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중간 저장조 운영방안을 고려한 비순차 다목적 회분식 공정의 최적조업순서 결정
Optimal Scheduling of Non-Sequential Multipurpose Batch Processes with Various Intermediate Storage Policies
포항공과대학교 화학공학과, 공정산업의 지능자동화 연구센터 1동국대학교 화학공학과
Automation Research Center, Dept. of Chemical Engineering, POSTECH, Korea 1Department of Chemical Engineering, Dongguk University, Korea
iblee@postech.ac.kr
HWAHAK KONGHAK, February 2001, 39(1), 16-22(7), NONE
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Abstract
이 논문에서는 다양한 중간 저장조 운영 방안에 따른 비순차 다목적 회분식 공정의 최적 조업 순서 결정을 위한 수학적 모델을 제안한다. 비순차 다목적 회분식 공정에서는 다품종 공정의 경우와 달리 각 제품의 제조 경로가 서로 다를 뿐 아니라 역방향 제조 흐름이 존재한다. 따라서, 장치 유휴시간을 줄여 공정의 효율을 높이려면 각 제품의 제조 경로와 중간 저장조 운영 방안을 고려해 각 장치에서 제품 처리 순서를 서로 다르게 결정해야만 한다. 이를 위한 접근 방법으로 주어진 중간 저장조 운영 방안에 대해 각 장치에서 이루어지는 조업의 시작과 완료 시간을 제품과 처리순서 기준으로 각각 표현한 후 이진 변수와 논리적 제약 조건을 이용해 두 표현에 사용된 변수를 일치시켰다. 모델은 혼합정수선형계획법(Mixed Integer Linear Programming, MILP)형태로 표현되었으며, 세 가지 예제에 적용하여 제안된 모델의 효용성을 보였다.
In this paper, we present mathematical models for optimal scheduling of non-sequential multipurpose batch processes under various intermediate storage policies. Compared with multiproduct processes, in non-sequential multipurpose batch processes, the production routes of products may be different from one another and may be backward direction. Consequently, in order to reduce idle time of units and to raise the efficiency of process, we have to make operation sequences of products in each unit differently by considering processing route of each product with a given intermediate storage policy. The basic concept of our approach for these problems is as follows. Firstly, we represented the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on sequences. Then, we matched the variables used in the two coordinates into one with binary variables and logical constraints. We formulated these problems as MILP(Mixed Integer Linear Programming) models and apply them to three examples to show the effectiveness of the model.
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