• 한국초등수학교육학회지
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• 제21권3호
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• pp.531-546
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• 2017

본 연구에서는 계산 순서를 지도하는데 유용한 교수법적 내용 지식을 제공하기 위해 사칙계산 사이의 우선권은 어떠한 근거로 결정되었는지 살펴보고, 계산 순서를 바라보는 입장에 관해 논의하였다. 이러한 논의 결과를 바탕으로 다음 다섯 가지 제언을 결론으로 제시한다. 첫째, 교사들에게 덧셈과 뺄셈의 혼합계산 및 곱셈과 나눗셈의 혼합계산의 경우, 각각 뺄셈과 나눗셈부터 계산해도 동일한 계산 결과를 구할 수 있다는 것을 확인하는 기회를 제공할 필요가 있다. 둘째, 교사들에게 식의 왼쪽부터 차례대로 계산하는 규칙이 관습으로 자리 잡은 이유에 관해 논의할 수 있는 기회를 제공할 필요가 있다. 셋째, 교사들에게 덧셈과 곱셈의 혼합계산에서 곱셈이 덧셈보다 우선한다는 규칙 설정의 동인을 설명해 보는 기회를 제공할 필요가 있다. 넷째, 교사들에게 괄호가 있는 식에서 하나의 수량이라는 괄호의 의미를 강조할 필요가 있다. 다섯째, 교사용 지도서에서 계산 순서의 입장을 기술할 때는 계산 순서의 관습적, 개념적 입장을 모두 기술하여 교사들의 계산 순서에 대한 이해를 심화시킬 필요가 있다.

• 한국국방경영분석학회지
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• 제11권2호
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• pp.15-22
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• 1985

Planning for the expansion of production capacity is of vital importance in many applications within the private and public sectors. This paper considers a sequencing expansion problem in which capacity can be added only at discrete points in time. Given the demand forecast of each period, capacity and cost of each expansion project, we are to determine the sequence of expansion necessary to provide sufficient capacity to meet the demand in all periods at minimum cost. This problem is formulated as a pure integer programming and solved by branch and bound method using Lagrangian relaxation. At first, simple sequencing expansion problem is presented, and in the latter part, extension to include precedence between projects is suggested.

• 한국경영과학회지
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• 제38권2호
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• pp.25-42
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• 2013

We consider a project time-cost tradeoff problem with two milestones, where one of the jobs has an uncertain processing time. Unless each milestone is completed on time, some penalty cost may be imposed. However, the penalty costs can be avoided by compressing the processing times of some jobs, which requires additional resources or costs. The objective is to minimize the expected total costs subject to the constraint on the expected project completion time. We show that the problem can be solved in polynomial time if the precedence graph of a project is a chain.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.517-522
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• 2005

This paper addresses scheduling heuristics for an assembly job-shop that includes at least an assembly process throughout its processes. The assembly job shop has certain characteristics not only considering the precedence relationship between the processes but also considering the processing progress between the parts. In addition, it probably presents a different processing time for the same product according to the order of processes and the point of workable time, due to the difference in the availability of equipments. The paper proposes several priority-based dispatching rules that consider these characteristics of the assembly job-shop, aiming to minimize the total tardiness of products in the shop floor. Computational tests showed that job due date based priority rules significantly outperform existing priority rules in terms of total tardiness.

• 한국해양공학회지
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• 제17권1호
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• pp.67-71
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• 2003

This paper presents the use of an evert system to automate process planning of block assembly, a task that is usually completed manually. In order to determine the sequence of assembly operation, a search method guided by rules, such as merging of related operations, grouping of similar operations, and precedence rules based on know-hows and geometrical reasoning, is used. In this paper, the expert system developed is explained in detail regarding a global database, control strategies, and rule bases. For verification purposes, the evert system has been applied to simple examples. Since the rule bases are isolated from the inference engine in the developed system, it is easy to add more rules in the future.

• 산업공학
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• 제13권3호
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• pp.512-520
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• 2000

An integrated process planning and scheduling model considering outsourcing in manufacturing supply chain is proposed in this paper. The process planning and scheduling considering outsourcing are actually interrelated and should be solved simultaneously. The proposed model considers the alternative process plans for job types, precedence constraints of job operations, due date of production, transportation time and production information for outsourcing. The integrated states include:(1) Operations sequencing, (2) Machine selection, (3) Scheduling with outsourcing under the due date. To solve the model, a heuristic approach based on genetic algorithm(GA) is developed. The proposed approach minimizes the makespan considering outsourcing and shows the best operation-sequences and schedule of all jobs.

• 한국경영과학회지
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• 제21권1호
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• pp.147-161
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• 1996

Generally the Multiprocessor Scheduling (MPS) problem is difficult to solve because of the precedence of the tasks, and it takes a lot of time to obtain its optimal solution. Though Genetic Algorithm (GA) does not guarantee the optimal solution, it is practical and effective to solve the MPS problem in a reasonable time. The algorithm developed in this research consists of a improved GA and GP/MISF (Critical Path/Most Immediate Successors First). An efficient genetic operator is derived to make GA more efficient. It runs parallel CP/MISF with GA to complement the faults of GA. The solution by the developed algorithm is compared with that of CP/MISF, and the better is taken as a final solution. As a result of comparative analysis by using numerical examples, although this algorithm does not guarantee the optimal solution, it can obtain an approximate solution that is much closer to the optimal solution than the existing GA's.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1995년도 추계학술대회발표논문집; 서울대학교, 서울; 30 Sep. 1995
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• pp.220-229
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• 1995

Generally the Multiprocessor Scheduling(MPS) problem is difficult to solve because of the precedence of the tasks, and it takes a lot of time to obtain its optimal solution. Though Genetic Algorithm(GA) does not guarantee the optimal solution, it is practical and effective to solve the MPS problem in a reasonable time. The algorithm developed in this research consists of a improved GA and CP/MISF(Critical Path/Most Immediate Successors First). A new genetic operator is derived to make GA more efficient. It runs parallel CP/MISF with Ga to complement the faults of GA. The solution by the developed algorithm is compared with that of CP/MISF, and the better is taken as a final solution. As a result of comparative analysis by using numerical examples, although this algorithm does not guarantee the optimal solution, it can obtain an approximate solution that is much closer to the optimal solution than the existing GA's.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회 1993년도 추계학술대회발표논문집; 서강대학교, 서울; 25 Sep. 1993
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• pp.12-19
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• 1993

In general, the line balancing problem is defined as of finding an assignment of the given jobs to the workstations under the precedence constraints given to the set of jobs. Usually, the objective is either minimizing the cycle time under the given number of workstations or minimizing the number of workstations under the given cycle time. In this paper, we present a new type of an assembly line balancing problem which occurs in an electronics company manufacturing home appliances. The main difference of the problem compared to the general line balancing problem lies in the structure of the precedence given to the set of jobs. In the problem, the set of jobs is partitioned into two disjoint subjects. One is called the set of fixed jobs and the other, the set of floating jobs. The fixed jobs should be processed in the linear order and some pair of the jobs should not be assigned to the same workstations. Whereas, to each floating job, a set of ranges is given. The range is given in terms of two fixed jobs and it means that the floating job can be processed after the first job is processed and before the second job is processed. There can be more than one range associated to a floating job. We present a procedure to find an approximate solution to the problem. The procedure consists of two major parts. One is to find the assignment of the floating jobs under the given (feasible) assignment of the fixed jobs. The problem can be viewed as a constrained bin packing problem. The other is to find the assignment of the whole jobs under the given linear precedence on the set of the floating jobs. First problem is NP-hard and we devise a heuristic procedure to the problem based on the transportation problem and matching problem. The second problem can be solved in polynomial time by the shortest path method. The algorithm works in iterative manner. One step is composed of two phases. In the first phase, we solve the constrained bin packing problem. In the second phase, the shortest path problem is solved using the phase 1 result. The result of the phase 2 is used as an input to the phase 1 problem at the next step. We test the proposed algorithm on the set of real data found in the washing machine assembly line.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.506-516
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• 2005

This paper deals with an investment scheduling problem of maximizing net present value of dividend with reinvestment allowed, where each investment has certain capital requirement and generates deterministic profit. Such deterministic profit is calculated at completion of each investment and then allocated into two parts, including dividend and reinvestment, at each predetermined reinvestment time point. The objective is to make optimal scheduling of investments over a fixed planning horizon which maximizes total sum of the net present values of dividends subject to investment precedence relations and capital limit but with reinvestment allowed. In the analysis, the scheduling problem is transformed to a kind of parallel machine scheduling problem and formulated as an integer programming which is proven to be NP-complete. Thereupon, a depth-first branch-and-bound algorithm is derived. To test the effectiveness and efficiency of the derived algorithm, computational experiments are performed with some numerical instances. The experimental results show that the algorithm solves the problem relatively faster than the commercial software package (CPLEX 8.1), and optimally solves the instances with up to 30 investments within a reasonable time limit.