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만기일 불이익을 갖는 다제품 생산용 회분식 공정의 스케쥴링을 위한 혼합 정수 비선형 모델
이호경,김민석,이인범 ( Ho Kyung Lee,Min Seok Kim,In Beum Lee ) 한국화학공학회 1996 Korean Chemical Engineering Research(HWAHAK KONGHA Vol.34 No.2
Using a mixed integer nonlinear model, we deal with the problem of scheduling in multiproduct batch processes with due-date penalties. So far this problem was treated for an unlimited intermediate storage policy using a BAB(Branch and Bound) and a SA(Simulated Anealing) method with heuristic algorithms. In this paper, we consider both tardiness and earliness penalties and no intermediate storage as well as unlimited intermediate storage policy.
박경태,류준형,Ho-Kyung Lee,이인범 한국화학공학회 2013 Korean Journal of Chemical Engineering Vol.30 No.2
This paper presents a heuristic algorithm for a two-dimensional two-stage guillotine cutting problem with multiple stock sizes by allowing the rotation of items by 90o. The proposed algorithm generates levels or strips where the first item or base item is selected according to the length of the strip and packs the next items beside the base item in the strip. For each type of item, strips are generated for packing each type of item in a base item. The best n orders in a yield of strips or the best n strips are selected for each type of item. The selected best n strips are packed in one type of bin. For the other types of bins, another best n strips are selected and packed in each type of bin. The best yield in all types of bins is then selected. This iteration is executed until the number of item demands in the overall demands is less than the number of item demands in the bin. Four numerical examples generated from actual industries are illustrated to highlight the applicability of the proposed algorithm with some comments.
중간 저장조 운영방안을 고려한 비순차 다목적 회분식 공정의 최적조업순서 결정
이호경,김상범,이인범,이의수 한국화학공학회 2001 Korean Chemical Engineering Research(HWAHAK KONGHA Vol.39 No.1
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 각제품의 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 Programing, 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 staging 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.