In the mathematical model, we provide the method that can reduce the number of variables and constraints. The proposed branch-and-bound method searches the optimal solution based on a depth-first-search. To efficiently search for the optimal solutions to the problems, an assignment rule is used in the method. Bounding strategies and dominance rules are also utilized. Some problems require a large amount of computation time to find the optimal solutions. For this reason. some heuristic fathoming rules are also proposed. Extensive experiments with test-bed problems in the literature are carried out to show the performance of the proposed method. The computational results show that our method is promising in solution quality.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.2
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• pp.137-151
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• 2008

This paper deals with two shops dealing with single perishable product the fresh items are sold at a list price in the primary shop and the unsold items that have reached a certain allowed age are transferred to the secondary shop to be sold at a discounted price. It is assumed that the demand rates in two shops are Independent each other and can be expressed as a function of inventory level and price. With the objective of maximizing the profit under a Last-In-first-Out. (LIFO) issuing policy, we develop mathematical models for the following two cases : (1) opening primary shop only and (2) opening both primary shop and secondary shop. There are three decision variables, i.e., the reduced price in the secondary shop, the allowed age at the primary shop, and the order quantities at the primary shop. A solution procedure is developed based on tabu search and its validity is illustrated through a comparative study.

• Journal of the Korean Operations Research and Management Science Society
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• v.23 no.4
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• pp.11-20
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• 1998

This paper deals with a mathematical model and an algorithm for the problem of determining k most vital arcs in the shortest path problem. First, we propose a 0-1 integer programming model for finding k most vital arcs in shortest path problem given the ordered set of paths with cardinality q. Next, we also propose an algorithm for finding k most vital arcs ln the shortest path problem which uses the 0-1 Integer programming model and shortest path algorithm and maximum flow algorithms repeatedly Malik et al. proposed a non-polynomial algorithm to solve the problem, but their algorithm was contradicted by Bar-Noy et al. with a counter example to the algorithm in 1995. But using our algorithm. the exact solution can be found differently from the algorithm of Malik et al.

• Journal of the Korean Society of Tobacco Science
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• v.20 no.1
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• pp.87-94
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• 1998

After we made the computer source code with mathematical model of Muramatsu et al. that was expressed by the set of simultaneous first-order ordinary differential equations in evaporation-pyrolysis zone of cigarette, we simulated the distribution profiles of temperature and density of flue-cured tobacco. Those equations were solved numerically with the Runge-Kutta-Gill algorithm assuming step size of 0.025mm by Muramatsu at at,, but in this study the advanced algorithm of Runge-Kutta 4th Order assuming step size of 0.0005mm. The initial conditions and physical parameters of Muramatsu et at. were used for solving them. The calculated values corresponded well with results of Muramatsu et al., especially the gradient of the temperature profile increased with smoldering speed and the thickness of the evaporation-pyrolysis zone decreased with increasing of smoldering speed. On the other hand, the temperature gradient decreased with increasing of the effective thermal-conductivity value and the thickness of the evaporation-pyrolysis zone increased with the effective thermal-conductivity value.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.53-66
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• 1989

The Public Vehicle Routing Problem (PVRP) is to find the minimum total cost routes of M or less Public-Vehicles to traverse the required arcs(streets) at least once, and return to their starting depot on a directed network. In this paper, first, a mathematical model is formulated as minimal cost flow model with illegal subtour elimination constraints, and with the fixed cost and routing cost as an objective function. Second, an efficient branch and bound algorithm is developed to obtain an exact solution. A subproblem in this method is a minimal cost flow problem relaxing illegal subtour elimination constraints. The branching strategy is a variable dichotomy method according to the entering nonrequired arcs which are candidates to eneter into an illegal subtour. To accelerate the fathoming process, a tighter lower bound of a candidate subproblem is calculated by using a minimum reduced coast of the entering nonrequired arcs. Computational results based on randomly generated networks report that the developed algorithm is efficient.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.795-834
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• 2016

The main purpose of this paper is to propose a scheme of a proof of the nonsimpleness of the group $Homeo^{\Omega}$ ($D^2$, ${\partial}D^2$) of area preserving homeomorphisms of the 2-disc $D^2$. We first establish the existence of Alexander isotopy in the category of Hamiltonian homeomorphisms. This reduces the question of extendability of the well-known Calabi homomorphism Cal : $Diff^{\Omega}$ ($D^1$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to a homomorphism ${\bar{Cal}}$ : Hameo($D^2$, ${\partial}D^2$)${\rightarrow}{\mathbb{R}}$ to that of the vanishing of the basic phase function $f_{\underline{F}}$, a Floer theoretic graph selector constructed in [9], that is associated to the graph of the topological Hamiltonian loop and its normalized Hamiltonian ${\underline{F}}$ on $S^2$ that is obtained via the natural embedding $D^2{\hookrightarrow}S^2$. Here Hameo($D^2$, ${\partial}D^2$) is the group of Hamiltonian homeomorphisms introduced by $M{\ddot{u}}ller$ and the author [18]. We then provide an evidence of this vanishing conjecture by proving the conjecture for the special class of weakly graphical topological Hamiltonian loops on $D^2$ via a study of the associated Hamiton-Jacobi equation.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1269-1282
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• 2010

We in this note consider a new concept, so called $\pi$-McCoy, which unifies McCoy rings and IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and upper (lower) triangular matrix rings, but the class of $\pi$-McCoy rings contain upper (lower) triangular matrix rings and many kinds of full matrix rings. We first study the basic structure of $\pi$-McCoy rings, observing the relations among $\pi$-McCoy rings, Abelian rings, 2-primal rings, directly finite rings, and ($\pi-$)regular rings. It is proved that the n by n full matrix rings ($n\geq2$) over reduced rings are not $\pi$-McCoy, finding $\pi$-McCoy matrix rings over non-reduced rings. It is shown that the $\pi$-McCoyness is preserved by polynomial rings (when they are of bounded index of nilpotency) and classical quotient rings. Several kinds of extensions of $\pi$-McCoy rings are also examined.