• 산업경영시스템학회지
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• 제27권4호
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• pp.141-146
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• 2004

This research considers the problem of scheduling jobs on unrelated parallel machines with a common due date. The objective is to minimize the total absolute deviation of job completion times about the common due date. This problem is motivated by the fact that a certain phase of printed circuit board manufacturing and other production systems is bottleneck and the processing speeds of parallel machines in this phase are different for each job. A zero-one integer programming formulation is presented and two dominance properties are proved. By these dominance properties, it is shown that the problem is reduced to asymmetric assignment problem and is solvable in polynomial time.

• 대한산업공학회지
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• 제40권3호
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• pp.305-312
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• 2014

This research deals with a problem that minimizes makespan in a non-identical parallel machine system with sequence and machine dependent setup times and machine dependent processing times. We first present a new mixed integer programming formulation for the problem, and using this formulation, one can easily find optimal solutions for small problems. However, since the problem is NP-hard and the size of a real problem is large, we propose four heuristic algorithms including genetic algorithm based heuristics to solve the practical big-size problems in a reasonable computational time. To assess the performance of the algorithms, we conduct a computational experiment, from which we found the heuristic algorithms show different performances as the problem characteristics are changed and the simple heuristics show better performances than genetic algorithm based heuristics for the case when the numbers of jobs and/or machines are large.

• Management Science and Financial Engineering
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• 제13권2호
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• pp.47-77
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• 2007

This paper considers a scheduling problem where a customer orders multiple products(jobs) from a production facility. The objective is to minimize the sum of the order(batch) completion times. While a machine can process only one job at a time, multiple machines can simultaneously process jobs in a batch. Although each job has a unique processing time, we consider the case where batch processing times are identical. This simplification allows us to develop heuristics with improved performance bounds. This problem was motivated by a real world problem encountered by foreign electronics manufacturers. We first establish the complexity of the problem. For the two parallel machine case, we introduce two simple but intuitive heuristics, and find their worst case relative error bounds. One bound is tight and the other bound goes to 1 as the number of orders goes to infinity. However, neither heuristic is superior for all instances. We extend one of the heuristics to an arbitrary number of parallel machines. For a fixed number of parallel machines, we find a worst case bound which goes to 1 as the number of orders goes to infinity. Then, a tighter bound is found for the three parallel machine case. Finally, the heuristics are empirically evaluated.

• 산업공학
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• 제9권2호
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• pp.75-82
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• 1996

A scheduling system is developed for a parallel machine flow shop which reflects the situations of the manufacturing processes in the tire industry. The schedule is generated via simulation using heuristic rules to get satisfaction on such constraints as due dates, demands, work-in-process, process capacity, set-up times and scheduling speed. This system, constructed with relational DB, SQL and C language, consumes less than 10 minutes of PC simulation to handle real size problems.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2003년도 춘계공동학술대회
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• pp.145-150
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• 2003

The parallel machine scheduling problem or assigning n jobs on m identical machines with the objective of minimizing makespan is considered. In this note, we apply the PTAS (Polynomial Time Approximation Scheme) or Hochbaum and Shmoys to our problem and show that it is still a PTAS for our problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.35-53
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• 1997

This paper analyzes the time complexity of Genetic Algorithm based Task Scheduling (GATS) which is designed for the scheduling of parallel programs with diverse embedded parallelism types in a heterogeneous network systems. The analysis of time complexity is performed based on two representation methods (REIA, REIS) which are proposed in this paper to encode the scheduling information. And the heterogeneous network systems consist of a set of loosely coupled parallel and vector machines connected via a high-speed network. The objective of heterogeneous network computing is to solve computationally intensive problems that have several types of parallelism, on a suite of high performance and parallel machines in a manner that best utilizes the capabilities of each machine. Therefore, when scheduling in heterogeneous network systems, the matching of the parallelism characteristics between tasks and parallel machines should be carefully handled in order to obtain more speedup. This paper shows how the parallelism type matching affects the time complexity of GATS.

• 경영과학
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• 제24권2호
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• pp.33-42
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• 2007

In this paper we consider an alternate m machine scheduling problem in which each job having at most two eligible machines should be assigned with the objective of makespan minimization. For this problem. we propose a $O(m2^m)$ time rounding algorithm with performance ratio at most 1.5. For a little general problem where each job can be processed in at most three machines, we prove that a polynomial time algorithm does not exist with performance ratio less than 1.5.

• 대한산업공학회지
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• 제33권3호
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• pp.329-338
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• 2007

This paper presents a dispatching algorithm for nonidentical parallel machines problem considering rework, sequence dependent setup times and release times. For each pair of a machine and a job type, rework probability of each job on a machine can be known through historical data acquisition. The heuristic scheduling scheme named by EDDR (Earliest Due Date with Rework probability) algorithm is proposed in this paper making use of the rework probability. The proposed dispatching algorithm is measured by two objective function value: 1) total tardiness and 2) the number of reworked jobs, respectively. The extensive computational results show that the proposed algorithm gives very efficient schedules superior to the existing dispatching algorithms.

• 산업경영시스템학회지
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• 제23권56호
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• pp.9-18
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• 2000

This paper considers the problem of two-machine, M-parallel flow shop scheduling to minimize makespan, and proposes a series of heuristic algorithms and a branch and bound algorithm. Two processing times of each job at two machines on each line are identical on any line. Since each flow-shop line consists of two machines, Johnson's sequence is optimal for each flow-shop line. Heuristic algorithms are developed in this paper by combining a "list scheduling" method and a "local search with global evaluation" method. Numerical experiments show that the proposed heuristics can efficiently give optimal or near-optimal schedules with high accuracy. with high accuracy.

• 산업경영시스템학회지
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• 제31권3호
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• pp.101-109
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• 2008

This paper considers an integrated decision for scheduling and outsourcing(or, subcontracting) of a finite number of jobs(or, orders) in a time-sensitive make-to-order manufacturing environment. The jobs can be either processed in a parallel in-house facilities or outsourced to subcontractors. We should determine which jobs should be processed in-house and which jobs should be outsourced. And, we should determine the schedule for the jobs to be processed in-house. If a job is determined to be processed in-house, then the scheduling cost(the completion time of the Job) is imposed. Otherwise(if the job should be outsourced), then an additional outsourcing cost is imposed. The objective is to minimize the linear combination of scheduling and outsourcing costs under a budget constraint for the total available outsourcing cost. In the problem analysis, we first characterize some solution properties and then derive dynamic programming and branch-and- bound algorithms. An efficient heuristic is also developed. The performances of the proposed algorithms are evaluated through various numerical experiments.