We examine a single machine scheduling problem with step-improving jobs in which job processing times decrease step-wisely over time according to their starting times. The objective is to minimize total completion time which is defined as the sum of completion times of jobs. The total completion time is frequently considered as an objective because it is highly related to the total time spent by jobs in the system as well as work-in-progress. Many applications of this problem can be observed in the real world such as data gathering networks, system upgrades or technological shock, and production lines operated with part-time workers in each shift. Our goal is to develop a scheduling algorithm that can provide an optimal solution. For this, we present an efficient branch and bound algorithm with an assignment-based node design and tight lower bounds that can prune branch and bound nodes at early stages and accordingly reduce the computation time. In numerical experiments well designed to consider various scenarios, it is shown that the proposed algorithm outperforms the existing method and can solve practical problems within reasonable computation time.

This paper proposes an algorithm for the Unrelated Parallel Machine Scheduling Problem(UPMSP) without setup times, aiming to minimize total tardiness. As an NP-hard problem, the UPMSP is hard to get an optimal solution. Consequently, practical scenarios are solved by relying on operator's experiences or simple heuristic approaches. The proposed algorithm has adapted two methods: a policy network method, based on Transformer to compute the correlation between individual jobs and machines, and another method to train the network with a reinforcement learning algorithm based on the REINFORCE with Baseline algorithm. The proposed algorithm was evaluated on randomly generated problems and the results were compared with those obtained using CPLEX, as well as three scheduling algorithms. This paper confirms that the proposed algorithm outperforms the comparison algorithms, as evidenced by the test results.

This paper is proposing a novel machine scheduling model for the unrelated parallel machine scheduling problem without setup times to minimize the total completion time, also known as “makespan”. This problem is a NP-complete problem, and to date, most approaches for real-life situations are based on the operator’s experience or simple heuristics. The new model based on the Memetic Algorithm, which was proposed by P. Moscato in 1989, is a hybrid algorithm that includes genetic algorithm and local search optimization. The new model is tested on randomly generated datasets, and is compared to optimal solution, and four scheduling models; three rule-based heuristic algorithms, and a genetic algorithm based scheduling model from literature; the test results show that the new model performed better than scheduling models from literature.

Many small and medium-sized manufacturing companies process various product types to respond different customer orders in a single production line. To improve their productivity, they often apply batch processing while considering various product types, constraints on batch sizes and setups, and due date of each order. This study introduces a batch scheduling heuristic for a production line with multiple product types and different due dates of each order. As the process times vary due to the different batch sizes and product types, a recursive equation is developed based on a flow line model to obtain the upper bound on the completion times with less computational complexity than full computation. The batch scheduling algorithm combines and schedules the orders with same product types into a batch to improve productivity, but within the constraints to match the due dates of the orders. The algorithm incorporates simple and intuitive principles for the purpose of being applied to small and medium companies. To test the algorithm, two case studies are introduced; a high pressure coolant (HPC) manufacturing line and a press process at a plate-type heat exchanger manufacturer. From the case studies, the developed algorithm provides significant improvements in setup frequency and thus convenience of workers and productivity, without violating due dates of each order.

We focus on the weapon target assignment and fire scheduling problem (WTAFSP) with the objective of minimizing the makespan, i.e., the latest completion time of a given set of firing operations. In this study, we assume that there are m available weapons to fire at n targets (> m). The artillery attack operation consists of two steps of sequential procedure : assignment of weapons to the targets; and scheduling firing operations against the targets that are assigned to each weapon. This problem is a combination of weapon target assignment problem (WTAP) and fire scheduling problem (FSP). To solve this problem, we define the problem with a mixed integer programming model. Then, we develop exact algorithms based on a dynamic programming technique. Also, we suggest how to find lower bounds and upper bounds to a given problem. To evaluate the performance of developed exact algorithms, computational experiments are performed on randomly generated problems. From the results, we can see suggested exact algorithm solves problems of a medium size within a reasonable amount of computation time. Also, the results show that the computation time required for suggested exact algorithm can be seen to increase rapidly as the problem size grows. We report the result with analysis and give directions for future research for this study. This study is meaningful in that it suggests an exact algorithm for a more realistic problem than existing researches. Also, this study can provide a basis for developing algorithms that can solve larger size problems.

This study focuses on a job-shop scheduling problem with the objective of minimizing total tardiness for the job orders that have different due dates and different process flows. We suggest the dispatching rule based scheduling algorithm to generate fast and efficient schedule. First, we show the delay schedule can be optimal for total tardiness measure in some cases. Based on this observation, we expand search space for selecting the job operation to explore the delay schedules. That means, not only all job operations waiting for process but also job operations not arrived at the machine yet are considered to be scheduled when a machine is available and it is need decision for the next operation to be processed. Assuming each job operation is assigned to the available machine, the expected total tardiness is estimated, and the job operation with the minimum expected total tardiness is selected to be processed in the machine. If this job is being processed in the other machine, then machine should wait until the job arrives at the machine. Simulation experiments are carried out to test the suggested algorithm and compare with the results of other well-known dispatching rules such as EDD, ATC and COVERT, etc. Results show that the proposed algorithm, MET, works better in terms of total tardiness of orders than existing rules without increasing the number of tardy jobs.

본 연구는 통합공정일정계획(Integrated Process Planning and Scheduling; IPPS)의 최적화를 위한 계산 효율성이 높은 탐욕적 휴리스틱과 유전알고리즘(Genetic Algorithm; GA)을 결합한 하이브리드형 유전 알고리즘을 제안한다. IPPS는 기존의 공정계획과 일정계획을 동시에 풀고자 하는 NP-Hard 문제이다. 특히, 본 연구에서 다루는 IPPS는 tool related constraints가 포함된 것으로서 전통적인 GA는 수행도중 infeasible schedule을 빈번히 발생시킨다. 제안하는 방법의 아이디어는 전체적인 schedule의 구조에 영향을 미치는 operation의 sequence와 machine의 결정은 GA의 procedure를 따르고, 목적함수의 부분계산이 가능한 tool과 Tool Access Direction(TAD)는 greedy heuristics을 통하여 infeasibility를 해소하자는 것이다. 이를 통하여 계산시간의 급격한 증가 없이 또는 기존에 비해 계산시간을 감소시키면서 좋은 품질의 해를 구할 수 있다. 본 연구에서 제안하는 알고리즘은 benchmark problems을 이용하여 성능을 평가한다.

This paper proposes an improved standard genetic algorithm (GA) of making a near optimal schedule for integrated process planning and scheduling problem (IPPS) considering tool flexibility and tool related constraints. Process planning involves the selection of operations and the allocation of resources. Scheduling, meanwhile, determines the sequence order in which operations are executed on each machine. Due to the high degree of complexity, traditionally, a sequential approach has been preferred, which determines process planning firstly and then performs scheduling independently based on the results. The two sub-problems, however, are complicatedly interrelated to each other, so the IPPS tend to solve the two problems simultaneously. Although many studies for IPPS have been conducted in the past, tool flexibility and capacity constraints are rarely considered. Various meta-heuristics, especially GA, have been applied for IPPS, but the performance is yet satisfactory. To improve solution quality against computation time in GA, we adopted three methods. First, we used a random circular queue during generation of an initial population. It can provide sufficient diversity of individuals at the beginning of GA. Second, we adopted an inferior selection to choose the parents for the crossover and mutation operations. It helps to maintain exploitation capability throughout the evolution process. Third, we employed a modification of the hybrid scheduling algorithm to decode the chromosome of the individual into a schedule, which can generate an active and non-delay schedule. The experimental results show that our proposed algorithm is superior to the current best evolutionary algorithms at most benchmark problems.

This paper considers the allocation and engagement scheduling problem of interceptor missiles, and the problem was formulated by using MIP (mixed integer programming) in the previous research. The objective of the model is the maximization of total intercept altitude instead of the more conventional objective such as the minimization of surviving target value. The concept of the time window was used to model the engagement situation and a continuous time is assumed for flying times of the both missiles. The MIP formulation of the problem is very complex due to the complexity of the real problem itself. Hence, the finding of an efficient optimal solution procedure seems to be difficult. In this paper, an efficient genetic algorithm is developed by improving a general genetic algorithm. The improvement is achieved by carefully analyzing the structure of the formulation. Specifically, the new algorithm includes an enhanced repair process and a crossover operation which utilizes the idea of the PSO (particle swarm optimization). Then, the algorithm is throughly tested on 50 randomly generated engagement scenarios, and its performance is compared with that of a commercial package and a more general genetic algorithm, respectively. The results indicate that the new algorithm consistently performs better than a general genetic algorithm. Also, the new algorithm generates much better results than those by the commercial package on several test cases when the execution time of the commercial package is limited to 8,000 seconds, which is about two hours and 13 minutes. Moreover, it obtains a solution within 0.13 ~33.34 seconds depending on the size of scenarios.

We focus on the fire scheduling problem (FSP), the problem of determining the sequence of targets to be fired at, for the objective of minimizing makespan to achieve tactical goals. In this paper, we assume that there are m available weapons to fire at n targets (> m) and the weapons are already allocated to targets. One weapon or multiple weapons can fire at one target and these fire operations should start simultaneously while the finish time of them may be different. We develop several dominance properties and a lower bound for the problem, and suggest a branch and bound algorithm implementing them. Also, In addition, heuristic algorithms that can be used for obtaining an initial upper bound in the B&B algorithm and for obtaining good solutions in a short time were developed. Computational experiments are performed on randomly generated test problems and results show that the suggested algorithm solves problems of a medium size in a reasonable amount of computation time. The proposed lower bound, the dominance properties, and the heuristics for upper bound are tested in B&B respectively, and the result showed that lower bound is effective to fathoming nodes and the dominance properties and heuristics also worked well. Also, it is showed that the CPU time required by this algorithm increases rapidly as the problem size increases. Therefore, the suggested B&B algorithm would be limited to solve large size problems. However, the employed heuristic algorithms can be effectively used in the B&B algorithm and can give good solutions for large problems within a few seconds.

This study develops a dynamic scheduling model for parallel machine scheduling problem based on genetic algorithm (GA). GA combined with discrete event simulation to minimize the makespan and verifies the effectiveness of the developed model. This research consists of two stages. In the first stage, work sequence will be generated using GA, and the second stage developed work schedule applied to a real work area to verify that it could be executed in real work environment and remove the overlapping work, which causes bottleneck and long lead time. If not, go back to the first stage and develop another schedule until satisfied. Small size problem was experimented and suggested a reasonable schedule within limited resources. As a result of this research, work efficiency is increased, cycle time is decreased, and due date is satisfied within existed resources.

In 450mm wafers production environment for next generation Fab, one of the most significant features is the adoption of full automation to the whole manufacturing processes involved. The full automation system will prevent the workers from intervening the manufacturing processes as much as possible and increase the importance of each individual wafer noticeably, and thus require a more robust scheduling system for entire semiconductor manufacturing processes. The scheduling system for 450mm wafers production also should be capable of monitoring the status of each individual wafer and collecting useful Fab data in real time. In this study, we first analysis of cluster tool in 450mm wafers production environment, and then propose a real-time scheduling algorithm based on timetabling algorithm.

This paper considers a coordinated scheduling problem between multi-suppliers and an manufacture. When the supplier has insufficient inventory to meet the manufacture's order, the supplier may use the expedited production and the expedited transportation. In this case, we consider a scheduling problem to minimize the total cost of suppliers and manufacture. We suggest an population management genetic algorithm with local search and crossover (GALPC). By the computational experiments comparing with general genetic algorithm, the objective value of GALPC is reduced by 8% and the calculation time of GALPC is reduced by 70%.

  HPI (High-speed Portable Internet) system which provides high speed internet services is going to be commercialized soon. Since HPI provides simultaneously four different service types such as UGS (Unsolicited Grant Service), rtPS (real time Polling Ser

  여러 형태의 고객이 외부로부터 포아송과정에 따라 각 대기행렬에 도착하고 정해진 서비스규칙에 따라 해당 서비스를 받은 후 마코비안 확률분포에 따라 시스템을 떠나거나 다른 형태의 고객으로 시스템을 다시 돌아 올 수도 있는 M/G1 대기행렬시스템을 고려한다. 본 연구에서는 기존의 연구 모형을 확장하여 계층적 서비스 규칙을 갖는 우선순위 대기행렬모형을 제시하고 이에 대한 시스템 성능척도를 보다 체계적으로 구할 수 있는 방법을 소개한다. 이를 위하여 먼저 대

시간과 공간의 제약을 받지 않는 초고속 무선 인터넷 사용을 목표로 하는 휴대 인터넷 시스템이 곧 상용화될 예정이다. 휴대 인터넷 시스템은 서로 다른 특성을 가지고 있는 UGS(Unsolicited Grant Service), rtPS(real time Polling Service), nrtPS(non-real time Polling Service), 그리고 BE(Best Effort)의 네 가지 서비스들을 동시에 제공하므로 이들의 QoS(Quality of Service)를 고려하면서 한정된 무선 채널을 효율적으로 할당하는 스케줄링 알고리즘이 필요하다. 본 연구에서는 처리해야 할 트래픽을 시계열 데이터로 하여 비모수 검정법을 적용하는 새로운 알고리즘을 제안한다. 다양한 파라미터 값들에 대한 스케줄링 기법의 성능을 평가할 수 있는 시뮬레이터를 이용하여 패킷의 지연시간, 데이터 전송률, 폐기 패킷수, 그리고 채널 이용률 등을 평가척도로 하여 제안 방법의 성능을 평가하였다.

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.