• Journal of the Korea Safety Management & Science
• /
• v.6 no.2
• /
• pp.141-154
• /
• 2004

The objective of this paper is to develop the efficient heuristic method for solving the minimum makespan problem of the job shop scheduling. The proposed heuristic method is based on a constraint satisfaction problem technique and a improved randomizing search algorithm. In this paper, ILOG programming libraries are used to embody the job shop model, and a constraint satisfaction problem technique is developed for this model to generate the initial solution. Then, a improved randomizing search algorithm is employed to overcome the increased search time of constrained satisfaction problem technique on the increased problem size and to find a improved solution. Computational experiments on well known MT and LA problem instances show that this approach yields better results than the other procedures.

• Korean Management Science Review
• /
• v.9 no.1
• /
• pp.3-15
• /
• 1992

In this paper, we study a manufacturing system of serial stages with general service times, in which the production of each stage and the coordination of stages are controlled by Kanban discipline. This Kanban discipline is modeled as a Discrete Event Dynamic System and a system of recursive equations is applied to study the dynamics of the system. The recursive relationship enables us to compare this Kanban discipline with the other blocking disciplines such as transfer blocking, service blocking, block-and-hold b, and block-and-hold K, and the Kanban is shown to be superior to the other disciplines in terms of makespan and throughput. As a special case, two stages Kanban system is modeled as $C_2/C_2/1/N$ queueing system, and a recursive algorithm is developed to calculate the system performance. In optimizing the system performance, the stochastic optimization approach of Robbins-Monro is employed via perturbation analysis, the way to estimate the stochastic partial derivative based on only one sample trajectory of the system, and the required commuting condition is verified. Then the stochastic convexity result is established to provide second-order optimality condition for this parametric optimization problem.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2004.05a
• /
• pp.615-619
• /
• 2004

This paper considers a variation of customer order scheduling problems. The variation is the case where machine-job assignment is fixed, and the objective is to minimize the sum of the completion times of the batches. In customer order scheduling problems, jobs are dispatched in batches. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. We first establish a couple of lower bounds. Then, we develop a dynamic programming (DP) algorithm that runs in exponential time on the number of batches when there exist two machines. For the same problem with arbitrary number of machines, we present two simple heuristics, which use simple scheduling rules such as shortest batch first and shortest makespan batch first rules. Finally, we empirically evaluate the heuristics.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1993.10a
• /
• pp.10-10
• /
• 1993

본 연구에서는 다품종(multiple products) 다단계(multi-stage) 흐름 생산시스템에서의 제품별 로트 투입순서결정무제를 다루었다. 다단계 흐름 생산시스템의 투입순서 결정문제에 대한 기존연구는 각 단계의 기계대수가 1대인 경우에 관한 것이 대부분이지만, 본 연구에서는 각 단계의 기계대수가 복수이고 각 제품의 생산량이 로트로 주어지며, 또한 각 단계마다의 이송이 로트로 이루어지는 것이 아니라 1단위로 이루어지는 생산시스템을 대상으로 하였다. 그리고 각 제품의 생산준비기간은 투입순서와 관계 없이 일정하며 앞 단계에서 제품이 도착하지 않더라도 생산준비는 먼저 수행될 수 있다고 가정하였다. 제품별 로트 투입순서 결정문제에서 사용된 성능평가기준(performance measure)은 총작업소요시간(makespan)이며 순열투입순서(permutation schedule)만을 대상으로 하였다. 결정기법으로는 투입순서 결정문제에서 효율적인 것으로 알려져 있는 분지한계법(Branch & Bound)이 사용되었으며 분지한계법에서 이용되는 부분투입순서(partial sequence)에 대한 하한값(lower bound)을 제시하였다. 제시된 기법을 사용하면 현실적인 크기의 제품별 로트 투입순서 결정문제를 적당한 시간내에 충분히 해결할 수 있을 것으로 보인다. 제시된 해법으로 해결된 수치예제가 주어져 있다.

• Journal of Korean Institute of Industrial Engineers
• /
• v.12 no.1
• /
• pp.19-30
• /
• 1986

This paper provides an evaluation of static flowshop scheduling heuristics for minimizing makespan as an objective function in the dynamic flowshop model, in which new jobs with stochastic processing times arrive at the shop randomly over time and are added into the waiting jobs for processing. A total of sixteen scheduling heuristics, including several revisions and combinations of previously reported me-sixteen scheduling heuristics, including several revisions and combinations of previously reported methods, are surmmarized. These scheduling rules are evaluated via computer using a SLAM discrete event simulation model. The results for the simulation are analyzed using both statistical and nonstatistical methods. The results from the study suggest which of the popular scheduling rules hold promise for application to practical dynamic flowshop problems.

• IE interfaces
• /
• v.13 no.3
• /
• pp.512-520
• /
• 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.

• Industrial Engineering and Management Systems
• /
• v.14 no.1
• /
• pp.22-31
• /
• 2015

In this paper, a two-stage hybrid flow shop problem is considered. Specifically, there exist identical parallel machines at stage 1 and two dedicated machines at stage 2, and the objective of the problem is to minimize makespan. After being processed by any machine at stage 1, a job must be processed by a specific machine at stage 2 depending on the job type, and one type of jobs can have different processing times on each machine. First, we introduce the problem and establish complexity of several variations of the problem. For some special cases, we develop optimal polynomial time solution procedures. Then, we establish some simple lower bounds for the problem. In order to solve this NP-hard problem, three heuristics based on simple rules such as the Johnson's rule and the LPT (Longest Processing Time first) rule are developed. For each of the heuristics, we provide some theoretical analysis and find some worst case bound on relative error. Finally, we empirically evaluate the heuristics.

• Management Science and Financial Engineering
• /
• v.5 no.2
• /
• pp.55-59
• /
• 1999

In this note, we introduce the Fire Sequencing Problem, which arises in military operations. Given m weapons, n fixed targets nad required duration of firing of the weapons on the targets, we want to determine the start time of firing on each target so that makespan is miniized while satisfying various operational constraints. We show that the decision problem of the Fire Sequencing problem is strongly NP-complete and remains strongly NP-complete even if the number of weapons is two. We also briefly discuss the results with respect to the complexities of several well-known scheduling models.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2000.04a
• /
• pp.99-102
• /
• 2000

전통적인 job shop 일정계획문제는 NP_hard 문제로 조합최적화 문제이다 일반적인 가정은 job이 방문하는 기계들의 경로가 고정되어 있다는 것이다. 경로 유연성을 가지는 job shop 일정계획문제는 job이 방문하는 기계들의 경로가 고정되어져 있지 않다는 것이다. 이러한 경우에 전통적인 job shop 문제를 복잡하게 만든다. 경로 유연성을 가지는 job shop 문제도 NP-hard 문제이다. 그러므로 휴레스틱이나 AI 기법들을 사용하는 하는 것이 불가피하게 되었다. 유전 알고리즘은 매우 복잡한 조합 최적화문제인 job shop 일정계획문제에 적용되어지고 있다. 이 논문은 최대완료시간(makespan)으로 경로 유연성을 가지는 job shop 일정계획문제를 풀기 위한 유전 알고리즘을 제시하고자 한다. 먼저 경로 유연성을 가지는 job shop 일정계획문제에 대한 정의를 내리고 유전 알고리즘을 구축하기 위한 첫 단계로 유전적 표현 즉, 개체 표현방법에 대해 설명하고 유전 연산자의 소개 그리고 알고리즘 재생과정을 제시하고 수치실험을 통해 알고리즘이 양질의 일정계획을 찾을 수 있다는 것을 보이고자 한다.

• Industrial Engineering and Management Systems
• /
• v.6 no.2
• /
• pp.119-124
• /
• 2007

The most difficult and time-intensive issue in the successful implementation of genetic algorithms is to find good parameter setting, one of the most popular subjects of current research in genetic algorithms. In this study, we present a new efficient experimental design method for parameter optimization in a genetic algorithm for general job shop scheduling problem using the Taguchi method. Four genetic parameters including the population size, the crossover rate, the mutation rate, and the stopping condition are treated as design factors. For the performance characteristic, makespan is adopted. The number of jobs, the number of operations required to be processed in each job, and the number of machines are considered as noise factors in generating various job shop environments. A robust design experiment with inner and outer orthogonal arrays is conducted by computer simulation, and the optimal parameter setting is presented which consists of a combination of the level of each design factor. The validity of the optimal parameter setting is investigated by comparing its SN ratios with those obtained by an experiment with full factorial designs.